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Results in Journal Advanced Modeling and Simulation in Engineering Sciences: 201

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Muhammad Zahid, Khalid S. Syed
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-14; https://doi.org/10.1186/s40323-021-00204-6

Abstract:
The current study aims at simulating the in-cylinder combustion process in a diesel engine and investigating the engine performance and pollutant formation. The combustion simulation is performed on a 3D sector employing appropriate models for various physical and chemical processes contributing in the combustion phenomenon. The overall model includes Transition SST turbulence model, eddy dissipation model for turbulence chemistry interaction, Moss–Brookes model for soot calculation and Zeldovich mechanism for NO production other than the usual transport equations. The numerical solutions are based on the finite volume discretization of the governing partial differential equations. Engine performance has been studied in terms of pressure, temperature and heat release rate while the pollutants formation has been investigated in terms of soot and thermal NO production. The results show that the ignition delay is quite short and that the injection timing may be successfully employed to control the combustion behavior. The simulation results are quite consistent with the expected behavior of the target variables indicating that the CFD analysis can be successfully employed in the diesel engine design. The results validation may be acknowledged in view of the mesh independence test, literature comparison and justification of the models.
Alexander Schein,
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-31; https://doi.org/10.1186/s40323-021-00203-7

Abstract:
This work proposes a framework for projection-based model order reduction (MOR) of computational models aiming at a mechanical analysis of abdominal aortic aneurysms (AAAs). The underlying full-order model (FOM) is patient-specific, stationary and nonlinear. The quantities of interest are the von Mises stress and the von Mises strain field in the AAA wall, which result from loading the structure to the level of diastolic blood pressure at a fixed, imaged geometry (prestressing stage) and subsequent loading to the level of systolic blood pressure with associated deformation of the structure (deformation stage). Prestressing is performed with the modified updated Lagrangian formulation (MULF) approach. The proposed framework aims at a reduction of the computational cost in a many-query context resulting from model uncertainties in two material and one geometric parameter. We apply projection-based MOR to the MULF prestressing stage, which has not been presented to date. Additionally, we propose a reduced-order basis construction technique combining the concept of subspace angles and greedy maximin distance sampling. To further achieve computational speedup, the reduced-order model (ROM) is equipped with the energy-conserving mesh sampling and weighting hyper reduction method. Accuracy of the ROM is numerically tested in terms of the quantities of interest within given bounds of the parameter domain and performance of the proposed ROM in the many-query context is demonstrated by comparing ROM and FOM statistics built from Monte Carlo sampling for three different patient-specific AAAs.
, Myriam Slama
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-16; https://doi.org/10.1186/s40323-021-00202-8

Abstract:
The paper deals with approximations of periodic functions that play a significant role in harmonic analysis. The approach revisits the trigonometric polynomials, seen as combinations of functions, and proposes to extend the class of models of the combined functions to a wider class of functions. The key here is to use structured functions, that have low complexity, with suitable functional representation and adapted parametrizations for the approximation. Such representation enables to approximate multivariate functions with few eventually random samples. The new parametrization is determined automatically with a greedy procedure, and a low rank format is used for the approximation associated with each new parametrization. A supervised learning algorithm is used for the approximation of a function of multiple random variables in tree-based tensor format, here the particular Tensor Train format. Adaptive strategies using statistical error estimates are proposed for the selection of the underlying tensor bases and the ranks for the Tensor-Train format. The method is applied for the estimation of the wall pressure for a flow over a cylinder for a range of low to medium Reynolds numbers for which we observe two flow regimes: a laminar flow with periodic vortex shedding and a laminar boundary layer with a turbulent wake (sub-critic regime). The automatic re-parametrization enables here to take into account the specific periodic feature of the pressure.
Jonas Nitzler, , Kei W. Müller, Wolfgang A. Wall, N. E. Hodge
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-39; https://doi.org/10.1186/s40323-021-00201-9

Abstract:
The elasto-plastic material behavior, material strength and failure modes of metals fabricated by additive manufacturing technologies are significantly determined by the underlying process-specific microstructure evolution. In this work a novel physics-based and data-supported phenomenological microstructure model for Ti-6Al-4V is proposed that is suitable for the part-scale simulation of laser powder bed fusion processes. The model predicts spatially homogenized phase fractions of the most relevant microstructural species, namely the stable $$\beta $$ β -phase, the stable $$\alpha _{\text {s}}$$ α s -phase as well as the metastable Martensite $$\alpha _{\text {m}}$$ α m -phase, in a physically consistent manner. In particular, the modeled microstructure evolution, in form of diffusion-based and non-diffusional transformations, is a pure consequence of energy and mobility competitions among the different species, without the need for heuristic transformation criteria as often applied in existing models. The mathematically consistent formulation of the evolution equations in rate form renders the model suitable for the practically relevant scenario of temperature- or time-dependent diffusion coefficients, arbitrary temperature profiles, and multiple coexisting phases. Due to its physically motivated foundation, the proposed model requires only a minimal number of free parameters, which are determined in an inverse identification process considering a broad experimental data basis in form of time-temperature transformation diagrams. Subsequently, the predictive ability of the model is demonstrated by means of continuous cooling transformation diagrams, showing that experimentally observed characteristics such as critical cooling rates emerge naturally from the proposed microstructure model, instead of being enforced as heuristic transformation criteria. Eventually, the proposed model is exploited to predict the microstructure evolution for a realistic selective laser melting application scenario and for the cooling/quenching process of a Ti-6Al-4V cube of practically relevant size. Numerical results confirm experimental observations that Martensite is the dominating microstructure species in regimes of high cooling rates, e.g., due to highly localized heat sources or in near-surface domains, while a proper manipulation of the temperature field, e.g., by preheating the base-plate in selective laser melting, can suppress the formation of this metastable phase.
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-33; https://doi.org/10.1186/s40323-021-00200-w

Abstract:
The present work proposes an approach for fluid–solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.
Maialen Areitioaurtena, Unai Segurajauregi, Ville Akujärvi, Martin Fisk, Iker Urresti, Eneko Ukar
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-19; https://doi.org/10.1186/s40323-021-00199-0

Abstract:
The numerical simulation of the induction heating process can be computationally expensive, especially if ferromagnetic materials are studied. There are several analytical models that describe the electromagnetic phenomena. However, these are very limited by the geometry of the coil and the workpiece. Thus, the usual method for computing more complex systems is to use the finite element method to solve the set of equations in the multiphysical system, but this easily becomes very time consuming. This paper deals with the problem of solving a coupled electromagnetic - thermal problem with higher computational efficiency. For this purpose, a semi-analytical modeling strategy is proposed, that is based on an initial finite element computation, followed by the use of analytical electromagnetic equations to solve the coupled electromagnetic-thermal problem. The usage of the simplified model is restricted to simple geometrical features such as flat or curved surfaces with great curvature to skin depth ratio. Numerical and experimental validation of the model show an average error between 0.9% and 4.1% in the prediction of the temperature evolution, reaching a greater accuracy than other analyzed commercial softwares. A 3D case of a double-row large size ball bearing is also presented, fully validating the proposed approach in terms of computational time and accuracy for complex industrial cases.
, P. Kerfriden, F. Moshfeghifar, S. Darkner, K. Erleben, C. Wong
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-23; https://doi.org/10.1186/s40323-021-00197-2

Abstract:
This paper presents a robust digital pipeline from CT images to the simulation of contact between multiple bodies. The proposed strategy relies on a recently developed immersed finite element algorithm that is capable of simulating unilateral contact between solids without meshing (Claus and Kerfriden in Int J Numer Methods Eng 113(6):938–966, 2018). It was shown that such an approach reduces the difficulties associated with the digital flow of information from analytically defined geometries to mechanical simulations. We now propose to extend our approach to include geometries, which are not defined mathematically but instead are obtained from images, and encoded in 3D arrays of voxels. This paper introduces two novel elements. Firstly, we reformulate our contact algorithm into an extension of an augmented Lagrangian CutFEM algorithm. Secondly, we develop an efficient algorithm to convert the surface data generated by standard segmentation tools used in medical imaging into level-set functions. These two elements give rise to a robust digital pipeline with minimum user intervention. We demonstrate the capabilities of our algorithm on a hip joint geometry with contact between the femur and the hip bone.
, Ramezan A. Izadifard
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-17; https://doi.org/10.1186/s40323-021-00198-1

Abstract:
The danger of fire is present always and everywhere. The imminent danger depends upon the actual type and length of fire exposure. Reinforced concrete structural members are loadbearing components in buildup structures and are therefore at high risk, since the entire structure might potentially collapse upon their failure. Thus, it is imperative to comprehend the behavior of reinforced concrete members at high temperatures in case of fire. In this study, the mechanical properties of concrete exposed to high temperatures were experimentally determined through the testing of 27 concrete cylinder starting at room temperature and increasing up to 260 °C. The concrete material behavior was implemented into the ABAQUS software and a finite simulation of reinforced concrete beams exposed to actual fire conditions were conducted. The finite element models compared favorably with the available experimental results. Thus, providing a valuable tool that allows for the prediction of failure in case of a fire event.
, Tomas Berglund, Samuel Nystedt
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-35; https://doi.org/10.1186/s40323-021-00196-3

Abstract:
A multiscale model for real-time simulation of terrain dynamics is explored. To represent the dynamics on different scales the model combines the description of soil as a continuous solid, as distinct particles and as rigid multibodies. The models are dynamically coupled to each other and to the earthmoving equipment. Agitated soil is represented by a hybrid of contacting particles and continuum solid, with the moving equipment and resting soil as geometric boundaries. Each zone of active soil is aggregated into distinct bodies, with the proper mass, momentum and frictional-cohesive properties, which constrain the equipment’s multibody dynamics. The particle model parameters are pre-calibrated to the bulk mechanical parameters for a wide range of different soils. The result is a computationally efficient model for earthmoving operations that resolve the motion of the soil, using a fast iterative solver, and provide realistic forces and dynamic for the equipment, using a direct solver for high numerical precision. Numerical simulations of excavation and bulldozing operations are performed to test the model and measure the computational performance. Reference data is produced using coupled discrete element and multibody dynamics simulations at relatively high resolution. The digging resistance and soil displacements with the real-time multiscale model agree with the reference model up to 10–25%, and run more than three orders of magnitude faster.
, Altuğ Emiroğlu, Shahrokh Shayegan, Fabien Péan, Kai-Uwe Bletzinger, Roland Wüchner
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-55; https://doi.org/10.1186/s40323-021-00190-9

Abstract:
In this study the isogeometric B-Rep mortar-based mapping method for geometry models stemming directly from Computer-Aided Design (CAD) is systematically augmented and applied to partitioned Fluid-Structure Interaction (FSI) simulations. Thus, the newly proposed methodology is applied to geometries described by their Boundary Representation (B-Rep) in terms of trimmed multipatch Non-Uniform Rational B-Spline (NURBS) discretizations as standard in modern CAD. The proposed isogeometric B-Rep mortar-based mapping method is herein extended for the transformation of fields between a B-Rep model and a low order discrete surface representation of the geometry which typically results when the Finite Volume Method (FVM) or the Finite Element Method (FEM) are employed. This enables the transformation of such fields as tractions and displacements along the FSI interface when Isogeometric B-Rep Analysis (IBRA) is used for the structural discretization and the FVM is used for the fluid discretization. The latter allows for diverse discretization schemes between the structural and the fluid Boundary Value Problem (BVP), taking into consideration the special properties of each BVP separately while the constraints along the FSI interface are satisfied in an iterative manner within partitioned FSI. The proposed methodology can be exploited in FSI problems with an IBRA structural discretization or to FSI problems with a standard FEM structural discretization in the frame of the Exact Coupling Layer (ECL) where the interface fields are smoothed using the underlying B-Rep parametrization, thus taking advantage of the smoothness that the NURBS basis functions offer. All new developments are systematically investigated and demonstrated by FSI problems with lightweight structures whereby the underlying geometric parametrizations are directly taken from real-world CAD models, thus extending IBRA into coupled problems of the FSI type.
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-23; https://doi.org/10.1186/s40323-021-00195-4

Abstract:
In this work we investigate the Brinkman volume penalization technique in the context of a high-order Discontinous Galerkin method to model moving wall boundaries for compressible fluid flow simulations. High-order approximations are especially of interest as they require few degrees of freedom to represent smooth solutions accurately. This reduced memory consumption is attractive on modern computing systems where the memory bandwidth is a limiting factor. Due to their low dissipation and dispersion they are also of particular interest for aeroacoustic problems. However, a major problem for the high-order discretization is the appropriate representation of wall geometries. In this work we look at the Brinkman penalization technique, which addresses this problem and allows the representation of geometries without modifying the computational mesh. The geometry is modelled as an artificial porous medium and embedded in the equations. As the mesh is independent of the geometry with this method, it is not only well suited for high-order discretizations but also for problems where the obstacles are moving. We look into the deployment of this strategy by briefly discussing the Brinkman penalization technique and its application in our solver and investigate its behavior in fundamental one-dimensional setups, such as shock reflection at a moving wall and the formation of a shock in front of a piston. This is followed by the application to setups with two and three dimensions, illustrating the method in the presence of curved surfaces.
Tristan Maquart, Thomas Elguedj, Anthony Gravouil, Michel Rochette
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-28; https://doi.org/10.1186/s40323-021-00194-5

Abstract:
This paper presents an effective framework to automatically construct 3D quadrilateral meshes of complicated geometry and arbitrary topology adapted for parametric studies. The input is a triangulation of the solid 3D model’s boundary provided from B-Rep CAD models or scanned geometry. The triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. This workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. This set of cuboids perfectly replicates the input surface topology. Using aligned global parameterization, patches are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. Based on the cuboid decomposition and global parameterization, a 3D quadrilateral mesh is extracted. For different parametric instances with the same topology but different geometries, the MEG-IsoQuad method allows to have the same representation: isotopological meshes holding the same connectivity where each point on a mesh has an analogous one into all other meshes. Faithful 3D numerical charts of parametric geometries are then built using standard data-based techniques. Geometries are then evaluated in real-time. The efficiency and the robustness of the proposed approach are illustrated through a few parametric examples.
Vincent Magnoux,
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-14; https://doi.org/10.1186/s40323-021-00192-7

Abstract:
Simulators for virtual surgery training need to perform complex calculations very quickly to provide realistic haptic and visual interactions with a user. The complexity is further increased by the addition of cuts to virtual organs, such as would be needed for performing tumor resection. A common method for achieving large performance improvements is to make use of the graphics hardware (GPU) available on most general-use computers. Programming GPUs requires data structures that are more rigid than on conventional processors (CPU), making that data more difficult to update. We propose a new method for structuring graph data, which is commonly used for physically based simulation of soft tissue during surgery, and deformable objects in general. Our method aligns all nodes of the graph in memory, independently from the number of edges they contain, allowing for local modifications that do not affect the rest of the structure. Our method also groups memory transfers so as to avoid updating the entire graph every time a small cut is introduced in a simulated organ. We implemented our data structure as part of a simulator based on a meshless method. Our tests show that the new GPU implementation, making use of the new graph structure, achieves a 10 times improvement in computation times compared to the previous CPU implementation. The grouping of data transfers into batches allows for a 80–90% reduction in the amount of data transferred for each graph update, but accounts only for a small improvement in performance. The data structure itself is simple to implement and allows simulating increasingly complex models that can be cut at interactive rates.
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-23; https://doi.org/10.1186/s40323-021-00193-6

Abstract:
The main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the Cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.
Sofia Farina, Susanne Claus, Jack S. Hale, Alexander Skupin, Stéphane P. A. Bordas
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-32; https://doi.org/10.1186/s40323-021-00191-8

Abstract:
A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions.
Paul-Baptiste Rubio, , François Louf
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-25; https://doi.org/10.1186/s40323-021-00188-3

Abstract:
This research work deals with the implementation of so-called Dynamic Data-Driven Application Systems (DDDAS) in structural mechanics activities. It aims at designing a real-time numerical feedback loop between a physical system of interest and its numerical simulator, so that (i) the simulation model is dynamically updated from sequential and in situ observations on the system; (ii) the system is appropriately driven and controlled in service using predictions given by the simulator. In order to build such a feedback loop and take various uncertainties into account, a suitable stochastic framework is considered for both data assimilation and control, with the propagation of these uncertainties from model updating up to command synthesis by using a specific and attractive sampling technique. Furthermore, reduced order modeling based on the Proper Generalized Decomposition (PGD) technique is used all along the process in order to reach the real-time constraint. This permits fast multi-query evaluations and predictions, by means of the parametrized physics-based model, in the online phase of the feedback loop. The control of a fusion welding process under various scenarios is considered to illustrate the proposed methodology and to assess the performance of the associated numerical architecture.
Matthew S. Bonney, Richard Evans, , Arthur Jones, Pierre Kerfriden, Maxime Hamadi
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-31; https://doi.org/10.1186/s40323-021-00189-2

Abstract:
A major challenge with modern aircraft design is the occurrence of structural features of varied length scales. Structural stiffness can be accurately represented using homogenisation, however aspects such as the onset of failure may require information on more refined length scale for both metallic and composite components. This work considers the errors encountered in the coarse global models due to the mesh size and how these are propagated into detailed local sub-models. The error is calculated by a goal oriented error estimator, formulated by solving dual problems and Zienkiewicz-Zhu smooth field recovery. Specifically, the novel concept of this work is applying the goal oriented error estimator to shell elements and propagating this error field into the continuum sub-model. This methodology is tested on a simplified aluminium beam section with four different local feature designs, thereby illustrating the sensitivity to various local features with a common global setting. The simulations show that when the feature models only contained holes on the flange section, there was little sensitivity of the von Mises stress to the design modifications. However, when holes were added to the webbing section, there were large stress concentrations that predicted yielding. Despite this increase in nominal stress, the maximum error does not significantly change. However, the error field does change near the holes. A Monte Carlo simulation utilising marginal distributions is performed to show the robustness of the multi-scale analysis to uncertainty in the global error estimation as would be expected in experimental measurements. This shows a trade-off between Saint-Venant’s principle of the applied loading and stress concentrations on the feature model when investigating the response variance.
Alexandre Imperiale, ,
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-47; https://doi.org/10.1186/s40323-020-00179-w

Abstract:
Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.
J. F. Ganghoffer, R. Rahouadj, A. Cheviakov
Advanced Modeling and Simulation in Engineering Sciences, Volume 8, pp 1-34; https://doi.org/10.1186/s40323-020-00187-w

Abstract:
A methodology based on Lie analysis is proposed to investigate the mechanical behavior of materials exhibiting experimental master curves. It is based on the idea that the mechanical response of materials is associated with hidden symmetries reflected in the form of the energy functional and the dissipation potential leading to constitutive laws written in the framework of the thermodynamics of irreversible processes. In constitutive modeling, symmetry analysis lets one formulate the response of a material in terms of so-called master curves, and construct rheological models based on a limited number of measurements. The application of symmetry methods leads to model reduction in a double sense: in treating large amounts number of measurements data to reduce them in a form exploitable for the construction of constitutive models, and by exploiting equivalence transformations extending point symmetries to efficiently reduce the number of significant parameters, and thus the computational cost of solving boundary value problems (BVPs). The symmetry framework and related conservation law analysis provide invariance properties of the constitutive models, allowing to predict the influence of a variation of the model parameters on the material response or on the solution of BVPs posed over spatial domains. The first part of the paper is devoted to the presentation of the general methodology proposed in this contribution. Examples of construction of rheological models based on experimental data are given for setting up a reduced model of the uniaxial creep and rupture behaviour of a Chrome-Molybdenum alloy (9Cr1Mo) at different temperatures and stress levels. Constitutive equations for creep and rupture master responses are identified for this alloy, and validated based on experimental data. Equivalence transformations are exemplified in the context of parameter reduction in fully nonlinear anisotropic fiber-reinforced elastic solids.
Muhammad S. Sarfaraz, Bojana V. Rosić, Hermann G. Matthies, Adnan Ibrahimbegović
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-35; https://doi.org/10.1186/s40323-020-00185-y

Abstract:
Multi-scale processes governed on each scale by separate principles for evolution or equilibrium are coupled by matching the stored energy and dissipation in line with the Hill-Mandel principle. We are interested in cementitious materials, and consider here the macro- and meso-scale behaviour of such a material. The accurate representations of stored energy and dissipation are essential for the depiction of irreversible material behaviour, and here a Bayesian approach is used to match these quantities on different scales. This is a probabilistic upscaling and as such allows to capture, among other things, the loss of resolution due to scale coarsening, possible model errors, localisation effects, and the geometric and material randomness of the meso-scale constituents in the upscaling. On the coarser (macro) scale, optimal material parameters are estimated probabilistically for certain possible behaviours from the class of generalised standard material models by employing a nonlinear approximation of Bayes’s rule. To reduce the overall computational cost, a model reduction of the meso-scale simulation is achieved by combining unsupervised learning techniques based on a Bayesian copula variational inference with functional approximation forms.
, Nina Korshunova, Stefan Kollmannsberger, Ernst Rank, Gershon Elber
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-33; https://doi.org/10.1186/s40323-020-00182-1

Abstract:
This paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.
, Andreas Reiter, Christoph Herrmann, , Britta Nestler
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-32; https://doi.org/10.1186/s40323-020-00178-x

Abstract:
A linear visco-elasticity ansatz for the multiphase-field method is introduced in the form of a Maxwell-Wiechert model. The implementation follows the idea of solving the mechanical jump conditions in the diffuse interface regions, hence the continuous traction condition and Hadamard’s compatibility condition, respectively. This makes strains and stresses available in their phase-inherent form (e.g. $$\varepsilon ^{\alpha }_{ij}$$ ε ij α , $$\varepsilon ^{\beta }_{ij}$$ ε ij β ), which conveniently allows to model material behaviour for each phase separately on the basis of these quantities. In the case of the Maxwell-Wiechert model this means the introduction of phase-inherent viscous strains. After giving details about the implementation, the results of the model presented are compared to a conventional Voigt/Taylor approach for the linear visco-elasticity model and both are evaluated against analytical and sharp-interface solutions in different simulation setups.
, , Philippe Moireau, Tobias Schaeffter,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-37; https://doi.org/10.1186/s40323-020-00186-x

Abstract:
A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A “Netlist” implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.
, Richard Meister, Thomas Steck, Leon Fadljević, Johann Gerdenitsch, Stefan Schuster, Lukas Schiefermüller, Stefanie Lindstaedt, Roman Kern
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-16; https://doi.org/10.1186/s40323-020-00184-z

Abstract:
In industrial electro galvanizing lines aged anodes deteriorate zinc coating distribution over the strip width, leading to an increase in electricity and zinc cost. We introduce a data-driven approach in predictive maintenance of anodes to replace the cost- and labor-intensive manual inspection, which is still common for this task. The approach is based on parasitic resistance as an indicator of anode condition which might be aged or mis-installed. The parasitic resistance is indirectly observable via the voltage difference between the measured and baseline (theoretical) voltage for healthy anode. Here we calculate the baseline voltage by means of two approaches: (1) a physical model based on electrical and electrochemical laws, and (2) advanced machine learning techniques including boosting and bagging regression. The data was collected on one exemplary rectifier unit equipped with two anodes being studied for a total period of two years. The dataset consists of one target variable (rectifier voltage) and nine predictive variables used in the models, observing electrical current, electrolyte, and steel strip characteristics. For predictive modelling, we used Random Forest, Partial Least Squares and AdaBoost Regression. The model training was conducted on intervals where the anodes were in good condition and validated on other segments which served as a proof of concept that bad anode conditions can be identified using the parasitic resistance predicted by our models. Our results show a RMSE of 0.24 V for baseline rectifier voltage with a mean ± standard deviation of 11.32 ± 2.53 V for the best model on the validation set. The best-performing model is a hybrid version of a Random Forest which incorporates meta-variables computed from the physical model. We found that a large predicted parasitic resistance coincides well with the results of the manual inspection. The results of this work will be implemented in online monitoring of anode conditions to reduce operational cost at a production site.
Carola Kruse, Vincent Darrigrand, Nicolas Tardieu, Mario Arioli, Ulrich Rüde
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00181-2

Abstract:
Kinematic relationships between degrees of freedom, also named multi-point constraints, are frequently used in structural mechanics. In this paper, the Craig variant of the Golub-Kahan bidiagonalization algorithm is used as an iterative method to solve the arising linear system with a saddle point structure. The condition number of the preconditioned operator is shown to be close to unity and independent of the mesh size. This property is proved theoretically and illustrated on a sequence of test problems of increasing complexity, including concrete structures enforced with pretension cables and the coupled finite element model of a reactor containment building. The Golub-Kahan algorithm converges in only a small number of steps for all considered test problems and discretization sizes. Furthermore, it is robust in practical cases that are otherwise considered to be difficult for iterative solvers.
Hailu Shimels Gebremedhen, Dereje Engida Woldemichael, Fakhruldin Mohd Hashim
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00183-0

Abstract:
In this paper, a firefly algorithm based hybrid algorithm through retaining global convergence of firefly algorithm and ability to generate connected topologies of optimality criteria (OC) method is proposed as an alternative method to solve stress-based topology optimization problems. The lower and upper limit of design variables (0 and 1) were used to find initial material distribution to initialize the firefly algorithm based section of the hybrid algorithm. Input parameters, the number of fireflies, and the number of function evaluations were determined before the implementation of the firefly algorithm to solve formulated problems. Since the direct application of the firefly algorithm cannot generate connected topologies, outputs from the firefly algorithm were used as an initial input material distribution for the OC method. The proposed method was validated using two-dimensional benchmark problems and the results were compared with results using the OC method. Weight percentage reduction, maximum stress-induced, optimal material distribution, and compliance were used to compare results. Results from the proposed method showed that the proposed method can generate connected topologies which are free from the interference of end-users, and only depend on boundary conditions or design variables. From the results, the objective function (weight of the design domain) can be further reduced in the range of 5 to 15% compared to the OC method.
Hanane Khatouri, Tariq Benamara, Piotr Breitkopf, Jean Demange, Paul Feliot
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00176-z

Abstract:
This article addresses the problem of constrained derivative-free optimization in a multi-fidelity (or variable-complexity) framework using Bayesian optimization techniques. It is assumed that the objective and constraints involved in the optimization problem can be evaluated using either an accurate but time-consuming computer program or a fast lower-fidelity one. In this setting, the aim is to solve the optimization problem using as few calls to the high-fidelity program as possible. To this end, it is proposed to use Gaussian process models with trend functions built from the projection of low-fidelity solutions on a reduced-order basis synthesized from scarce high-fidelity snapshots. A study on the ability of such models to accurately represent the objective and the constraints and a comparison of two improvement-based infill strategies are performed on a representative benchmark test case.
Jonatha Reis, José Paulo Moitinho De Almeida, , Sergio Zlotnik
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-22; https://doi.org/10.1186/s40323-020-00180-3

Abstract:
Reduced order methods are powerful tools for the design and analysis of sophisticated systems, reducing computational costs and speeding up the development process. Among these reduced order methods, the Proper Generalized Decomposition is a well-established one, commonly used to deal with multi-dimensional problems that often suffer from the curse of dimensionality. Although the PGD method has been around for some time now, it still lacks mechanisms to assess the quality of the solutions obtained. This paper explores the dual error analysis in the scope of the PGD, using complementary solutions to compute error bounds and drive an adaptivity process, applied to a simple 1D problem. The energy of the error obtained from the dual analysis is used to determine the quality of the PGD approximations. We define a new adaptivity indicator based on the energy of the error and use it to drive parametric h- and p- adaptivity processes. The results are positive, with the indicator accurately capturing the parameter that will lead to lowest errors.
, Roger Ohayon
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-22; https://doi.org/10.1186/s40323-020-00172-3

Abstract:
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order models (ROMs) have a place to alleviate the computational burden. Assuming that the parametric entity takes values in a linear space, we show how is is associated to a linear map or operator. This provides a general point of view on how to consider and analyse different representations of such entities. Analysis of the associated linear map in turn connects such representations with reproducing kernel Hilbert spaces and affine-/linear-representations in terms of tensor products. A generalised correlation operator is defined through the associated linear map, and its spectral analysis helps to shed light on the approximation properties of ROMs. This point of view thus unifies many such representations under a functional analytic roof, leading to a deeper understanding and making them available for appropriate analysis.
Marco Tezzele, Nicola Demo, Giovanni Stabile, Andrea Mola,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-19; https://doi.org/10.1186/s40323-020-00177-y

Abstract:
In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD.
Ryo Hatano, Seishiro Matsubara, Shuji Moriguchi, , Julien Yvonnet
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-28; https://doi.org/10.1186/s40323-020-00175-0

Abstract:
This study presents a method for constructing a surrogate localization model for a periodic microstructure, or equivalently, a unit cell, to efficiently perform micro-macro coupled analyses of hyperelastic composite materials. The offline process in this approach is to make a response data matrix that stores the microscopic stress distributions in response to various patterns of macroscopic deformation gradients, which is followed by the proper orthogonal decomposition (POD) of the matrix to construct a reduced order model (ROM) of the microscopic analysis (localization) with properly extracted POD bases. Then, response surfaces of the POD coefficients are constructed so that the ROM can be continuous with respect to the input datum, namely, the macroscopic deformation gradient. The novel contributions of this study are the application of the L2 regularization to the interpolation approximations of the POD coefficients by use of radial basis functions (RBFs) to make the response surfaces continuous and the combined use of the cross-validation and the Bayesian optimization to search for the optimal set of parameters in both the RBFs and L2regularization formula. The resulting model can be an alternative to microscopic finite element (FE) analyses in the conventional $${\text {FE}}^2$$ FE 2 method and realizes $${\text {FE}}^r$$ FE r with $$1 1 < r < < 2 accordingly. Representative numerical examples of micro-macro coupled analysis with the $${\text {FE}}^r$$ FE r are presented to demonstrate the capability and promise of the surrogate localization model constructed with the proposed approach in comparison with the results with high-fidelity direct $${\text {FE}}^2$$ FE 2 .
Luca Rosafalco, Andrea Manzoni, Stefano Mariani,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-31; https://doi.org/10.1186/s40323-020-00174-1

Abstract:
We propose a novel approach to structural health monitoring (SHM), aiming at the automatic identification of damage-sensitive features from data acquired through pervasive sensor systems. Damage detection and localization are formulated as classification problems, and tackled through fully convolutional networks (FCNs). A supervised training of the proposed network architecture is performed on data extracted from numerical simulations of a physics-based model (playing the role of digital twin of the structure to be monitored) accounting for different damage scenarios. By relying on this simplified model of the structure, several load conditions are considered during the training phase of the FCN, whose architecture has been designed to deal with time series of different length. The training of the neural network is done before the monitoring system starts operating, thus enabling a real time damage classification. The numerical performances of the proposed strategy are assessed on a numerical benchmark case consisting of an eight-story shear building subjected to two load types, one of which modeling random vibrations due to low-energy seismicity. Measurement noise has been added to the responses of the structure to mimic the outputs of a real monitoring system. Extremely good classification capacities are shown: among the nine possible alternatives (represented by the healthy state and by a damage at any floor), damage is correctly classified in up to $$95 \%$$ 95 % of cases, thus showing the strong potential of the proposed approach in view of the application to real-life cases.
, R. Chen, V. Mallet
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-22; https://doi.org/10.1186/s40323-020-00173-2

Abstract:
Urban air quality simulation is an important tool to understand the impacts of air pollution. However, the simulations are often computationally expensive, and require extensive data on pollutant sources. Data on road traffic pollution, often the predominant source, can be obtained through sparse measurements, or through simulation of traffic and emissions. Modeling chains combine the simulations of multiple models to provide the most accurate representation possible, however the need to solve multiple models for each simulation increases computational costs even more. In this paper we construct a meta-modeling chain for urban atmospheric pollution, from dynamic traffic modeling to air pollution modeling. Reduced basis methods (RBM) aim to compute a cheap and accurate approximation of a physical state using approximation spaces made of a suitable sample of solutions to the model. One of the keys of these techniques is the decomposition of the computational work into an expensive one-time offline stage and a low-cost parameter-dependent online stage. Traditional RBMs require modifying the assembly routines of the computational code, an intrusive procedure which may be impossible in cases of operational model codes. We propose a non-intrusive reduced order scheme, and study its application to a full chain of operational models. Reduced basis are constructed using principal component analysis (PCA), and the concentration fields are approximated as projections onto this reduced space. We use statistical emulation to approximate projection coefficients in a non-intrusive manner. We apply a multi-level meta-modeling technique to a chain using the dynamic traffic assignment model LADTA, the emissions database COPERT IV, and the urban dispersion-reaction air quality model SIRANE to a case study on the city of Clermont-Ferrand with over 45, 000 daily traffic observations, a 47, 000-link road network, a simulation domain covering $$180\,\text {km}^2$$ 180 km 2 . We assess the results using hourly NO $$_2$$ 2 concentration observations measured at stations in the agglomeration. Computational times are reduced from nearly 3 h per simulation to under 0.1 s, while maintaining accuracy comparable to the original models. The low cost of the meta-model chain and its non-intrusive character demonstrate the versatility of the method, and the utility for long-term or many-query air quality studies such as epidemiological inquiry or uncertainty quantification.
Pierre Phalippou, , Salim Bouabdallah, Malek Zarroug, Pierre Villon
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-23; https://doi.org/10.1186/s40323-020-00167-0

Abstract:
The hyper-reduction problem for reduced-order internal forces evaluation in transient, nonlinear, explicit dynamics is reformulated, employing Mixed-Integer Programming (MIP), taking into account consistency constraints. Constraint reduction is introduced. Resulting quadratures, as well as reduced runs, are compared against the standard Energy Conserving Sampling and Weighting (ECSW) scheme, on a reference example. Rather than searching for optimal performance, the goal is to provide a benchmark solution, for evaluation of heuristic hyper-reduction formulations along with a non-greedy approach.
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-26; https://doi.org/10.1186/s40323-020-00161-6

Abstract:
We present a variational framework for the computational homogenization of chemo-mechanical processes of soft porous materials. The multiscale variational framework is based on a minimization principle with deformation map and solvent flux acting as independent variables. At the microscopic scale we assume the existence of periodic representative volume elements (RVEs) that are linked to the macroscopic scale via first-order scale transition. In this context, the macroscopic problem is considered to be homogeneous in nature and is thus solved at a single macroscopic material point. The microscopic problem is however assumed to be heterogeneous in nature and thus calls for spatial discretization of the underlying RVE. Here, we employ Raviart–Thomas finite elements and thus arrive at a conforming finite-element formulation of the problem. We present a sequence of numerical examples to demonstrate the capabilities of the multiscale formulation and to discuss a number of fundamental effects.
Correction
Márton Petö, Fabian Duvigneau, Sascha Eisenträger
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-1; https://doi.org/10.1186/s40323-020-00165-2

Abstract:
An amendment to this paper has been published and can be accessed via the original article.
Carlo Sansour, Tien Long Nguyen, Mohammed Hjiaj, Sophy Chhang
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-37; https://doi.org/10.1186/s40323-020-00166-1

Abstract:
A new formulation of geometrically exact planar Euler-Bernoulli beam in multi-body dynamics is proposed. For many applications, the use of the Euler-Bernoulli model is sufficient and has the advantage of being a nodal displacement-only formulation avoiding the integration of rotational degrees of freedom. In this paper, an energy momentum method is proposed for the nonlinear in-plane dynamics of flexible multi-body systems, including the effects of revolute joints with or without torsional springs. Large rotational angles of the joints are accurately calculated. Several numerical examples demonstrate the accuracy and the capabilities of the new formulation.
, Erasmo Carrera
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-28; https://doi.org/10.1186/s40323-020-00169-y

Abstract:
This paper presents a novel methodology to assess the accuracy of shell finite elements via neural networks. The proposed framework exploits the synergies among three well-established methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FE), and neural networks (NN). CUF generates the governing equations for any-order shell theories based on polynomial expansions over the thickness. FE provides numerical results feeding the NN for training. Multilayer NN have the generalized displacement variables, and the thickness ratio as inputs, and the target is the maximum transverse displacement. This work investigates the minimum requirements for the NN concerning the number of neurons and hidden layers, and the size of the training set. The results look promising as the NN requires a fraction of FE analyses for training, can evaluate the accuracy of any-order model, and can incorporate physical features, e.g., the thickness ratio, that drive the complexity of the mathematical model. In other words, NN can trigger fast informed decision-making on the structural model to use and the influence of design parameters without the need of modifying, rebuild, or rerun an FE model.
, Pedro Bonilla-Villalba, Iulia C. Mihai, Waled F. Alnaas, Anthony D. Jefferson
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00171-4

Abstract:
A new specialised finite element for simulating the cracking and healing behaviour of quasi-brittle materials is presented. The element employs a strong discontinuity approach to represent displacement jumps associated with cracks. A particular feature of the work is the introduction of healing into the element formulation. The healing variables are introduced at the element level, which ensures consistency with the internal degrees freedom that represent the crack; namely, the crack opening, crack sliding and rotation. In the present work, the element is combined with a new cohesive zone model to simulate damage-healing behaviour and implemented with a crack tracking algorithm. To demonstrate the performance of the new element and constitutive models, a convergence test and two validation examples are presented that consider the response of a vascular self-healing cementitious material system for three different specimens. The examples show that the model is able to accurately capture the cracking and healing behaviour of this type of self-healing material system with good accuracy.
Corentin Le Gourriérec, ,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00170-5

Abstract:
Digital image correlation (DIC) is a full-field measurement technique. In instantaneous approaches (i.e., registering two images), DIC only gives access to displacement (or velocity) fields. Consequently, acceleration fields are not one of the primary measured variables. To evaluate acceleration fields, a regularization scheme has to be used. The latter may be either heuristic or mechanically motivated. The key idea of the paper is to use spatiotemporal analyses in order to explicitly measure acceleration fields. Various regularization schemes will be assessed, and their relative merits will be studied when performing uncertainty quantifications. Pyrotechnic cutting simulations will provide a set of artificial pictures to be studied in order to validate the new implementations. This analysis enables the measurement performances to be evaluated for the new implementations.
Annika Robens-Radermacher, Jörg F. Unger
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00168-z

Abstract:
One of the most important goals in civil engineering is to guarantee the safety of the construction. Standards prescribe a required failure probability in the order of $$10^{-4}$$10-4 to $$10^{-6}$$10-6 . Generally, it is not possible to compute the failure probability analytically. Therefore, many approximation methods have been developed to estimate the failure probability. Nevertheless, these methods still require a large number of evaluations of the investigated structure, usually finite element (FE) simulations, making full probabilistic design studies not feasible for relevant applications. The aim of this paper is to increase the efficiency of structural reliability analysis by means of reduced order models. The developed method paves the way for using full probabilistic approaches in industrial applications. In the proposed PGD reliability analysis, the solution of the structural computation is directly obtained from evaluating the PGD solution for a specific parameter set without computing a full FE simulation. Additionally, an adaptive importance sampling scheme is used to minimize the total number of required samples. The accuracy of the failure probability depends on the accuracy of the PGD model (mainly influenced on mesh discretization and mode truncation) as well as the number of samples in the sampling algorithm. Therefore, a general iterative PGD reliability procedure is developed to automatically verify the accuracy of the computed failure probability. It is based on a goal-oriented refinement of the PGD model around the adaptively approximated design point. The methodology is applied and evaluated for 1D and 2D examples. The computational savings compared to the method based on a FE model is shown and the influence of the accuracy of the PGD model on the failure probability is studied.
Werner Wagner,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7; https://doi.org/10.1186/s40323-020-00162-5

Abstract:
In this paper a robust and effective 4-node shell element for the structural analysis of thin structures is described. A Hu–Washizu functional with independent displacements, stress resultants and shell strains is the variational basis of the theory. Based on a previous paper an additional interpolation part using quadratic shape functions is introduced for the independent shell strains. Especially for unstructured meshes this leads to an improved convergence behavior. The expanded element formulation proves to be insensitive to mesh distortion. Another well-known feature of the mixed hybrid element is the robustness in nonlinear applications with large deformations.
Erik Burman, , Mats G. Larson
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-20; https://doi.org/10.1186/s40323-020-00164-3

Abstract:
We present and analyze a method for thin plates based on cut Bogner-Fox-Schmit elements, which are $$C^1$$C1 elements obtained by taking tensor products of Hermite splines. The formulation is based on Nitsche’s method for weak enforcement of essential boundary conditions together with addition of certain stabilization terms that enable us to establish coercivity and stability of the resulting system of linear equations. We also take geometric approximation of the boundary into account and we focus our presentation on the simply supported boundary conditions which is the most sensitive case for geometric approximation of the boundary.
Thomas Groensfelder, Fabian Giebeler, Marco Geupel, David Schneider, Rebecca Jaeger
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-29; https://doi.org/10.1186/s40323-020-00163-4

Abstract:
This article presents an investigation about prediction accuracy of multi-parametric models derived from numerical data. Three different mechanical test-cases are used for the generation of the numerical data. From this data, models are derived for the prediction of characteristic variation to arbitrary changes of the input parameters. Different modeling approaches are evaluated regarding their prediction accuracy. Polynomial matrix equations are compared to regression models and neural network models provided by Machine-Learning toolboxes. Similarities and differences of the models are worked out. An exponential matrix-equation-model is proposed to increase accuracy for certain applications. Influences and their causes to the prediction accuracy for the model predictions are evaluated. From this minimum requirements for deriving valuable models are defined. Leading to a comparison of the modelling approaches in relation to physical plausibility and model efficiency. Where efficiency is related to the effort for data creation and training-procedure. For one of the sample cases, a prediction-model is applied to demonstrate the model application and capabilities. The model equation is used to calculate the value of a penalty function in a multi-input/multi-output optimization task. As outcome of the optimization, four natural frequencies are fitted to measured values by updating material parameters. For all other cases sensitivity-studies including verification to numerical results are conducted.
Correction
, Jan Zeman, Martin Doškář, Petr Krysl
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-1; https://doi.org/10.1186/s40323-020-00160-7

Abstract:
Following publication of the original article [1], the authors reported the errors in the equations.
Sebastian D. Proell, Wolfgang A. Wall,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-32; https://doi.org/10.1186/s40323-020-00158-1

Abstract:
This work proposes an extension of phase change and latent heat models for the simulation of metal powder bed fusion additive manufacturing processes on the macroscale and compares different models with respect to accuracy and numerical efficiency. Specifically, a systematic formulation of phase fraction variables is proposed relying either on temperature- or enthalpy-based interpolation schemes. Moreover, two well-known schemes for the numerical treatment of latent heat, namely the apparent capacity and the so-called heat integration scheme, are critically reviewed and compared with respect to numerical efficiency and overall accuracy. Eventually, a novel variant of the heat integration scheme is proposed that allows to directly control efficiency and accuracy by means of a user-defined tolerance. Depending on the chosen tolerance, it is shown that this novel approach offers increased numerical efficiency for a given level of accuracy or improved accuracy for a given level of numerical efficiency as compared to the apparent capacity and the original heat integration scheme. The investigation and comparison of all considered schemes is based on a series of numerical test cases that are representative for application scenarios in metal powder bed fusion additive manufacturing.
Francesco Maria Filotto, Falk Runkel, Gerald Kress
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-15; https://doi.org/10.1186/s40323-020-00159-0

Abstract:
This paper introduces a shape optimization of wire strands subjected to tensile loads. The structural analysis relies on a recently developed reduced helical finite element model characterized by an extreme computational efficacy while accounting for complex geometries of the wires. The model is extended to consider interactions between components and its applicability is demonstrated by comparison with analytical and finite element models. The reduced model is exploited in a design optimization identifying the optimal shape of a 1 + 6 strand by means of a genetic algorithm. A novel geometrical parametrization is applied and different objectives, such as stress concentration and area minimization, and constraints, corresponding to operational limitations and requirements, are analyzed. The optimal shape is finally identified and its performance improvements are compared and discussed against the reference strand. Operational benefits include lower stress concentration and higher load at plastification initiation.
, Asven Gariah, Christian Rey, Frederic Feyel
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-19; https://doi.org/10.1186/s40323-020-00156-3

Abstract:
In this work, we consider a transient thermal problem, with a nonlinear term coming from the radiation boundary condition and a nonparametrized variability in the form complex scenarios for the initial condition and the convection coefficients and external temperatures. We use a posteriori reduced order modeling by snapshot Proper Orthogonal Decomposition. To treat the nonlinearity, hyperreduction is required in our case, since precomputing the polynomial nonlinearities becomes too expensive for the radiation term. We applied the Empirical Cubature Method, originally proposed for nonlinear structural mechanics, to our particular problem. We apply the method to the design of high-pressure compressors for civilian aircraft engines, where a fast evaluation of the solution temperature is required when testing new configurations. We also illustrate that when using in the reduced solver the same model as the one from the high-fidelity code, the approximation is very accurate. However, when using a commercial code to generate the high-fidelity data, where the implementation of the model and solver is unknown, the reduced model is less accurate but still within engineering tolerances in our tests. Hence, the regularizing property of reduced order models, together with a nonintrusive approach, enables the use of commercial software to generate the data, even under some degree of uncertainty in the proprietary model or solver of the commercial software.
, Fabian Duvigneau, Sascha Eisenträger
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-42; https://doi.org/10.1186/s40323-020-00157-2

Abstract:
In the present work, we propose a new approach, the so-called compressed adaptive integration scheme (C-AIS), for the computation of the stiffness and mass matrices in fictitious domain methods requiring the integration of discontinuous functions. The novel approach extends the conventional quadtree-decomposition-based adaptive integration scheme (AIS) by an additional step, in which established image-compression techniques are exploited to decrease the number of integration sub-cells. The benefits of the C-AIS are manifold: First, the compression of the sub-cells inevitably leads to significant savings in terms of computational time required by the numerical integration. Second, the compression procedure, which is executed directly after the quadtree-decomposition algorithm, can be easily included in existing codes. Third, if applied to polynomial integrands, the C-AIS yields exactly the same accuracy as the conventional AIS. Finally, the fourth advantage is seen in the fact that the C-AIS can readily be combined with other approaches seeking a reduction of the number of integration points such as the Boolean-FCM. The efficiency of the C-AIS approach is presented in the context of the FCM based on Cartesian meshes applied to problems of linear elastostatics and modal analysis, while it is also suitable for the quadrature in other fictitious domain approaches, e.g., CutFEM and cgFEM.
, Thomas Jailin,
Advanced Modeling and Simulation in Engineering Sciences, Volume 7, pp 1-18; https://doi.org/10.1186/s40323-020-00155-4

Abstract:
A new in situ vibration mode measurement method within a tomograph is proposed based on Projection-based Digital Volume Correlation techniques. Several projection angles are selected and a large number of radiographs of the vibrating sample are acquired at random instants with a small exposure time in order to ‘freeze out’ the displacement and avoid motion blurring. Based on an initial reconstruction acquired in a static configuration, the displacement field measurement is performed using a Proper Generalized Decomposition technique. All projections are analyzed as being due to a few vibration modes deforming the known reference volume. The different projection directions are related to each other assuming that the modal amplitude probability distribution functions are statistically similar. A synthetic test case, mock-up of a liver, is used to illustrate and validate the approach. In this case, 5 projection angles were chosen, 300 radiographs per angle, and the first three vibration modes could be recovered with a good accuracy.
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