Journal of Applied Mechanics

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ISSN / EISSN : 0021-8936 / 1528-9036
Published by: ASME International (10.1115)
Total articles ≅ 15,279
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Published: 13 September 2021
Journal of Applied Mechanics pp 1-15; https://doi.org/10.1115/1.4052375

Abstract:
Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the Transient Microsphere Model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker-Planck equation which incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.
, , Jizeng Wang
Published: 9 September 2021
Journal of Applied Mechanics pp 1-32; https://doi.org/10.1115/1.4052367

Abstract:
In the process of inflammation, the hydrodynamic process of circulating leukocyte recruitment to the inflammatory site requires the rolling adhesion of leukocytes in blood vessels mediated by selectin and integrin molecules. Although a number of experiments have demonstrated that cooperative effects exist between selectins and integrins in leukocyte rolling adhesion under shear flow, the mechanisms underlying how the mechanics of selectins and integrins synergistically may govern the dynamics of cell rolling is not yet fully resolved. Here we present a mechanical model on selectin- and integrin- jointly mediated rolling adhesion of leukocyte in shear flow, by considering two pairs' binding/unbinding events as Markov processes and describing kinetics of leukocyte by the approach of continuum mechanics. Through examining the dynamics of leukocyte rolling as a function of relative fraction of selectin and integrin pairs, we show that, during recruitment, the elongation of intermittent weak selectin bonds consuming the kinetic energy of rolling leukocyte decelerates the rolling speed and enables the integrin pairs to form strong bonds, therefore achieving the arrestment of leukocyte (firm adhesion). The coexistence of selectins and integrins may also be required for effective phase transition from firm adhesion to rolling adhesion, due to dynamic competition in pairs' formation and elongation. These results are verified by the relevant Monte Carlo simulations and related to reported experimental observations.
Correction
Published: 7 September 2021
Journal of Applied Mechanics, Volume 89, pp 1-1; https://doi.org/10.1115/1.4052196

Abstract:
This note is to correct errata in the paper “quot;Analytical Solution for the Lifetime of a Spherical Shell of Arbitrary Thickness Under the Pressure of Corrosive Environments: The Effect of Thermal and Elastic Stresses”quot; published in Journal of Applied Mechanics, Vol.~88, P.~061004 (2021), doi: 10.1115/1.4050280.
Published: 7 September 2021
Journal of Applied Mechanics, Volume 89, pp 1-15; https://doi.org/10.1115/1.4052106

Abstract:
A micromechanics-based ductile fracture initiation theory is developed and applied for high-throughput assessment of ductile failure in plane stress. A key concept is that of inhomogeneous yielding such that microscopic failure occurs in bands with the driving force being a combination of band-resolved normal and shear tractions. The new criterion is similar to the phenomenological Mohr–Coulomb model, but the sensitivity of fracture initiation to the third stress invariant constitutes an emergent outcome of the formulation. Salient features of a fracture locus in plane stress are parametrically analyzed. In particular, it is shown that a finite shear ductility cannot be rationalized based on an isotropic theory that proceeds from first principles. Thus, the isotropic formulation is supplemented with an anisotropic model accounting for void rotation and shape change to complete the prediction of a fracture locus and compare with experiments. A wide body of experimental data from the literature is explored, and a simple procedure for calibrating the theory is outlined. Comparisons with experiments are discussed in some detail.
, Arne J. Pearlstein
Published: 6 September 2021
Journal of Applied Mechanics, Volume 88, pp 1-59; https://doi.org/10.1115/1.4051998

Abstract:
Free response of a rotational nonlinear energy sink (NES) inertially coupled to a linear oscillator is investigated for dimensionless initial rectilinear displacements ranging from just above the smallest amplitude at which nonrotating, harmonically rectilinear motion is unstable absent direct rectilinear damping, up to the next-largest amplitude at which such motion is orbitally stable. With motionless initial conditions (MICs), i.e., initial velocity of the primary mass and initial angular velocity of the NES mass both zero, predicted behavior for two previously investigated combinations of the dimensionless parameters (characterizing rotational damping, and coupling of rectilinear and rotational motions) differs strongly from that found at smaller initial displacements (Ding and Pearlstein, 2021, “Free Response of a Rotational Nonlinear Energy Sink: Complete Dissipation of Initial Energy for Small Initial Rectilinear Displacements,” J. Appl. Mech., 88(1), p. 011005). For both combinations, a wide range of MICs leads to solutions displaying transient chaos and depending sensitively on initial conditions, giving rise to fractality and riddling in the relationship between initial conditions and asymptotic solutions. Absent direct rectilinear damping of the linear oscillator, for one combination of parameters there exists a wide range of MICs with trajectories leading to time-harmonic, orbitally stable “special” solutions with a single amplitude, but no MICs are found for which all initial energy is dissipated. For the other combination, no such special solutions are found, but there exist MICs for which all initial energy is dissipated. With direct rectilinear damping, sensitivity extends to a measure of settling time, which can be extremely sensitive to initial conditions. A statistical approach to this sensitivity is discussed, along with implications for design and implementation.
, Longhui Qin,
Published: 2 September 2021
Journal of Applied Mechanics pp 1-11; https://doi.org/10.1115/1.4052289

Abstract:
Motivated by the observations of snap-through phenomena in pre-stressed strips and curved shells, we numerically investigate the snapping of a pre-buckled hemispherical gridshell under apex load indentation. Our experimentally validated numerical framework on elastic gridshell simulation combines two components: (i) Discrete Elastic Rods method, for the geometrically nonlinear description of one dimensional rods; and (ii) a naive penalty-based energy functional, to perform the non-deviation condition between two rods at joint. An initially planar grid of slender rods can be actuated into a three dimensional hemispherical shape by loading its extremities through a prescribed path, known as buckling induced assembly; next, this pre-buckled structure can suddenly change its bending direction at some threshold points when compressing its apex to the other side. We find that the hemispherical gridshell can undergo snap-through buckling through two different paths based on two different apex loading conditions. The first critical snap-through point slightly increases as the number of rods in gridshell structure becomes denser, which emphasizes the mechanically nonlocal property in hollow grids, in contrast to the local response of continuum shells. The findings may bridge the gap among rods, grids, knits, and shells, for a fundamental understanding of a group of thin elastic structures, and inspire the design of novel micro-electro-mechanical systems and functional metamaterials.
, Zuguang Bian, Xiaoliang Zhou,
Published: 2 September 2021
Journal of Applied Mechanics pp 1-18; https://doi.org/10.1115/1.4052290

Abstract:
Stretchable electronics employing island-bridge structure design can achieve controllable and reversible stretchability. The use of a porous substrate, which provides excellent breathability for wearable devices bonded to skin, not only satisfies this static superiority but also has a profound impact on the dynamic performance of the stretchable electronics. In this paper, the vibration characteristics of the island-bridge structure based on porous polydimethylsiloxane (p-PDMS) substrates are studied by utilizing an analytical model, which takes account of geometric nonlinearity due to mid-plane stretching, buckling configuration, elastic boundary conditions considering the p-PDMS substrates and the mass of the island. In numerical examples, the accuracy of the analytical model is first verified by finite element analysis (FEA). After that, we investigate the effects of some primary factors, i.e. the prestrain of the substrate, spring stiffnesses at the ends of the interconnect, porosity and thickness of the substrate, and the mass of the island, on the natural frequencies and vibration mode shapes of the island-bridge structure. Results show that the vibration characteristics of the island-bridge structure can be tuned conveniently by adjusting the porosity of the substrate and the mass of the island, which are expected to be helpful to mechanical design and optimization of stretchable electronics in complex noise environments.
Published: 24 August 2021
Journal of Applied Mechanics, Volume 88; https://doi.org/10.1115/1.4052105

Abstract:
Conventional models of the structure of the Earth, such as the Preliminary Reference Earth Model (PREM), assume a bonded interface between the crust and the upper mantle. The bonded contact model is consistent with the observation of Love waves during an earthquake. However, anomalies in the Love wave dispersion have been reported in the literature. When slip occurs at the crust-mantle interface, another kind of an interfacial wave, called the slip wave can exist. It is shown that the dispersion relation of the slip wave, with a slip weakening friction law, appears to be in agreement with the observations at seismic frequencies. This suggests that slip could occur at the crust-mantle interface.
Published: 24 August 2021
Journal of Applied Mechanics, Volume 88; https://doi.org/10.1115/1.4052107

Abstract:
Reversible dry adhesives rely on short-ranged intermolecular bonds, hence requiring a low elastic modulus to conform to the surface roughness of the adhered material. Under external loads, however, soft adhesives accumulate strain energy, which release drives the propagation of interfacial flaws prompting detachment. The trade-off between the required compliance, for surface conformity, and the desire for a reduced energy release rate, for better strength, can be achieved with a bi-material adhesive having a soft tip and a rigid backing (RB). This design strategy is widely observed in nature across multiple species. However, the detachment mechanisms of these adhesives are not completely understood and quantitative analysis of their adhesive strength is still missing. Based on linear elastic fracture mechanics (LEFM), we analyze the strength of axisymmetric bi-material adhesives. We observed two main detachment mechanisms, namely (i) center crack propagation and (ii) edge crack propagation. If the soft tip is sufficiently thin, mechanism (i) dominates and provides stable crack propagation, thereby toughening the interface. We ultimately provide the maximum theoretical strength of these adhesives obtaining closed-form estimation for an incompressible tip. In some cases, the maximum adhesive strength is independent of the crack size, rendering the interface flaw tolerant. We finally compare our prediction with experiments in the literature and observe good agreement.
, Nami Mogharabin
Published: 24 August 2021
Journal of Applied Mechanics, Volume 88; https://doi.org/10.1115/1.4052002

Abstract:
Zero-mass particles are, as a rule, never used in analytical dynamics, because they lead to singular mass matrices. However, recent advances in the development of the explicit equations of motion of constrained mechanical systems with singular mass matrices permit their use under certain circumstances. This paper shows that the use of such particles can be very efficacious in some problems in analytical dynamics that have resisted easy, general formulations, and in obtaining the equations of motion for complex multi-body systems. We explore the ease and simplicity that suitably used zero-mass particles can provide in formulating and simulating the equations of motion of a rigid, non-homogeneous sphere rolling under gravity, without slipping, on an arbitrarily prescribed surface. Computational results comparing the significant difference in the motion of a homogeneous sphere and a non-homogeneous sphere rolling down an asymmetric arbitrarily prescribed surface are obtained, along with measures of the accuracy of the computations. While the paper shows the usefulness of zero-mass particles applied to the classical problem of a rolling sphere, the development given is described in a general enough manner to be applicable to numerous other problems in analytical and multi-body dynamics that may have much greater complexity.
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