Reduced Parameter Formulation for Incorporating Fiber Level Viscoelasticity into Tissue Level Biomechanical Models

Abstract

Collagen is known to be a viscoelastic material and therefore is an important source of time dependent behavior in soft tissue. Though there are material models for soft tissue that rely on properties and structure of constituent collagen fibers, such models generally utilize only the elastic properties of collagen, and thus the resulting tissue level response does not possess any viscoelastic features. Here, the time dependent properties of collagen are directly incorporated into a fiber based hyperelastic model using the one dimensional theory of quasi-linear viscoelasticity within the context of a locally defined, anisotropic representation of extracellular matrix structure. The resulting model possesses seven material parameters and, using numerical and computational analysis, is shown to successfully predict many key features of soft tissue response including anisotropy, strain hardening, preconditioning, and rate independent hysteresis. A formulation is also introduced for incorporating fiber level viscoelasticity into structural models derived from a continuous representation of fiber structure.