A microstructurally motivated constitutive description of collagenous soft biological tissue towards the description of their non-linear and time-dependent properties

Abstract

A versatile constitutive model for load-carrying soft biological tissue should incorporate salient microstructural deformation mechanisms and be able to reliably predict complex non-linear viscoelastic behavior. The advancement of treatment and rehabilitation strategies for soft tissue injuries is inextricably linked to our understanding of the underlying tissue microstructure and how this defines its macroscopic material properties. Towards this long-term objective, we present a generalized multiscale constitutive framework based on a novel description of collagen, the most mechanically significant extracellular matrix protein. The description accounts for the gradual recruitment of undulated collagen fibrils and introduces proteoglycan mediated time-dependent fibrillar sliding. Crucially, the proteoglycan deformation allows for the reduction of overstressed fibrils towards a preferential homeostatic stress. An implicit Finite Element implementation of the model uses an interpolation strategy towards collagen fiber stress determination and results in a memory-efficient representation of the model. A number of test cases, including patient-specific geometries, establish the efficiency of the description and demonstrate its ability to explain qualitative properties reported from macroscopic experimental studies of tendon and vascular tissue.