A variational framework for fiber‐reinforced viscoelastic soft tissues including damage

Abstract

SummaryFibrous soft biological tissues such as skin, ligaments, tendons, and arteries are non‐homogeneous composite materials composed of fibers embedded in a ground substance. Cyclic tensile tests on these type of materials usually show a hysteretic stress–strain behavior in which strain rate dependence (viscoelasticity) and softening (Mullins' effect) play a coupled role. The main contribution of the present paper is to present unified variational approach to model both coupled phenomena: nonlinear viscoelasticity and Mullins‐like softening behavior. The approach is labeled as variational because viscous‐strain and damage internal variables are updated based on the minimization of a hyperelastic‐like potential that takes a renewed value at each time step. Numerical examples explores (a) the versatility of the proposed model to account for the two described phenomena according to the chosen functions for the free‐energy and dissipative potentials, (b) the ability of the time‐integration scheme embedded in the incremental potential definition to allow for large time increments, and (c) the capability of the model to mimic experimentally obtained stress–strain cyclic curves of soft tissues. The model implementation on standard finite elements is also tested in which symmetric analytic tangent matrices are used as a natural consequence of the variational nature of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.