A VARIATIONAL APPROACH FOR FIBER REINFORCED VISCOELASTIC MATERIALS SUBJECT TO DAMAGE

Abstract

A variational approach for fiber reinforced viscoelastic materials subject to dam- age The mechanical properties of soft biological tissues vary depending on how the internal structure is organized. Classical examples of tissues are ligaments, tendons, skin, arteries, and annulus fibrous. The main element of such tissues is the fibers which are responsible for the tissue resistance and the main mechanical characteristic is their viscoelastic anisotropic behavior. The objective of this paper is to extend an existing model for viscoelastic materials with (anisotropic) reinforcement of fibers in order to include damage that arises when strains assumes values greater than some physiological range. The model is based on a variational framework in which its mechanical behavior is described by a free energy incremental po- tential whose local minimization provides the constraints for the internal variable updates for each load increment. Among the advantages of these variational approaches we should mention the ability to represent different material models depending on the choice of suit- able potential functions and the obtention of symmetric constitutive tangent matrices. Some numerical examples are shown in order to evaluate the performance of the proposed model.