The concept of frozen elastic energy as a consequence of changes in microstructure morphology

Abstract

Constitutive modelling of soft biological tissues has been the topic of abundant literature. These biological tissues, made of variously oriented and crimped fibers embedded in a soft matrix, exhibit a highly nonlinear anisotropic behavior with the ability to sustain large reversible strains. The existing constitutive models are mainly phenomenological hyperelastic models developed at the macroscopic scale (Holzapfel & Gasser 2000). Experimental mechanical tests performed on soft tissues and coupled to confocal microscopic imaging (Schrauwen et al. 2012) reveal that this nonlinear behavior originates in geometrical changes in the microstructure, such as progressive decrimping and re-alignement of the fibers along the load direction. This confirms the growing need to understand the relationship between phenomena taking place in the microstructure and macroscopic mechanical response; subsequently driving forward multi-scale approaches (Morin & Hellmich 2014). We here propose to model the reorientation of the fibers within the matrix through extension of the framework of continuum micromechanics (Zaoui 2002) and Eshelby’s inclusion problems (Eshelby 1957). We investigate the ability of the proposed model to capture, through microstructure morphology changes, the non-linear mechanical response of soft tissues, the possible path dependence of their response to multiaxial loading, and a remaining frozen elastic energy after complete unloading of the tissue.