Rupture in soft biological tissues modeled by a phase‐field method

Abstract

AbstractWe present an application of the phase‐field method of fracture to the simulation of artery rupture at large strains. To achieve this, the crack driving force function associated with the evolution of the crack phase‐field is modified to account for the inherent anisotropy of the soft biological tissues. The phase‐field methods present a promising and innovative approach to the thermodynamically consistent modeling of fracture. A key advantage lies in the prediction of the complex crack topologies where the cohesive zone approaches to fracture are known to suffer. A regularized crack surface functional is introduced that Γ‐converges to a sharp crack topology for vanishing length scale parameter. The evaluation of the phase‐field follows the minimization of this crack surface functional. The phase‐field variable can be treated as a geometric quantity whose evolution is coupled to the anisotropic bulk response in a modular format in terms of a crack driving state function. A stress‐based anisotropic failure criterion is introduced whose maximum value from the deformation history drives the irreversible crack phase‐field. The formulation is verified by the finite element based simulation of a real arterial cross‐section undergoing rupture in a two‐dimensional setting when subjected to inflation pressure. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)