A brief review on computational modeling of rupture in soft biological tissues

Abstract

Physiological and pathological aspects of soft biological tissues in terms of, e.g., aortic dissection, aneurysmatic and atherosclerotic rupture, tears in tendons and ligaments are of significant concern in medical science. The past few decades have witnessed noticeable advances in the fundamental understanding of the mechanics of soft biological tissues. Furthermore, computational biomechanics, with an ever-increasing number of publications, has now become a third pillar of investigation, next to theory and experiment. In the present chapter we provide a brief review of some constitutive frameworks and related computational models with the potential to predict the clinically relevant phenomena of rupture of soft biological tissues. Accordingly, Euler-Lagrange equations are presented in regard to a recently developed crack phase-field method (CPFM) for soft tissues. The theoretical framework is supplemented by some recently documented numerical results, with a focus on evolving failure surfaces that are predicted by a range of different failure criteria. A peel test of arterial tissue is analyzed using the crack phase-field approach. Subsequently, discontinuous models of tissue rupture are described, namely the cohesive zone model (CZM) and the extended finite element method (XFEM). Traction-separation laws used to determine the crack growth are described, together with the kinematic and numerical foundations. Simulation of a peel test of arterial tissue is then presented for both the CZM and the XFEM. Finally we provide a critical discussion and overview of some open problems and possible improvements of the computational modeling concepts for soft tissue rupture.