A numerical study of Mullins softening effects on mode I crack propagation in viscoelastic solids

Abstract

This paper presents a finite element analysis of steady-state crack propagation in viscoelastic soft solids exhibiting Mullins softening. A cohesive-zone model is employed to simulate the localized processes at the tip of a Mode I crack in materials governed by viscoelastic behavior and damage-induced Mullins effects. The study numerically evaluates the intrinsic dissipation characteristics of typical rubber-like materials, focusing on the influence of key factors such as Mullins damage, relaxation modulus, and relaxation time. The impact of these factors on material toughening is examined, with particular emphasis on their role in crack propagation. The results reveal that crack propagation velocity is highly sensitive to the interplay between energy dissipation mechanisms. Specifically, Mullins damage parameters are shown to increase fracture toughness by raising the local energy release rate threshold at the crack tip. Additionally, the relaxation modulus enhances viscous dissipation, further elevating this threshold and subsequently reducing crack propagation velocity. Interestingly, an inverse relationship between relaxation time and crack propagation velocity is observed. The study provides a detailed analysis of the dissipation mechanisms at the crack tip, offering valuable insights for improving material toughness.