Large strained fracture of nearly incompressible hyperelastic materials: Enhanced assumed strain methods and energy decomposition

Abstract

Tracking crack propagation at large strains of hyperelastic solids is a challenging task due to the high nonlinearity, nearly incompressibility and ordered tendency in microstructure of the rubbery material under stretch. On the basis of the diffusive crack model, this work presents a new phase-field model by combining the strain energy decomposition and the enhanced assumed strain method. The proposed fracture formulation is indeed Griffith's theory-based framework but further accounting for the coupled effects of the stretches, damage and incompressibility to predict the crack growth in both compressible and incompressible hyperelastic solids. There are three innovations contained in this study: (i) The developed phase-field framework is capable to capture the effect of hole collapse, which is an intrinsic phenomenon of hyperelastic material and difficult to be detected by the others. (ii) The developed energy decomposition method provides a reasonable description of the physical reality that the hyperelastic fracture is driven by the changes in the internal energy of the stretched molecular chains in the polymer network. This continuum description automatically distinguishes the strain energy that really contributes to crack growth at multiaxial stress states, reducing significantly the numerical instability caused by material softening. (iii) By introducing the assumed strain method to the present fracture scheme, the physical consistency of energy decomposition and the mathematical nonnegativeness of strain energy can be satisfied simultaneously for incompressible problem. We demonstrate the performance of the enhanced phase-field framework through representative examples and highlight the importance of positive deviatoric energy for incompressible problem by comparing with experiments and classical models.