Quasi-static crack propagation in soft materials using the material-sink theory

In the present study, a finite element formulation for the material-sink approach aimed at modeling quasi-static crack propagation in hyperelastic solids is developed. Breakage of molecular bonds leads to material separation and appearance of two new surfaces of a crack. However, the bond breakage is diffusive, and the loss of local bonds leads to the localized material (molecular) loss. The latter notion triggers consideration of mass density as a variable that numerically decreases in the area where damage localizes into a crack. This physical notion requires mathematical consideration of mass balance as an additional and active law, which regularizes the computational model. From the numerical point of view, the developed finite element formulation has displacement and density degrees of freedom. Also, a monolithic approach was applied that ensures stable incrimination of the nonlinear problem. Numerical examples of the fracture of aneurysm material demonstrate the high robustness of the proposed approach.