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

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.

Automated summary

In this study, a finite element formulation is developed to model quasi-static crack propagation in hyperelastic solids using the material-sink approach. Breakage of molecular bonds leads to material separation and appearance of new crack surfaces. The diffusion of bond breakage causes localized material loss. To account for this, mass density is considered as a variable that decreases in the damaged area. Mathematically, mass balance is included as an additional law to regularize the computational model. The developed finite element formulation has displacement and density degrees of freedom and a monolithic approach is applied for stable solution of the nonlinear problem. Numerical examples demonstrate the robustness of the proposed approach for modeling aneurysm material fracture.