A phase field approach to fracture for hyperelastic and visco-hyperelastic materials applied to pre-stressed cylindrical structures

In this investigation, the mechanical modeling of nonlinear visco-hyperelastic residually stressed materials obtained from an invariant-based constitutive energy framework is coupled with the phase field approach to fracture. The main target regards the extension of the phase field method to simulate pre-stressed cylindrical structures subjected to monotonic axial pulling load upon failure. This formulation is incorporated into a numerical procedure using the Finite Element Method (FEM), in particular, it is implemented in the commercial FE package ABAQUS as a user subroutine UMAT. Results suggest the dependence of the mechanical behavior and the crack pattern of these structures on not only viscous parameters like the relaxation time and the displacement rate, but also on the strength of the residual stress field, which in turn depends on geometrical characteristics of the cylindrical structure such as the radius or the length. A range of solutions related to crack propagation is shown for different cylindrical structures, from azimuthal crack propagation to axial one. The proposed framework aims to provide an extended application for the already-defined visco-hyperelastic formulation by the inclusion of residual stresses.