Numerical Studies of Different Mixed Phase-Field Fracture Models for Simulating Crack Propagation in Punctured EPDM Strips

Abstract

We consider a monolithic phase-field description for fractures in nearly incompressible materials, i.e., carbon black filled ethylene propylene diene monomer rubber (EPDM). A quasi-static phasefield fracture problem is formulated in mixed form based on three different energy functionals (AT2, AT1 and Wu's model) combined with two different stress splitting approaches (according to Miehe and Amor). It leads to six different phase-field fracture formulations in mixed form. The coupled variational inequality systems are solved in a quasi-monolithic manner with the help of a primal-dual active set method handling the inequality constraint. Further, adaptive mesh refinement is used to get a sharper crack zone. Numerical results based on the six different problem setups are validated on crack propagation experiments of punctured EPDM strips with five different test configurations. As a quantity of interest, the crack paths of experiments and numerical computations are discussed.

Nonlocal geometric fracture theory: A nonlocal‐local asymptotically compatible framework for continuous–discontinuous deformation of solid materials

“…Note that, similar to the modified gradient damage model, 14 the variational formulation of phase field fracture theory is given on a fixed mesh and the Galerkin finite element method can be used, hence there is no need to update the basis function of each element and the error estimations and mesh adaptivity can be easily employed. 26 Compared with Phase-field fracture theory, Peridynamics adopts a distinct idea for fracture problems of solid materials. In Peridynamics, the partial differential equations in classical continuum mechanics is reformulated as an integral form, in which the concept of force-state vector is developed to eliminate the singularity inherent in classical differential operators.…”

“…Governing equations for deformation of the continuum and the evolution of cracks are obtained by the variational principle. Note that, similar to the modified gradient damage model, 14 the variational formulation of phase field fracture theory is given on a fixed mesh and the Galerkin finite element method can be used, hence there is no need to update the basis function of each element and the error estimations and mesh adaptivity can be easily employed 26 . Compared with Phase‐field fracture theory, Peridynamics adopts a distinct idea for fracture problems of solid materials.…”