Phase‐field Fracture Based on Representative Crack Elements (RCE): Inelastic Materials, Friction, Finite Deformations, Multi‐physics

Abstract

AbstractThe concept of representative crack elements has been successfully introduced to phase‐field fracture in previous publications, where anisotropic elasticity [1], visco‐elasticity [2], elasto‐plasticity and crack surface friction [3] are considered at small deformations. This framework allows to overcome unrealistic predictions for the crack kinematics, reported e.g. in Strobl and Seelig [4], and Steinke and Kaliske [5], known from phase‐field models with approximations for the crack closure behaviour based on volumetric‐deviatoric, spectral or similar splits of stress or strain tensors.In the current contribution to the method of phase‐field fracture, the framework for representative crack elements is shown for finite deformations and fully coupled thermo‐mechanics. The iterative solution scheme for the representative crack element and the variational homogenisation method are sketched. Applications to elasto‐plasticity, crack surface friction, finite deformations and thermo‐mechanics with heat radiation through the crack demonstrate the flexibility of the framework.