Phase‐field Fracture with Representative Crack Elements for Non‐linear Material Behaviour

Abstract

AbstractThe mechanical energy potential of phase‐field fracture models is subdivided into a portion which (actively) drives the crack and a passive portion. This decompositions depends further on the crack state (opened, closed) in order to consider the re‐contact of the crack surfaces. The identification of the crack state and the decomposition is mostly approximated based on splits of the deformation or stress tensor. Stobel and Seelig [1], and Steinke and Kaliske [2] have shown unrealistic predictions for the crack kinematic for those models in quasi‐static and dynamic analyses. The approach proposed by these authors allows to predict the crack kinematic consistently. Nevertheless, this model is restricted to linear, isotropic elasticity and small deformations.In Storm et al. [3], the underlying concept is generalised. The crack kinematics is consistently obtained from a representative, discrete crack model and coupled to the phase‐field model by means of a variational homogenisation formulation. Thus, the crack driving force is a unique result of the framework of Representative Crack Elements. Analytical solutions for the mechanical problem of the representative crack element applied to linear, anisotropic elasticity and linear thermo‐elasticity at small deformations are presented there.In the current contribution to the method of phase‐field fracture, the framework for Representative Crack Elements is applied to non‐linear bulk materials. The iterative solution scheme for the representative crack element is presented and applied to elasticity with crack surface friction, visco‐elastic and elasto‐plastic materials.