Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 294, Issue -, Pages 449-485Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.11.016
Keywords
Brittle fracture; Crack propagation; Phase field modeling; Finite strain; Coupled multi-field problems; Thermo-elasticity
Funding
- German Research Foundation (DFG) within the Cluster of Excellence Simulation Technology at the University of Stuttgart [Exc 310]
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This work presents a generalization of recently developed continuum phase field models for brittle fracture towards fully coupled thermo-mechanical and multi-physics problems at large strains. It outlines a rigorous geometric approach to the diffusive crack modeling based on the introduction of a balance of regularized crack surface, governed by a crack phase field. The regularized crack surface functional is based on a crack surface density function, that describes the macroscopic crack surface in the bulk material per unit of the reference volume. The approach overcomes difficulties associated with the computational realization of sharp crack discontinuities, in particular when it comes to complex crack topologies. The formulation proposed is essentially a gradient damage theory, however, equipped with critical ingredients rooted in fracture mechanics. A modular concept is outlined for the linking of the diffusive crack modeling with complex multi-field response of the bulk material, where focus is put on the model problem of finite thermo-elasticity. This concerns a generalization of crack driving forces from the energetic definitions towards stress-based criteria, the constitutive modeling of heat conduction across cracks and convective heat exchanges at crack faces based on additional constitutive functions. This is achieved by approximating surface load integrals of the sharp crack approach by distinct volume integrals. We demonstrate the performance of the phase field formulation of fracture at large strains by means of representative numerical examples. (C) 2014 Elsevier B.V. All rights reserved.
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