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Thermodynamically consistent algorithms for a finite‐deformation phase‐field approach to fracture
Author(s) -
Hesch C.,
Weinberg K.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4709
Subject(s) - phase field models , nonlinear system , dissipation , integrator , field (mathematics) , multiplicative function , fracture (geology) , phase (matter) , fracture mechanics , function (biology) , compression (physics) , deformation (meteorology) , tension (geology) , finite element method , mechanics , computer science , algorithm , mathematics , physics , structural engineering , mathematical analysis , engineering , thermodynamics , geotechnical engineering , computer network , bandwidth (computing) , quantum mechanics , evolutionary biology , biology , meteorology , pure mathematics
SUMMARY Phase‐field approaches to fracture offer new perspectives toward the numerical solution of crack propagation. In this paper, a phase‐field method for finite deformations and general nonlinear material models is introduced using a novel multiplicative split of the principal stretches to account for the different behavior of fracture in tension and compression. An energy‐momentum consistent integrator is developed and applied to the arising nonlinear coupled phase‐field model. This approach is thermodynamically consistent in the sense that the first law of thermodynamics if fulfilled with respect to the dissipation function. The capabilities and the performance of the proposed approach is demonstrated in several representative examples. Copyright © 2014 John Wiley & Sons, Ltd.