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A ThermodynamicallyConsistent Phase Field Model for Electromechanical Diffusive Crack Propagation
Author(s) -
Hofacker Martina,
Miehe Christian,
Welschinger Fabian
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010051
Subject(s) - fracture mechanics , classification of discontinuities , mechanics , phase field models , dissipation , fracture (geology) , classical mechanics , physics , phase (matter) , materials science , mathematical analysis , mathematics , thermodynamics , quantum mechanics , composite material
The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and for crack initiation in bodies free of defects. This drawback can be overcome by a diffusive crack modeling based on the introduction of a crack phase field. In [1,2], we developed a phase‐field‐model of brittle fracture, which is conceptually in line with gradient‐type continuum damage models. Its global response is governed by an incremental variational principle, whose Euler equations describe the balance of linear momentum and the evolution of the crack topology. In this paper, the proposed model is extended to a thermodynamically consistent four‐field setting of coupled electromechanical fracture, based on a degrading mixed energy‐enthalpy functional and an over‐force‐type dissipation functional. These functionals are expressed in terms of the displacement, the electric potential, the fracture phase and its dual driving‐force fields. Evaluation of the necessary condition yields, in addition to the above mentioned Euler equations, the Gauss‐law of electrostatics. The capability of the proposed framewok for the description of electromechanically coupled crack propagation is demonstrated by means of a representative numerical example. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)