Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations |
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Authors: | Yongmei M Jin Yu U Wang Armen G Khachaturyan |
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Institution: | Department of Ceramic and Materials Engineering , Rutgers University , 607 Taylor Road, Piscataway, New Jersey, 08854-8065, USA |
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Abstract: | The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered. |
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