期刊
CONTINUUM MECHANICS AND THERMODYNAMICS
卷 26, 期 5, 页码 639-681出版社
SPRINGER
DOI: 10.1007/s00161-013-0322-9
关键词
Micromorphic elasticity; Symmetric Cauchy stresses; Dynamic problem; Dislocation dynamics; Gradient plasticity; Symmetric micromorphic model; Dislocation energy; Earthquake processes; Generalized continua; Nonpolar material; Microstructure; Micro-elasticity; Size effects; Fracture; Non-smooth solutions; Gradient elasticity; Strain gradient elasticity; Couple stresses; Cosserat couple modulus; Wave propagation; Band gaps
资金
- Romanian National Authority for Scientific Research (CNCS-UEFISCDI) [PN-II-ID-PCE-2011-3-0521]
- INSA-Lyon [BQR 2013-0054]
We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict nonpolar size effects. It is intended for the homogenized description of highly heterogeneous, but nonpolar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models, our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models.
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