On the grade consistent theories of micromorphic elastic solids
- Department of Mathematics, 'Al.I. Cuza' University, and 'O. Mayer' Institute of Mathematics, Romanian Academy, 700506 Iasi (Romania)
For the investigation of specific nonlocal phenomena the second-order displacement gradient has been added to the independent constitutive variables used in the classical theories of elastic solids. In this paper we outline the hystorical development of the subject and present a nonlinear grade consistent theory of micromorphic elastic solids in which the independent constitutive variables are the deformation gradient, the second-order displacement gradient, microdeformation tensor, and microdeformation gradient. Then, we present the linearized theory and establish a uniqueness result with no definiteness assumption on the elastic coefficients. The theory is used to obtain the basic eqations of a grade consistent theory of microstretch elastic bodies. The field equations for an isotropic and homogeneous elastic body are presented. A counterpart of the Cauchy-Kowalevski-Somigliana solution of the classical elastodynamics is established.
- OSTI ID:
- 21511464
- Journal Information:
- AIP Conference Proceedings, Vol. 1329, Issue 1; Conference: Alexandru Myller mathematical seminar centennial conference, Iasi (Romania), 21-26 Jun 2010; Other Information: DOI: 10.1063/1.3559165; (c) 2011 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DEFORMATION
ELASTICITY
FIELD EQUATIONS
FUNCTIONAL ANALYSIS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PLASTICITY
QUANTUM ELECTRODYNAMICS
SOLIDS
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
EQUATIONS
FIELD THEORIES
MATHEMATICS
MECHANICAL PROPERTIES
QUANTUM FIELD THEORY