期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 48, 期 18, 页码 2496-2510出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2011.05.002
关键词
Couple stress; Size-dependent solid mechanics; Elasticity; Curvature tensor; Micro- and nano-mechanics; Size effect
类别
资金
- U.S. National Science Foundation [0836768]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [0836768] Funding Source: National Science Foundation
By relying on the definition of admissible boundary conditions, the principle of virtual work and some kinematical considerations, we establish the skew-symmetric character of the couple-stress tensor in size-dependent continuum representations of matter. This fundamental result, which is independent of the material behavior, resolves all difficulties in developing a consistent couple stress theory. We then develop the corresponding size-dependent theory of small deformations in elastic bodies, including the energy and constitutive relations, displacement formulations, the uniqueness theorem for the corresponding boundary value problem and the reciprocal theorem for linear elasticity theory. Next, we consider the more restrictive case of isotropic materials and present general solutions for two-dimensional problems based on stress functions and for problems of anti-plane deformation. Finally, we examine several boundary value problems within this consistent size-dependent theory of elasticity. (C) 2011 Elsevier Ltd. All rights reserved.
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