International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000487

Scale Effects of The Stress Symmetry in Generalized Elasticity

Zhanfang Liu^a and Zhi Fu^b Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, China. ^azhanfang@cqu.edu.cn ^bcopyfuzhi@sina.com

ABSTRACT

Generalized elasticity is introduced in which the deformation is split into translational and rotational deformation. The curvature tensor and the corresponding couple stress are both the deviatoric tensor and they are satisfied with a linear constitutive law. Finite element formulation is presented whereas the constrained variational principle is used so that the displacement and rotational angle at element nodes are treated as independent variables. Numerical analyses are implemented for a plane simple shearing. It is found that the curvature tensor is far larger than the strain but the couple stress is far less than Cauchy stress for macro-scale structures, and thus reciprocal theorem of shear stresses in elasticity is available. With decreasing the dimensions of structure, symmetry of the total stress decreases remarkably for structure dimensions from millimeters to micrometers. Scale effects of total stress symmetry in elastic bodies are reflected very well with the generalized elasticity.

Keywords: Finite element method, Generalized elasticity, Rotational deformation, Scale effects, Stress symmetry.

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