Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 46, Issue 25-26, Pages 4261-4276Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2009.07.014
Keywords
Gradient elasticity; Strain gradients; Invariance conditions; Couple stress; Microstructure; Conformal transformations; Symmetry of moment stresses; Micromorphic; Micropolar; Cosserat
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We present a micromechanically motivated form of the curvature energy in infinitesimal isotropic gradient elasticity. The basis is a homogenization/averaging scheme using a micro-randomness assumption imposed on a directional higher gradient interaction term. These directional interaction terms are matrix valued allowing to apply the standard orthogonal Cartan Lie-algebra decomposition. Averaging over all (subgrid) directions leads to three quadratic curvature terms, which are conformally invariant when neglecting volumetric effects. Restricted to rotational inhomogeneities we motivate thereby a symmetric couple stress tensor in the infinitesimal indeterminate couple stress model of Koiter-Mindlin-Toupin-type. Relations are established to a novel conformally invariant linear Cosserat model. (C) 2009 Elsevier Ltd. All rights reserved.
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