Subgrid interaction and micro-randomness - Novel invariance requirements in infinitesimal gradient elasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:46

Article

Neff, Patrizio¹  Jeong, Jena³  Ramezani, Hamidreza² 

[1] Univ Duisburg Essen, Chair Nonlinear Anal & Modelling, Fak Math, D-45141 Essen, Germany

[2] Univ Orleans, Ecole Polytech, CNRS CRMD, F-45072 Orleans, France

[3] ESTP, F-94234 Cachan, France

关键词: Gradient elasticity;    Strain gradients;    Invariance conditions;    Couple stress;    Microstructure;    Conformal transformations;    Symmetry of moment stresses;    Micromorphic;    Micropolar;    Cosserat;   

DOI  :  10.1016/j.ijsolstr.2009.07.014

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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