Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials |
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| Institution: | 1. Department of Mechanical Engineering, Linköping University, S-581 83 Linköping, Sweden;2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA;3. Department of Engineering and Architecture, University of Parma, Viale Usberti 181/A, 43124 Parma, Italy;1. IMT School for Advanced Studies, Lucca, Italy;2. Department of Civil, Environmental and Mechanical Engineering, University of Trento, Italy;1. TKC Global Contractor at Army Research Laboratory, RDRL-WMP-B, Aberdeen Proving Ground, MD 21005, USA;2. Army Research Laboratory, RDRL-WMP-B, Aberdeen Proving Ground, MD 21005, USA;1. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK;2. Fakultät für Mathematik, Universität Duisburg–Essen, Thea-Leymann-Straße 9, 45127 Essen, Germany |
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| Abstract: | The homogenization results obtained by Bacca et al. (2013a), to identify the effective second-gradient elastic materials from heterogeneous Cauchy elastic solids, are extended here to the case of phases having non-isotropic tensors of inertia. It is shown that the nonlocal constitutive tensor for the homogenized material depends on both the inertia properties of the RVE and the difference between the effective and the matrix local elastic tensors. Results show that: (i) orthotropic nonlocal effects follow from homogenization of a dilute distribution of aligned elliptical holes and, in the limit case, of cracks; (ii) even under the dilute assumption and isotropic local effective behaviour, homogenization may lead to effective nonlocal orthotropic properties. |
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| Keywords: | Second-order homogenization Higher-order elasticity Effective nonlocal continuum Characteristic length-scale Cracked materials Dilute suspension |
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