Near optimal pentamodes as a tool for guiding stress while minimizing compliance in 3d-printed materials: A complete solution to the weak G-closure problem for 3d-printed materials
For a composite containing one isotropic elastic material, with positive Lame moduli, and void, with the elastic material occupying a prescribed volume fraction f, and with the composite being subject to an average stress, σ0, Gibiansky, Cherkaev, and Allaire provided a sharp lower bound Wf(σ0) on t...
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Published in | Journal of the mechanics and physics of solids Vol. 114; pp. 194 - 208 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
London
Elsevier Ltd
01.05.2018
Elsevier BV |
Subjects | |
Online Access | Get full text |
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Summary: | For a composite containing one isotropic elastic material, with positive Lame moduli, and void, with the elastic material occupying a prescribed volume fraction f, and with the composite being subject to an average stress, σ0, Gibiansky, Cherkaev, and Allaire provided a sharp lower bound Wf(σ0) on the minimum compliance energy σ0:ϵ0, in which ϵ0 is the average strain. Here we show these bounds also provide sharp bounds on the possible (σ0,ϵ0)-pairs that can coexist in such composites, and thus solve the weak G-closure problem for 3d-printed materials. The materials we use to achieve the extremal (σ0,ϵ0)-pairs are denoted as near optimal pentamodes. We also consider two-phase composites containing this isotropic elasticity material and a rigid phase with the elastic material occupying a prescribed volume fraction f, and with the composite being subject to an average strain, ϵ0. For such composites, Allaire and Kohn provided a sharp lower bound W˜f(ϵ0) on the minimum elastic energy σ0:ϵ0. We show that these bounds also provide sharp bounds on the possible (σ0,ϵ0)-pairs that can coexist in such composites of the elastic and rigid phases, and thus solve the weak G-closure problem in this case too. The materials we use to achieve these extremal (σ0,ϵ0)-pairs are denoted as near optimal unimodes. |
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ISSN: | 0022-5096 1873-4782 |
DOI: | 10.1016/j.jmps.2018.02.003 |