首页> 外文期刊>Journal of the Mechanics and Physics of Solids >Near optimal pentamodes as a tool for guiding stress while minimizing compliance in 3d-printed materials: A complete solution to the weak G-dosure problem for 3d-printed materials
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Near optimal pentamodes as a tool for guiding stress while minimizing compliance in 3d-printed materials: A complete solution to the weak G-dosure problem for 3d-printed materials

机译:接近最佳的五模态作为引导应力的工具,同时最大程度地降低了3D打印材料的顺应性:完整解决方案,解决了3D打印材料的弱G-dosure问题

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摘要

For a composite containing one isotropic elastic material, with positive Lame moduli, and void, with the elastic material occupying a prescribed volume fractionf, and with the composite being subject to an average stress,σ0,Gibiansky, Cherkaev, and Allaire provided a sharp lower boundWf(σ0)on the minimum compliance energyσ0:ϵ0,in whichϵ0is 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 weakG-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 fractionf, and with the composite being subject to an average strain,ϵ0. For such composites, Allaire and Kohn provided a sharp lower boundW˜f(ϵ0)on the minimum elastic energyσ0: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 weakG-closure problem in this case too. The materials we use to achieve these extremal(σ0,ϵ0)-pairs are denoted as near optimal unimodes.
机译:对于包含一种具有各向同性弹性材料的复合材料,该复合材料具有正的Lame模量和空隙,并且该弹性材料占据了规定的体积分数f,并且复合材料受到平均应力的作用,σ0,Gibiansky,Cherkaev和Allaire最小顺应能σ0:ϵ0上的边界Wf(σ0),其中ϵ0是平均应变。在这里,我们表明这些边界还为可能在此类复合物中共存的(σ0,ϵ0)对提供了清晰的边界,从而解决了3D打印材料的弱G闭合问题。我们用于实现极值(σ0,ϵ0)对的材料表示为接近最佳五模态。我们还考虑了包含这种各向同性弹性材料和刚性相的两相复合材料,其中弹性材料占据了规定的体积分数f,并且复合材料的平均应变为0。对于这种复合材料,Allaire和Kohn在最小弹性能σ0:ϵ0上提供了一个尖锐的下界W〜f(ϵ0)。我们表明,这些边界还在可能存在的(σ0,ϵ0)对上提供了尖锐的边界,这些对可以共存于这种弹性和刚性相的复合物中,因此也解决了这种情况下的弱G闭合问题。我们用于实现这些极值(σ0,ϵ0)对的材料称为接近最佳单模。

著录项

  • 来源
    《Journal of the Mechanics and Physics of Solids》 |2018年第5期|194-208|共15页
  • 作者单位

    Department of Mathematics, University of Utah;

    Institut de Recherche Mathématique de Rennes, INSA de Rennes;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-18 02:59:43

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