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Multi-step homogenization in the Mori-Tanaka-Benveniste theory

机译：Mori-Tanaka-Benveniste理论中的多步均质化

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摘要

Micromechanical schemes homogenizing elastic properties as well as thermal and electrical conductivities of heterogeneous materials are most often developed as one-step procedures when all inhomogeneities are drawn into calculations at once, leaving no possibility for a multi-step approach. However, in practice, the multi-step homogenization is involved more often than expected, sometimes not on purpose. The reason is unknown microstructure of composite constituents while micromechanical schemes typically require their phases to be homogeneous. Thereby, constituents' properties, submitted to schemes, are effective, not intrinsic, contrary to schemes' requirements. This implicitly introduces preliminary homogenization steps to provide these effective properties, and the actual scheme considered corresponds to the last step of a multi-step homogenization process. However, our knowledge on applicability of multi-step homogenization techniques is more limited in comparison with the well-studied one-step schemes. Our study explores differences among one-, two-, and multi-step procedures in the Mori-TanakaBenveniste theory. For two-phase unidirectional composites, two- and one-step procedures differ by change in effective field related to change in concentration tensors. For porosity, two- and one-step homogenizations become identical if Eshelby tensor is multiplied by a scalar coefficient depending on volume fractions. Finally, applicability of the two-step procedure is verified for anisotropic three-phase composites.
机译：当立即将所有不均匀性都纳入计算中时，使异质材料的弹性以及热导率和电导率均匀化的微机械方案最常被开发为一步式方法，而没有多步法的可能性。但是，实际上，多步均质化的参与比预期的更多，有时不是故意的。原因是未知的复合材料成分的微观结构，而微机械方案通常要求它们的相是均匀的。因此，与计划的要求相反，提交给计划的选民的属性是有效的，而不是固有的。这隐含地引入了预均化步骤以提供这些有效的特性，并且所考虑的实际方案对应于多步骤均化过程的最后一步。但是，与经过精心研究的单步方案相比，我们对多步均化技术的适用性的了解更加有限。我们的研究探索了Mori-TanakaBenveniste理论中一，二和多步骤程序之间的差异。对于两相单向复合材料，两步法和一步法的不同之处在于有效场的变化与浓度张量的变化有关。对于孔隙率，如果根据体积分数将Eshelby张量乘以标量系数，则两步和一步的均化将变得相同。最后，验证了两步法在各向异性三相复合材料中的适用性。

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  • 来源
    《Composite Structures》 |2019年第9期|110801.1-110801.15|共15页
  • 作者

    Abaimov Sergey G.; Trofimov Anton; Sergeichev Ivan V; Akhatov Iskander S.;

  • 作者单位

    Skolkovo Inst Sci & Technol, Ctr Design Mfg & Mat, Moscow, Russia;

    Skolkovo Inst Sci & Technol, Ctr Design Mfg & Mat, Moscow, Russia;

    Skolkovo Inst Sci & Technol, Ctr Design Mfg & Mat, Moscow, Russia;

    Skolkovo Inst Sci & Technol, Ctr Design Mfg & Mat, Moscow, Russia;

  • 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
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