Model reduction by mean-field homogenization in viscoelastic composites. III. Dual theory
Model reduction by mean-field homogenization in viscoelastic composites. III. Dual theory
复制标题
通过粘弹性复合材料中的平均场均匀化来简化模型。
DOI：
10.1098/rspa.2020.0869
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
P. Suquet
中科院分区：
文献类型：
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作者：
N. Lahellec;M. I. Idiart;P. Suquet
从最近在一篇配套论文（Idiart MI et al. 2020 Proc. R. Soc. A 20200407（doi：10.1098/rspa.2020.0407））。结果表明，该计划产生一个降阶近似，其中的复合材料的微观动力学描述的一组有限的宏观力与相平均和相内协方差的各种微观力场，这可以通过平均场均匀化技术进行评估。近似表现出一个两个潜在的结构与凸的互补能量密度，但非凸的力势。暴露的近似结果的属性和它们的影响进行了讨论。论述补充本计划和其他候选计划在文献中提出的复合材料与基本局部麦克斯韦型流变学之间的等价性证明。
The mean-field homogenization scheme for viscoelastic composites proposed by Lahellec & Suquet (2013 Int. J. Plasticity 42, 1–13 (doi:10.1016/j.ijplas.2012.09.005)) is revisited from the standpoint recently adopted in a companion paper (Idiart MI et al. 2020 Proc. R. Soc. A 20200407 (doi:10.1098/rspa.2020.0407)). It is shown that the scheme generates a reduced-order approximation wherein the microscopic kinetics of the composite are described in terms of a finite set of macroscopic forces identified with the phase averages and intraphase covariances of the various microscopic force fields, which can be evaluated by mean-field homogenization techniques. The approximation exhibits a two-potential structure with a convex complementary energy density but a non-convex force potential. The consequential properties of the approximation are exposed and their implications are discussed. The exposition is supplemented by proofs of equivalence between the present scheme and other candidate schemes proposed in the literature for composites with elementary local rheologies of Maxwellian type.