Elastomers filled with liquid inclusions: Theory, numerical implementation, and some basic results
Elastomers filled with liquid inclusions: Theory, numerical implementation, and some basic results
复制标题
充满液体包裹体的弹性体：理论、数值实现和一些基本结果
DOI：
10.1016/j.jmps.2022.104930
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发表时间：
2022
影响因子：
5.3
通讯作者：
Lopez-Pamies, Oscar
中科院分区：
文献类型：
--
作者：
Ghosh, Kamalendu;Lopez-Pamies, Oscar
最近的实验和理论结果表明，填充各种类型的液体夹杂物的弹性体是一种具有前所未有的性能的有前途的新型材料。基于这些发现，本文的两个目标中的第一个目标是建立描述充液夹杂弹性体在有限准静态变形下的宏观力学响应的均匀化问题。当弹性体是超弹性固体，组成夹杂物的液体是超弹性流体，固体弹性体和液体夹杂物的界面具有自己的超弹性行为(作为特例包括表面张力)，夹杂物最初是球形的时，重点讨论了无耗散情况。这种填充弹性体的宏观行为被证明是超弹性固体的行为，尽管它直接取决于夹杂物的大小和界面的本构行为。因此，它的特征是宏观变形梯度F‘的有效储能函数W’(F‘)。值得注意的是，尽管夹杂物内部存在局部残余应力(由于初始界面力的存在)，但所产生的宏观行为是没有残余应力的，即∂W‘(I)/∂F’=0。此外，尽管块体和小变形极限界面的局部弹性模数不具有次要对称性(由于残馀应力和初始界面力的存在)，但所得到的有效弹性模数确实具有标准的次要对称性，即L i j k L=L j i k L=L i j L k。其中L‘i j k L≔∂2 W’(I)/∂F‘i j∂F’k L。本文的第二个目标是实现和部署一个有限元格式来数值生成一类基本的充满液体夹杂的弹性体的宏观响应的解，即嵌入不可压缩Neo-Hookean弹性体中的单分散尺寸的不可压缩液体夹杂的各向同性悬浮液的宏观响应的解。在数值解的指导下，本文的最后部分致力于提出有效储能函数W(F)的一个简单的显式近似。
Experimental and theoretical results of late have pointed to elastomers filled with various types of liquid inclusions as a promising new class of materials with unprecedented properties. Motivated by these findings, the first of two objectives of this paper is to formulate the homogenization problem that describes the macroscopic mechanical response of elastomers filled with liquid inclusions under finite quasistatic deformations. The focus is on the non-dissipative case when the elastomer is a hyperelastic solid, the liquid making up the inclusions is a hyperelastic fluid, the interfaces separating the solid elastomer from the liquid inclusions feature their own hyperelastic behavior (which includes surface tension as a special case), and the inclusions are initially spherical in shape. The macroscopic behavior of such filled elastomers turns out to be that of a hyperelastic solid, albeit one that depends directly on the size of the inclusions and the constitutive behavior of the interfaces. It is hence characterized by an effective stored-energy function W¯(F¯) of the macroscopic deformation gradient F¯. Strikingly, in spite of the fact that there are local residual stresses within the inclusions (due to the presence of initial interfacial forces), the resulting macroscopic behavior is free of residual stresses, that is,∂ W¯(I)/∂ F¯= 0. What is more, in spite of the fact that the local moduli of elasticity in the bulk and the interfaces in the small-deformation limit do not possess minor symmetries (due to the presence of residual stresses and initial interfacial forces), the resulting effective modulus of elasticity does possess the standard minor symmetries, that is, L¯ i j k l= L¯ j i k l= L¯ i j l k, where L¯ i j k l≔∂ 2 W¯(I)/∂ F¯ i j∂ F¯ k l. The second objective of this paper is to implement and deploy a finite-element scheme to numerically generate solutions for the macroscopic response of a basic class of elastomers filled with liquid inclusions, that of isotropic suspensions of incompressible liquid inclusions of monodisperse size embedded in incompressible Neo-Hookean elastomers wherein the interfaces feature a constant surface tension. With guidance from the numerical solutions, the last part of this paper is devoted to proposing a simple explicit approximation for the effective stored-energy function W¯(F¯).