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A generalized Vlasov-Jones foundation model for micromechanics studies of syntactic foams

机译：用于语法泡沫微力学研究的广义Vlasov-Jones基础模型

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摘要

Syntactic foams are lightweight paniculate composites that are synthesized by dispersing thin hollow inclusions in a matrix material. A spherical elastic inclusion embedded in a dissimilar medium is often used as a unit cell model to study syntactic foams' micromechanics. The analysis of such unit cell problem is generally conducted by modeling both the inclusion and the matrix using three-dimensional linear elasticity. In this paper, we take a different approach by developing a generalized Vlasov-Jones foundation model for the matrix and describing the inclusion using Donnell shell theory. This framework is specialized to uniaxial tensile loading of a spherical matrix in the presence of two equal interfacial cracks introduced to model inclusion-matrix debonding. A variational method is used to formulate a nonlinear boundary value problem for the shell and foundation displacements and an iterative solution procedure based on the Ritz method is presented. For a polymer matrix-glass inclusion system, a parametric study is performed to investigate the effect of debonding extent, inclusion volume fraction, and shell thickness on debonding energetics and effective elastic modulus. The proposed model is validated using finite element results and experimental data on Young's modulus of epoxy-glass syntactic foams.
机译：句法泡沫是轻质的颗粒状复合材料，是通过将薄的空心夹杂物分散在基质材料中而合成的。嵌入不同介质中的球形弹性夹杂物通常用作单元格模型来研究句法泡沫的微力学。通常通过使用三维线性弹性对内含物和基质进行建模来对这种晶胞问题进行分析。在本文中，我们通过为矩阵开发通用的Vlasov-Jones基础模型并使用Donnell壳理论来描述包含关系，采用了不同的方法。该框架专门用于在存在两个相等的界面裂纹以模拟夹杂物-基质脱胶的情况下球形基体的单轴拉伸载荷。采用变分法来求解壳体和地基的非线性边界值问题，并提出了基于Ritz方法的迭代求解程序。对于聚合物基质玻璃夹杂物体系，进行了参数研究，以研究脱胶程度，夹杂物体积分数和壳厚度对脱胶能和有效弹性模量的影响。利用有限元结果和环氧玻璃复合泡沫材料的杨氏模量的实验数据验证了该模型的有效性。

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