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Probabilistic homogenization of hyper-elastic particulate composites with random interface

机译：具有随机界面的超弹性颗粒复合材料的概率均质化

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A principal aim of this study is determination of deterministic and basic probabilistic characteristics of the effective material properties and stresses in hyper-elastic particulate composites with spherical reinforcement and uncertain volume fraction of the interface defects. This is done on the basis of laboratory tests of Laripur LPR 5020 High Density Polyurethane (HDPU) using the FEM homogenization method applied on the cubic multi-particle Representative Volume Element (RVE). This 3D homogenization scheme is based upon numerical determination of strain energy density in the RVE under uniaxial stretch. Each particle is spherical, linear elastic and embedded in the hyper-elastic matrix. The interphase is a thin layer around particle and contains all the particle-matrix interface defects; these defects are of the semi-spherical shape lying with the diameters on the interface. A constitutive relation of the matrix is experimentally recovered through the uniaxial stretch test and computationally approximated with three best fitting available hyper-elastic material potentials. The coincidence of these results serves for verification of the numerical results. Uncertainty of volume fraction of interface defects is assumed to be Gaussian, whose coefficient of variation does not excess 0.25. A relation of the effective stress to this uncertain parameter is recovered as some polynomial basis via the Least Squares Method (LSM) with two different approaches. The first one introduces a functional based directly on the potentials with parameters related to the strain level and to the volume fraction of interface defects, while the alternative approach is based upon a bivariate polynomial. This polynomial order is optimized via simultaneous maximization of correlation and minimization of LSM error and variance and its order is optimized for minimum LSM error. The RVE meshing is completed with the use of 20-noded brick or 10-noded tetrahedral elements. Probabilistic computations have been carried out with three independent approaches, namely the Stochastic Finite Element Method (SFEM), the crude Monte-Carlo simulation and probabilistic semi-analytical method. Probabilistic characteristics of the effective constitutive tensor include expected values, coefficients of variation, skewness and kurtosis of the effective stress. It is investigated numerically (1) if the resulting homogenized characteristics are also Gaussian, (2) how fluctuation of the interface defects volume fraction affects an effective stress in context of the deterministic and probabilistic analysis and (3) how these characteristics vary together with an increase of the applied strain.
机译：这项研究的主要目的是确定具有球形增强和界面缺陷的体积分数不确定的超弹性颗粒复合材料有效材料性能和应力的确定性和基本概率特征。这是在Laripur LPR 5020高密度聚氨酯（HDPU）的实验室测试的基础上完成的，使用的是应用于立方多颗粒代表体积元素（RVE）的FEM均质化方法。该3D均质化方案基于在单轴拉伸下RVE中应变能密度的数值确定。每个粒子均为球形，线性弹性并嵌入超弹性基体中。中间相是颗粒周围的薄层，包含所有颗粒-基体界面缺陷。这些缺陷为半球形，其直径位于界面上。基质的本构关系通过单轴拉伸试验通过实验恢复，并通过三种最佳拟合可用的超弹性材料势进行计算近似。这些结果的重合用于验证数值结果。界面缺陷的体积分数不确定度假定为高斯，其变异系数不超过0.25。通过最小二乘法（LSM）用两种不同的方法将有效应力与该不确定参数的关系作为多项式基础进行恢复。第一种方法直接基于具有与应变水平和界面缺陷的体积分数相关的参数的电势引入函数，而替代方法基于双变量多项式。通过相关性的同时最大化以及LSM误差和方差的最小化来优化该多项式阶，并且针对最小LSM误差来优化其阶数。 RVE网格划分是通过使用20节点的砖块或10节点的四面体单元完成的。概率计算已通过三种独立的方法进行，即随机有限元方法（SFEM），蒙特卡洛模拟和概率半分析方法。有效本构张量的概率特征包括期望值，有效应力的变异系数，偏度和峰度。在数值上进行了研究（1）如果所得的均质特性也为高斯分布;（2）在确定性和概率分析的背景下，界面缺陷体积分数的波动如何影响有效应力;（3）这些特性如何随应力的变化而变化。施加应变的增加。

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