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Perturbation-based stochastic finite element analysis of the interface defects in composites via Response Function Method

机译：基于响应函数法的复合材料界面缺陷基于摄动的随机有限元分析

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摘要

The main aim of this paper is to present a mathematical model and its numerical realization for the composite material with stochastic interface defects employing the perturbation-based stochastic finite elements. The defects are modeled as the semicircular micro-cavities ("bubbles") lying with their diameters on the reinforcement-matrix interface inside the weaker material region (matrix). Both total number of the defects as well as their radii may be defined as the truncated Gaussian random variables with the given first two probabilistic moments. The composite micro-geometry is simulated according to these parameters and the entire structure is discretized in both scales using traditional Finite Element Method procedures. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value enable to determine the structural response and, thanks to the Least Squares Method, its final probabilistic moments. The proposed technique has been validated on the shear test for the carbon-epoxy composite with the few interface defects and Young modulus of the matrix being Gaussian random variable, where three meshes with various density show overall convergence of the numerical procedure.
机译：本文的主要目的是利用基于扰动的随机有限元，为具有随机界面缺陷的复合材料提供数学模型及其数值实现。将缺陷建模为半圆形微腔（“气泡”），其直径位于较弱材料区域（矩阵）内部的增强矩阵界面上。缺陷的总数及其半径都可以定义为具有给定的前两个概率矩的截断的高斯随机变量。根据这些参数对复合材料的微几何进行了模拟，并使用传统的有限元方法对整个结构进行了离散化。借助响应函数方法提供了其概率版本，在该函数中，数个随机参数值在其平均值附近变化的数值测试可以确定结构响应，并借助最小二乘法确定其最终概率矩。所提出的技术已在碳-环氧复合材料的剪切试验中得到验证，该复合材料的界面缺陷少，基体的杨氏模量为高斯随机变量，其中三个密度不同的网格显示出数值过程的整体收敛性。

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