Energy Fluctuations in the Homogenized Hyper-Elastic Particulate Composites with Stochastic Interface Defects

Damian Sokołowski,Marcin Kamiński,Artur Wirowski

doi:10.3390/en13082011

Abstract

The principle aim of this study is to analyze deformation energy of hyper-elastic particulate composites, which is the basis for their further probabilistic homogenization. These composites have some uncertain interface defects, which are modelled as small semi-spheres with random radius and with bases positioned on the particle-matrix interface. These defects are smeared into thin layer of the interphase surrounding the reinforcing particle introduced as the third component of this composite. Matrix properties are determined from the experimental tests of Laripur LPR 5020 High Density Polyurethane (HDPU). It is strengthened with the Carbon Black particles of spherical shape. The Arruda–Boyce potential has been selected for numerical experiments as fitting the best stress-strain curves for the matrix behavior. A homogenization procedure is numerically implemented using the cubic Representative Volume Element (RVE). Spherical particle is located centrally, and computations of deformation energy probabilistic characteristics are carried out using the Iterative Stochastic Finite Element Method (ISFEM). This ISFEM is implemented in the algebra system MAPLE 2019 as dual approach based upon the stochastic perturbation method and, independently, upon a classical Monte-Carlo simulation, and uniform uniaxial deformations of this RVE are determined in the system ABAQUS and its 20-noded solid hexahedral finite elements. Computational experiments include initial deterministic numerical error analysis and the basic probabilistic characteristics, i.e., expectations, deviations, skewness and kurtosis of the deformation energy. They are performed for various expected values of the defects volume fraction. We analyze numerically (1) if randomness of homogenized deformation energy can correspond to the normal distribution, (2) how variability of the interface defects volume fraction affects the deterministic and stochastic characteristics of composite deformation energy and (3) whether the stochastic perturbation method is efficient in deformation energy computations (and in FEM analysis) of hyper-elastic media.

Highlights

Interface defects are the very important engineering problem in composite materials
We analyze numerically (1) if randomness of homogenized deformation energy can correspond to the normal distribution, (2) how variability of the interface defects volume fraction affects the deterministic and stochastic characteristics of composite deformation energy and (3) whether the stochastic perturbation method is efficient in deformation energy computations of hyper-elastic media
Interface defects can be represented as imperfect interfaces, which commonly serve for a realistic prediction

Summary

Introduction

Interface defects are the very important engineering problem in composite materials. This is because they are the result of many manufacturing processes, they remarkably affect their mechanical (and coupled) response and occupy relatively small total volume fraction of the entire composite.They affect failure [1,2], reliability [3], durability [4] and thermal conductivity [5] of the composite and can be included in numerical analysis as geometrical imperfections [6]. Interface defects are the very important engineering problem in composite materials This is because they are the result of many manufacturing processes, they remarkably affect their mechanical (and coupled) response and occupy relatively small total volume fraction of the entire composite. Other numerical approaches to the interface defects include introduction of a system of springs [14] or addition of specific contact finite elements [15] As it has been documented, this interphase is the weakest link in composite structures and significantly affects effective (homogenized) material properties of multiple composites irrespective to their degree of anisotropy and outside of the deterministic context. An influence of the interphase could be either negative, in the case when the bond between the main constituents is weak or defective [18], or positive in the presence of chemical bonds between the principal phases [19,20], for example in bound rubber

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