Open Access

ARTICLE

A Chain Approach of Boundary Element Row-Subdomains for Simulating the Failure Processes in Heterogeneous Brittle Materials

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1 Department of Engineering Mechanics, Tsinghua University, Beijing, 100084 China

Computers, Materials & Continua 2009, 9(1), 1-24. https://doi.org/10.3970/cmc.2009.009.001

Abstract

To improve the effectiveness of the lattice model for simulating the failure processes of heterogeneous brittle materials, each lattice element is refined as a subdomain with homogenous material, and is modeled by the boundary element method in this paper. For simplicity, each subdomain is modeled with constant boundary elements. To enhance the efficiency, a row of sub-domains is formed, and then a chain structure of such row-subdomain is constructed. The row-equation systems are solved one by one, and then back substituted, to obtain the final solution. Such a chain subdomain approach of the boundary element method not only reduces the operations, but also the memory requirements. By ``failure'' of the heterogeneous brittle material is meant to be the debonding of the interface of subdomains, and each homogeneous subdomain remains to be linear elastic. For the simulation of the failure process, a quasi-static approach is adopted. The criterion of interface strength is used to determine the element wherein the interface debonding will occur, and then the interface continuity condition is replaced by the interface debonding condition for the next computation. The simulation of the failure process is controlled by the sequential debonding of the boundary elements. Some results are given to show the applicability of the presented BEM scheme, and the complexity of the failure process of heterogeneous material.

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