Chapter 1 - Introduction: Virtual experiments with iBEM

Abstract

The inclusion-based boundary element method (iBEM) is a powerful tool, which is developed to efficiently solve the boundary value problems (BVPs) for a finite domain with multiple particles for modeling of composite materials. It is particularly suitable for virtual experiments with computer to simulate physical experiments and predict the test results. The equivalent inclusion method (EIM) and boundary element method (BEM) provide the foundation of the iBEM. Unlike traditional BEM, which requires to mesh all the surfaces of particles, each particle is treated as a source with an eigenfield, such as eigenstrain for elasticity, eigenstrain rate for Stokes' flow, or others for different BVPs, and the response can be obtained by analytical volume integrals for rapid computation and exactness of the integral. Different from discrete element method (DEM), iBEM is based on continuum mechanism and provides detailed local fields for analysis and design of advanced materials. Since iBEM adopts analytical integrals over the inclusion, it does not need to mesh the matrix domain and is able to converge to the exact solution more rapidly than the finite element method (FEM). Moreover, because iBEM solves the field variables on the boundary, which can directly describe the effective material response, iBEM can be an ideal tool for virtual experiments of composite materials and structures.