Similar Subdomain Boundary Element Method And Its Application In Simulation Of Particle Composite Material

Along with the development of modern industry and technology, various composite materials are increasingly applied in engineering projects. Therefore, the investigation of the macroscopically effective mechanical properties of the composite materials attracts much attention of both researchers and engineers. Generally, the composite materials can be regarded as a matrix material with plenty of separated inclusions. Their macroscopically effective mechanical properties strongly depend on the sizes, shapes, properties, volume fraction and spatial distribution of the inclusion phases. Consequently the solids with randomly distributed inclusions of various shapes, sizes and materials can be regarded as the mechanical model of such composite materials.For the investigation of the heterogeneity due to different inclusion phases, multi-region BEM can be regarded as a feasible numerical method, which is more accurate than FEM and other numerical methods. As for the solids with n randomly distributed inclusion phases, if the conventional multi-region BEM is adopted, the equation system for n + \ subdomains should be formulated. If such equation system is solved directly, the computational complexity will increase significantly as the number of inclusions increases.In order to overcome the above-mentioned difficulty, similar subdomain BEM scheme is presented in this paper, based on the similarity of the integral area of inclusion phases. The solid with randomly distributed various inclusions can be reduced to a multiply connected domain of the matrix with inner boundary conditions. In this way, the computational efficiency is enhanced significantly. A lot of numerical examples indicate that the presented similar subdomain BEM has a higher computational accuracy and computational efficiency than FEM, so it is more suitable for the numerical simulation of the macroscopically effective mechanical properties of composite materials.Using the similar subdomain BEM, various 2D problems have been computed in this paper, including: the plane stress problem with randomly distributed circularinclusions (granular reinforced composite material), the plane strain problem with randomly distributed elliptical inclusions (long fibrous reinforced composite material), and thin plate with randomly distributed various inclusions. These computational schemes provide reliable numerical simulation methods for the investigation of the macroscopically effective properties of the corresponding composite materials.As numerical examples, plenty of numerical computation for the plates with 100 randomly distributed circular inclusions is carried out by the similar subdomain BEM, and the numerical solution of the macroscopically effective mechanical properties have been obtained. Based on the above numerical solution, the classical approximate solutions of the effective medium approximation have been analyzed in detail and some important referential conclusions have been obtained.The similar subdomain BEM presented in this paper can also be successfully applied to the numerical simulation of the composite materials with different interphase layer. On the other hand, similar subdoamin BEM can be generalized to the numerical simulation of 3D solids with randomly distributed inclusions combining with the fast multipole BEM scheme. In a word, similar subdomain BEM scheme has an extensive applied prospect.