Eigenstrain formulation of boundary integral equations for modeling 2D solids with fluid-filled pores

Abstract

By introducing Eshelby's idea of eigenstrain and equivalent inclusion into the boundary integral equations (BIE), the computational model of eigenstrain boundary integral equations and the corresponding iterative solution procedures are presented in the paper for the numerical simulation of solids with fluid-filled pores in great numbers. As there are effects of interactions among fluid-filled pores in proportion to distances, all the fluid-filled pores are divided, according to the distances to the current pore, into the near-field group around the current pore and the far-field group for others with relatively large distances but relatively small influences to the current pore in the solution procedures. In order to guarantee the convergence of iteration sufficiently, the local Eshelby matrix has been proposed and constructed from the BIE combined with Eshelby's idea, which can be considered as an extension of Eshelby tensor in numerical form defined on the near-field group of fluid-filled pores in full space.In the numerical examples, the feasibility and correctness of the proposed computational model are verified in comparison with the results of the analytical solution in the case of a single circular fluid-filled pore in full space and of the subdomain BIE in other cases. The overall mechanical properties of solids are computed using a representative volume element (RVE) with more than one thousand fluid-filled pores distributed either regularly or randomly with the proposed computational model, showing the feasibility and high efficiency of the present model and the solution procedures.