Efficient Solution of 3D Solids with Large Numbers of Fluid-Filled Pores Using Eigenstrain BIEs with Iteration Procedure

Abstract

To deal with the problems encountered in the large scale numerical simulation of three dimensional (3D) elastic solids with fluid-filled pores, a novel computational model with the corresponding iterative solution procedure is developed, by introducing Eshelby’s idea of eigenstrain and equivalent inclusion into the boundary integral equations (BIE). Moreover, by partitioning all the fluid-filled pores in the computing domain into the near- and the far-field groups according to the distances to the current pore and constructing the local Eshelby matrix over the near-field group, the convergence of iterative procedure is guaranteed so that the problem can be solved effectively and efficiently in the numerical simulation of solids with large numbers of fluid-filled pores. The feasibility and correctness of the proposed computational model are verified in the numerical examples in comparison with the results of the analytical solution in the case of a single spherical fluid-filled pore under uniform pressure in full space and with the results of the subdomain BIE in a number of other cases. The overall mechanical properties of solids are simulated using a representative volume element (RVE) with a single or multiple fluid-filled pores, up to one thousand in number, with the proposed computational model, showing the feasibility and high efficiency of the model. The effect of random distribution of fluid-filled on overall properties is also discussed. Through some examples, it is observed that the effective elastic properties of solids with a large number of fluid-filled pores in random distributions could be studied to some extent by those of solids with regular distributions.