The Lippmann-Schwinger equation in elasticity for porous media

The numerical computation of effective elastic properties of heterogeneous materials using the Lippmann-Schwinger equation in elasticity becomes problematic in the presence of pores. Under mild conditions on the interface of the pore the Lippmann-Schwinger equation is well-posed, but ill-conditioned. Introducing a fictitious soft material renders the problem well-conditioned again. We will discuss the exact rate of convergence of these regularized problems to the porous problem.