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The Lippmann-Schwinger equation in elasticity for porous media

: Schneider, Matti; Kabel, Matthias

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Schröder, J.:
Second Seminar on The Mechanics of Multifunctional Materials 2014. Proceedings : Bad Honnef, May 5 - 9, 2014
Duisburg: Universität Duisburg-Essen, 2014
ISBN: 978-3-9809679-8-3
ISBN: 3-9809679-8-0
Seminar on The Mechanics of Multifunctional Materials <2, 2014, Bad Honnef>
Conference Paper, Electronic Publication
Fraunhofer ITWM ()

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.