Skip to Main content Skip to Navigation
Journal articles

A variational form of the equivalent inclusion method for numerical homogenization

Abstract : Due to its relatively low computational cost, the equivalent inclusion method is an attractive alternative to traditional full-field computations of heterogeneous materials formed of simple inhomogeneities (spherical, ellipsoidal) embedded in a homogeneous matrix. The method can be seen as the discretization of the Lippmann--Schwinger equation with piecewise polynomials. Contrary to the original approach of Moschovidis and Mura, who discretized the strong form of the Lippmann--Schwinger equation through Taylor expansions, we propose in the present paper a Galerkin discretization of the weak form of this equation. Combined with the new, mixed boundary conditions recently introduced by the authors, the resulting method is particularly well-suited to homogenization. It is shown that this new, variational approach has a number of benefits: (i) the resulting linear system is well-posed, (ii) the numerical solution converges to the exact solution as the maximum degree of the polynomials tends to infinity and (iii) the method can provide rigorous bounds on the apparent properties of the statistical volume element, provided that the matrix is stiffer (or softer) than all inhomogeneities. This paper presents the formulation and implementation of the new, variational form of the equivalent inclusion method. Its efficiency is investigated through numerical applications in 2D and 3D elasticity.
Complete list of metadatas

Cited literature [44 references]  Display  Hide  Download
Contributor : Sébastien Brisard <>
Submitted on : Monday, December 30, 2013 - 3:16:36 PM
Last modification on : Tuesday, December 8, 2020 - 10:21:04 AM
Long-term archiving on: : Sunday, March 30, 2014 - 10:15:10 PM


Files produced by the author(s)



Sébastien Brisard, Luc Dormieux, Karam Sab. A variational form of the equivalent inclusion method for numerical homogenization. International Journal of Solids and Structures, Elsevier, 2014, 51 (3-4), pp.716-728. ⟨10.1016/j.ijsolstr.2013.10.037⟩. ⟨hal-00922779⟩



Record views


Files downloads