Cell-centered finite-volume method for elastic deformation of heterogeneous media with full-tensor properties

We propose a cell-centered finite-volume method for the heterogeneous anisotropic linear elasticity problem. The internal traction vector is represented as a discrete flux on the interface. This 'elastic' flux is decomposed into a discrete two-point flux approximation and a semi-discrete transversal part. We introduce an interpolation method in the presence of discontinuity in the full-tensor material properties. The scheme yields an accurate reconstruction of the gradient of the displacement in each cell. The formulation is based on the assumption of linearity of the displacement, and we enforce continuity of the internal traction vector and the displacement at the interface. The treatment of the boundary conditions can be complicated in finite-volume methods. Here, we describe a general treatment of boundary conditions that does not entail the introduction of additional degrees of freedom. The finite-volume method is tested for a series of challenging elasticity problems. (C) 2019 Elsevier B.V. All rights reserved.