MULTISCALE MODEL WITH EMBEDDED DISCONTINUITY DISCRETE APPROXIMATION CAPABLE OF REPRESENTING FULL SET OF 3D FAILURE MODES FOR HETEROGENEOUS MATERIALS WITH NO SCALE SEPARATION

Abstract

In this paper we present a 3D strongly coupled multiscale computational procedure for failure analysis of heterogeneous materials capable of representing a full set of different failure modes under various stress states. The proposed approach targets structural failure modeling by a multiscale method with no need for scale separation where a homogenized structural response is described at the macroscale, while microscale is utilized for representing a full set of 3D damage mechanisms inside the domain. The main novelty in terms of finite element method (FEM) implementation concerns macroscale elements that provide the adequate discrete approximation with embedded discontinuity for capturing localized failure with softening. Computation of element tangent stiffness matrices and residual vectors is performed by assembly of microscale elements whose contributions are statically condensed at the coarse level. A refined mesh built with corresponding microscale element discretization entirely fits in each macroscale element which acts as a container for microscale computational results. The compatibility between both scales is enforced by imposing constraint on the displacement field over the macroelement boundary producing a displacement based coupling in the spirit of localized Lagrange multipliers. Dealing with localized failure mechanisms is enabled through enlargement of such scale coupling through implementation of embedded strong discontinuity in macroscale elements. The computation is performed by using the operator split iterative solution procedure treating sequentially micro- and macroscales. Through several numerical simulations, it is demonstrated that the proposed methodology can reproduce a full set of 3D failure modes with very satisfying performance in dealing with localized failure problems.