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The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of the deformation. In order to resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. However, modeling the entire body at this level of resolution is computationally prohibitive. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost.

The Schwarz alternating method is a well-established technique for the solution of elliptic PDEs by means of domain decomposition. This concurrent multiscale method enables the flow of information between fine and coarse scales to achieve strong two-way coupling, which is critical in the accurate simulation of localization of plastic deformation leading to void or crack initiation in the incipient failure regime. The Schwarz method avoids the use of Lagrange multipliers or gradients that afflict other coupling methods, instead directly imposing the solution of each domain on the others in a way that guarantees convergence of the combined problem. This presentation will discuss the formulation of the Schwarz method and its implementation in the open-source Albany finite element platform developed at Sandia National Laboratories and demonstrate the use of the method as an effective approach for concurrent coupling in finite deformation solid mechanics.

In particular, the Schwarz method is applied in this study to analyze the behavior of tension specimens undergoing the localization of plastic deformation during the necking process. The gauge section of the specimen--where localization occurs--is resolved at a scale where the polycrystalline microstructure is discretized explicitly, and an anisotropic crystal elasto-viscoplasticity constitutive model is employed. The far field domain is coarsely discretized, and a simplified, isotropic elastoplastic constitutive relation is employed to capture the aggregate response of a polycrystalline region in a phenomenological manner. A suite of microstructural realizations are simulated to investigate the effects of microstructural variability on the necking process.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

multiscale modeling; localization