Agradecimentos: Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Yue Yu would like to acknowledge support from the National Science Foundation under awards DMS 1620434. Fabiano F. Bargos and Marco L. Bittencourt would like to acknowledge support from CNPq (grant 140501/2009-6), CAPES (grant PDEE - 5379/10-5). Huaiqian You was partially supported by the National Science Foundation under awards DMS 1620434. Michael L. Parks acknowledges support from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4). George E. Karniadakis would like to acknowledge support from NIH (grant U01HL116323 “Multi-scale, Multiphysics Model of Thrombus Biomechanics in Aortic Dissection”). This work also used resources of the “Centro Nacional de Processamento de Alto Desempenho em São Paulo (CENAPAD-SP). https://www.cenapad.unicamp.br/diversos/guia/guia.shtml” Ver menos

We develop and analyze a concurrent framework for coupling peridynamics and the corresponding classical elasticity theory, with applications to the numerical simulations of damage problems. In this framework, the peridynamic model and the elastic model are solved separately and coupled with a partitioned approach. In the region where material failure is expected to initiate, we employ the peridynamic theory. In the rest of the problem domain, the material is modeled by the classical elasticity theory. On the peridynamic–classical theory interface, there is a transition region where the two subdomains overlap. The two solvers communicate by exchanging proper boundary conditions at the peridynamic–classical theory interface, which enables a modular software implementation. We analyze different coupling strategies on a 1D simplified problem and obtain expressions for the optimal reduction factor (convergence rate index). The selection of optimal coupling parameters is verified with numerical experiments, where we demonstrate that the optimal Robin coefficient from 1D simplified problem analysis can be extrapolated to more complicated problems, including cases with damage. Both the analysis and the numerical results suggest that the optimal Robin boundary condition on the classical theory side combined with a Dirichlet boundary condition with Aitken relaxation rule on the peridynamic side would be the most robust choice. Comparing with the commonly employed Dirichlet interface conditions, the optimal Robin boundary condition together with Aitken relaxation accelerates the coupling convergence rate by 10 times. With the developed optimal coupling strategy, we also numerically demonstrate the coupling framework’s asymptotic convergence to the local solution and its capability to capture crack initiation and growth in 2D problems Ver menos