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International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2014011338
pages 91-113

CONCURRENT COUPLING OF BOND-BASED PERIDYNAMICS AND THE NAVIER EQUATION OF CLASSICAL ELASTICITY BY BLENDING

Pablo Seleson
Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th St. Stop C0200, Austin, TX 78712-1229, USA
Youn Doh Ha
Department of Naval Architecture, Kunsan National University, 558 Daehak-ro (San 68, Miryong-dong) Gunsan, Jeonbuk, 573-701, Korea
Samir Beneddine
Fundamental and Experimental Aerodynamics Department, ONERA Meudon, 8 rue des Vertugadins, 92190 Meudon, France

RESUMO

The peridynamics theory of solid mechanics has been proposed as a suitable framework for material failure and damage simulation. As a nonlocal model, based upon integro-differential equations, peridynamics is computationally expensive. Concurrent multiscale methods are thus of interest for efficient and accurate solutions of peridynamic problems. The goal is to restrict the use of peridynamic models to regions where discontinuities are present or may be generated, while employing classical local models in domains characterized by smooth displacement fields. In this article, we derive a blending scheme to concurrently couple bond-based peridynamic models and the Navier equation of classical elasticity. We extend the work for one-dimensional linear peridynamic models presented by Seleson et al. (2013a), to general bond-based peridynamic models in higher dimensions, and we provide an error estimate for the coupling scheme. We show analytically and numerically that the blended model does not exhibit ghost forces and is also patch-test consistent. Numerical results demonstrate the accuracy and efficiency of the blended model proposed, suggesting an alternative framework for cases where peridynamic models are too expensive, whereas classical local models are not accurate enough.