Publicado 6 números por año
ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352
Indexed in
ADAPTIVE REFINEMENT AND MULTISCALE MODELING IN 2D PERIDYNAMICS
SINOPSIS
The original peridynamics formulation uses a constant nonlocal region, the horizon, over the entire domain. We propose here adaptive refinement algorithms for the bond-based peridynamic model for solving statics problems in two dimensions that involve a variable horizon size. Adaptive refinement is an essential ingredient in concurrent multiscale modeling, and in peridynamics changing the horizon is directly related to multiscale modeling. We do not use any special conditions for the "coupling" of the large and small horizon regions, in contrast with other multiscale coupling methods like atomistic-to-continuum coupling, which require special conditions at the interface to eliminate ghost forces in equilibrium problems. We formulate, and implement in two dimensions, the peridynamic theory with a variable horizon size and we show convergence results (to the solutions of problems solved via the classical partial differential equations theories of solid mechanics in the limit of the horizon going to zero) for a number of test cases. Our refinement is triggered by the value of the nonlocal strain energy density. We apply the boundary conditions in a manner similar to the way these conditions are enforced in, for example, the finite-element method, only on the nodes on the boundary. This, in addition to the peridynamic material being effectively "softer" near the boundary (the so-called "skin effect") leads to strain energy concentration zones on the loaded boundaries. Because of this, refinement is also triggered around the loaded boundaries, in contrast to what happens in, for example, adaptive finite-element methods.
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Nguyen Cong Tien, Oterkus Selda, Oterkus Erkan, Amin Islam, Ozdemir Murat, El-Aassar Abdel-Hameed, Shawky Hosam, Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator, Ocean Engineering, 239, 2021. Crossref
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Sun Wei, Fish Jacob, Coupling of non‐ordinary state‐based peridynamics and finite element method for fracture propagation in saturated porous media, International Journal for Numerical and Analytical Methods in Geomechanics, 45, 9, 2021. Crossref
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Wang Longzhen, Bobaru Florin, Connections Between the Meshfree Peridynamics Discretization and Graph Laplacian for Transient Diffusion Problems, Journal of Peridynamics and Nonlocal Modeling, 3, 4, 2021. Crossref
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Galadima Yakubu Kasimu, Oterkus Erkan, Oterkus Selda, Model order reduction of linear peridynamic systems using static condensation, Mathematics and Mechanics of Solids, 26, 4, 2021. Crossref
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Mei Tie, Zhao Jiangming, Liu Zian, Peng Xuhao, Chen Ziguang, Bobaru Florin, The Role of Boundary Conditions on Convergence Properties of Peridynamic Model for Transient Heat Transfer, Journal of Scientific Computing, 87, 2, 2021. Crossref
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You Huaiqian, Lu Xin Yang, Trask Nathaniel, Yu Yue, An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems, ESAIM: Mathematical Modelling and Numerical Analysis, 55, 2021. Crossref
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