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International Journal for Multiscale Computational Engineering

Publication de 6  numéros par an

ISSN Imprimer: 1543-1649

ISSN En ligne: 1940-4352

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ADAPTIVE REFINEMENT AND MULTISCALE MODELING IN 2D PERIDYNAMICS

Volume 9, Numéro 6, 2011, pp. 635-660
DOI: 10.1615/IntJMultCompEng.2011002793
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RÉSUMÉ

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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  79. Chen Jingkai, Jiao Yiyu, Jiang Wenchun, Zhang Yanting, Peridynamics boundary condition treatments via the pseudo-layer enrichment method and variable horizon approach, Mathematics and Mechanics of Solids, 26, 5, 2021. Crossref

  80. Isiet Mewael, Mišković Ilija, Mišković Sanja, Review of peridynamic modelling of material failure and damage due to impact, International Journal of Impact Engineering, 147, 2021. Crossref

  81. Nikpayam Jaber, Kouchakzadeh Mohammad Ali, On the validity of peridynamic equation of motion in variable horizon domains, International Journal of Mechanical Sciences, 195, 2021. Crossref

  82. Wu Pan, Zhao Jiangming, Chen Ziguang, Bobaru Florin, Validation of a stochastically homogenized peridynamic model for quasi-static fracture in concrete, Engineering Fracture Mechanics, 237, 2020. Crossref

  83. Prudhomme Serge, Diehl Patrick, On the treatment of boundary conditions for bond-based peridynamic models, Computer Methods in Applied Mechanics and Engineering, 372, 2020. Crossref

  84. Wu Liwei, Huang Dan, Bobaru Florin, A reformulated rate-dependent visco-elastic model for dynamic deformation and fracture of PMMA with peridynamics, International Journal of Impact Engineering, 149, 2021. Crossref

  85. Guo Li, Zhang Xiaoyu, Li Wanjin, Zhou Xin, Multi-scale peridynamic formulations for chloride diffusion in concrete, Engineering Analysis with Boundary Elements, 120, 2020. Crossref

  86. Jin Dingyi, Liu Wenyang, A peridynamic modeling approach of solid state impact bonding and simulation of interface morphologies, Applied Mathematical Modelling, 92, 2021. Crossref

  87. Fallah Arash S., Giannakeas Ilias N., Mella Rizgar, Wenman Mark R., Safa Yasser, Bahai Hamid, On the Computational Derivation of Bond-Based Peridynamic Stress Tensor, Journal of Peridynamics and Nonlocal Modeling, 2, 4, 2020. Crossref

  88. Niazi Sina, Chen Ziguang, Bobaru Florin, Crack nucleation in brittle and quasi-brittle materials: A peridynamic analysis, Theoretical and Applied Fracture Mechanics, 112, 2021. Crossref

  89. Buryachenko Valeriy A., Peridynamic Micromechanics of Random Structure Composites, in Local and Nonlocal Micromechanics of Heterogeneous Materials, 2022. Crossref

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  91. 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

  92. 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

  93. 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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