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- W2787503313 abstract "This chapter focuses exclusively on the meshfree approach of Silling andAskari [33]. To date, the vast majority of peridynamic simulations have utilized thisapproach. The decision to focus on this particular computational strategy is not meantto imply that it is superior to alternative approaches. Applying the finite elementtechnique to peridynamics, for example, may provide superior results in some cases.Nonetheless, the meshfree approach of Silling and Askari has proven to be a reliable and efficient strategy for addressing problems in solid mechanics with pervasivematerial failure and fracture. Advantages include ease of implementation, computational efficiency, and the presence of a natural mechanism for material separation.The method of Silling and Askari is a direct discretization of the strong form of theperidynamic balance of linear momentum [34],ρ (x) u¨(x, t) =∫Hx(T [x, t]〈q−x〉−T [q, t]〈x−q〉)dVq+b(x, t) , (5.1)where ρ is the material density, u¨ is acceleration, t is time, x and q are material points,Hx is a spherical neighborhood of radius δ centered at x, T denotes a peridynamicforce state, dVq denotes the infinitesimal volume associated with q, and b is a bodyforce density. For problems in three-dimensional space, the approach of Silling andAskari requires evaluation of a three-dimensional integral. In contrast, solution ofthe weak form of the peridynamic balance of linear momentum, for example usinga finite element discretization, requires evaluation of a six-dimensional integral. Forthis reason, solution strategies for peridynamic models based on the weak form entailsignificant geometric complexity and computational expense relative to strong-formstrategies." @default.
- W2787503313 created "2018-02-23" @default.
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- W2787503313 date "2016-10-25" @default.
- W2787503313 modified "2023-09-23" @default.
- W2787503313 title "Roadmap for Software Implementation" @default.
- W2787503313 doi "https://doi.org/10.1201/9781315373331-5" @default.
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