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Bond-Based Peridynamics

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Local and Nonlocal Micromechanics of Heterogeneous Materials

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Abstract

In this chapter, we consider a nonlocal peridynamic theory proposed by Silling (J Mech Phys Solids 48:175–209, 2000) where the equilibrium of a material point is achieved by a summation of internal forces produced by surrounding points over finite distance (called a horizon). A simplified version being derived from this approach is the so-called bond-based approach, in which interactions only occur between pairs of material points within a horizon. One defines linear admissibility condition and angular admissibility condition, isotropy property. Definitions of the microelastic material, pairwise potential function, and peridynamic stress are presented. Volumetric boundary conditions are defined, and the linearized microelastic model is considered. Damage is introduced by permitting damaged bonds to break irreversibly by bond removing if the bond stretch exceeds a critical stretch.

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Authors and Affiliations

  1. Micromechanics and Composites LLC, Cincinnati, OH, USA

    Valeriy A. Buryachenko

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  1. Valeriy A. Buryachenko
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Buryachenko, V.A. (2022). Bond-Based Peridynamics. In: Local and Nonlocal Micromechanics of Heterogeneous Materials. Springer, Cham. https://doi.org/10.1007/978-3-030-81784-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-81784-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81783-1

  • Online ISBN: 978-3-030-81784-8

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