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• W2000897527 abstract "The peridynamic model of solid mechanics is a nonlocal theory containing a length scale. It is based on direct interactions between points in a continuum separated from each other by a finite distance. The maximum interaction distance provides a length scale for the material model. This paper addresses the question of whether the peridynamic model for an elastic material reproduces the classical local model as this length scale goes to zero. We show that if the motion, constitutive model, and any nonhomogeneities are sufficiently smooth, then the peridynamic stress tensor converges in this limit to a Piola-Kirchhoff stress tensor that is a function only of the local deformation gradient tensor, as in the classical theory. This limiting Piola-Kirchhoff stress tensor field is differentiable, and its divergence represents the force density due to internal forces. The limiting, or collapsed, stress-strain model satisfies the conditions in the classical theory for angular momentum balance, isotropy, objectivity, and hyperelasticity, provided the original peridynamic constitutive model satisfies the appropriate conditions." @default.
• W2000897527 created "2016-06-24" @default.
• W2000897527 creator A5057121475 @default.
• W2000897527 creator A5063747280 @default.
• W2000897527 date "2008-04-25" @default.
• W2000897527 modified "2023-10-11" @default.
• W2000897527 title "Convergence of Peridynamics to Classical Elasticity Theory" @default.
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• W2000897527 doi "https://doi.org/10.1007/s10659-008-9163-3" @default.
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