Convergence of Peridynamics to Classical Elasticity Theory

摘要: The peridynamic model of solid mechanics is a nonlocal theory containing length scale. It based on direct interactions between points in continuum separated from each other by finite distance. maximum interaction distance provides scale for the material model. This paper addresses question whether an elastic reproduces classical local as this goes to zero. We show that if motion, constitutive model, and any nonhomogeneities are sufficiently smooth, then stress tensor converges limit Piola-Kirchhoff function only deformation gradient tensor, theory. limiting field differentiable, its divergence represents force density due internal forces. limiting, or collapsed, stress-strain satisfies conditions angular momentum balance, isotropy, objectivity, hyperelasticity, provided original appropriate conditions.