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Silling, S.A. (2000) Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces. Journal of the Mechanics and Physics of Solids, 83, 1526-1535.

has been cited by the following article:

  • TITLE: Peridynamic Solutions for Timoshenko Beams

    AUTHORS: E. Thomas Moyer, Michael J. Miraglia

    KEYWORDS: Peridynamics, Timoshenko Beam, Beam Bending, Dynamic Deformation

    JOURNAL NAME: Engineering, Vol.6 No.6, May 26, 2014

    ABSTRACT: Peridynamics is a recently developed formulation for continuum mechanics which describes material deformation using a nonlocal approach. Unlike Classical Continuum Mechanics (CCM) where the conservation equations are cast into partial differential equations, Peridynamics describes the deformation in terms of integro-differential equations. Additionally, peridynamics permits a natural length scale that is absent in CCM. This facilitates the modeling of complex material behavior and fracture which is not dependent on the numerical discretization length scale. In this paper, we develop a Peridynamic formulation for a Timoshenko beam. Full details and numerical examples are presented for both bending and axial behavior. While the development in this paper is limited to elastic, infinitesimal deformations, the approach can be extended to finite inelastic deformations.