On Gradient Elasticity and Discrete Peridynamics with Applications to Beams and Plates
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In this paper two different nonlinear elasticity theories that account for (a) geometric nonlinearity and (b) microstructure-dependent size effects are revisited to establish the connection between the two theories. The first theory is based on modified couple stress theory of Yang et al.  and the second one is based on Srinivasa-Reddy gradient elasticity theory . The modified couple stress theory includes a material length scale parameter that can capture the size effect in a material. The gradient elasticity theory was developed for finitely deforming hyperelastic cosserat continuum, and it is a generalization of small deformation couple stress theories. The Srinivasa-Reddy theory contains, as a special case, the first one. These two theories are used to derive the governing equations of beams and plates. In addition, a discrete peridynamics idea as an alternative to the conventional peridynamics is also presented. © (2013) Trans Tech Publications, Switzerland.
author list (cited authors)
Reddy, J. N., Srinivasa, A., Arbind, A., & Khodabakhshi, P.