Buckling analysis of elastic–plastic nanoplates resting on a Winkler–Pasternak foundation based on nonlocal third-order plate theory

The paper analyzes the elastic–plastic buckling behavior of thick, rectangular nanoplates embedded in a Winkler–Pasternak foundation, adopting the Reddy third-order plate theory in nonlocal elasticity. Elasto-plasticity is accounted for by considering two alternative plasticity theories, namely the J2 flow incremental and the J2 deformation theory, with material properties defined by a Ramberg–Osgood relation. An iterative procedure is proposed to obtain the critical load, and the corresponding critical mode, of plates simply supported on two opposite edges under applied uniaxial and biaxial loading conditions. Extensive analysis investigates the effects of geometrical, constitutive, and nonlocal parameters on the critical behavior of plates with different boundary conditions. To the best of the authors’ knowledge, there are no findings about elastoplastic buckling of nanoplates in the existing literature. It is therefore hoped that the results obtained may provide a helpful basis for comparison for future investigations.