To explain the size effect found in the testing of plastic behavior of metals on the micrometer scale, four theories of strain-gradient plasticity, representing generalizations of the deformation theory of plasticity, have been developed since 1993––the pioneering original theory of Fleck and Hutchinson in two subsequent versions, the mechanism-based strain-gradient (MSG) plasticity of Gao and ...

A meshless numerical implementation is reported of the 2-D Fleck-Hutchinson phenomenological strain-gradient theory, which fits within the framework of the Toupin-Mindlin theories and deals with firstorder strain gradients and the associated work-conjugate higher-order stresses. From a mathematical point of view, the two-dimensional Toupin-Mindlin strain gradient theory is a generalization of t...

We present an atomic scale theory of lattice distortions using strain-related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at several length scales. We apply the approach to a two-dimensional square lattice with a monatomic basis and find the elastic deformations and hierarchical atomi...

In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless...

To improve the structural stiffness, strength and reduce weight of nanoplate structure, functionally graded (FG) graphene-reinforced nanocomposite (GRNC) laminated plates are exploited in this paper. The bending buckling behaviors FG-GRNC nanoplates investigated by using novel quasi-3D hyperbolic higher order shear deformation plate theory conjunction with modified continuum nonlocal strain gra...

A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and the solution agrees with the classical solution for the edge dislocation in the far field. The components of the stress, strain, distortion and displacement...