We study the steady-state and transient responses of a second-order elastic plate by implementing an asymptotic analysis three-dimensional equations with respect to two geometric characteristics seen as parameters: thickness inner material length. Depending on their ratio, four different models arise. Conditions under which Reissner–Mindlin kinematics may appear are discussed while influence cr...

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 can describe elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures aroun...

This article investigates the theoretical and numerical analysis as well applications of three-dimensional theory first strain gradient elasticity. The corresponding continuous discrete variational formulations are established with error estimates stemming from continuity coercivity within a Sobolev space framework. An implementation isogeometric Ritz–Galerkin method is provided open-source sof...

-Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocations. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological...

B Pingbing Ming [email protected] Hongliang Li [email protected] Zhong-ci Shi [email protected] 1 Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China 2 The State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Beijing 100190, China...

Abstract In this paper, we analyze some properties of a sixth-order elliptic operator arising in the framework strain gradient linear elasticity theory for nanoplates flexural deformation. We first rigorously deduce weak formulation underlying Neumann problem as well its posedness. Under suitable smoothness assumptions on coefficients and geometry, derive interior boundary regularity estimates ...

In this article, the influence of hydrostatic stress and gravity on a clamped- free non homogeneous magneto electro elastic plate of polygonal cross sections is studied using linear theory of elasticity. The equations of motion based on two-dimensional theory of elasticity are applied under the plane strain assumption of prestressed and gravitated magneto electro elastic plate of polygonal cros...