We present a brief survey of nonclassical linear theories continuum mechanics. Thus, we give concise characterization the Eringen–Edelen nonlocal theory elasticity, polar and micropolar media, Toupin couple-stress Eringen–Suhubi–Mindlin micromorphic theory, Mindlin gradient also local deformation elastic media that takes into account mass displacements.

Abstract In this manuscript two BMO estimates are obtained, one for Linear Elasticity and Nonlinear Elasticity. It is first shown that the BMO-seminorm of gradient a vector-valued mapping bounded above by constant times symmetric part its gradient, is, Korn inequality in BMO. The uniqueness equilibrium finite deformation whose principal stresses everywhere nonnegative then considered. when seco...

A nonlocal theory for thermoelastic materials with voids based on Mindlin’s strain gradient was derived in this paper some qualitative properties. We have also established the size effect of heat conduction aids extended irreversible thermodynamics and generalized free energy. The obtained system equations is a coupling three higher gradients terms due to length scale parameters ϖ l . This pose...

In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with regard to nonlocal relationship of stress, shear theory of the first order, and obtained linear strains using developed Kantorovich...