Abstract In this paper, we consider the time decay of solutions to some problems arising in strain gradient thermoelasticity. We restrict two-dimensional case, and assume that two dissipative mechanisms are introduced, temperature mass dissipation. First, show problem is well-posed proving operator defining it generates a contractive semigroup linear operators. Then, assuming function involving...

Within the framework of strain gradient elasticity under finite deformations we formulate strong ellipticity conditions equilibrium equations. model a energy density is function first and second deformation gradients. Ellipticity involves certain constraints on tangent elastic moduli. It also closely related to infinitesimal stability which defined as positive definiteness variation potential f...

In this paper we obtain the constitutive equation for the second Piola-Kirchhoff stress tensor according to the linearized finite theory of elasticity for hyperelastic constrained materials. We show that in such a theory the three stress tensors (Cauchy stress tensor, first and second Piola-Kirchhoff stress tensor) differ by terms that are first order in the strain, while in classical linear th...

The general relativistic theory of elasticity is reviewed from a Lagrangian, as opposed to Eulerian, perspective. equations motion and stress-energy-momentum tensor for hyperelastic body are derived the gauge-invariant action principle first considered by DeWitt. This natural extension single particle. central object in Lagrangian treatment Landau-Lifshitz radar metric, which version right Cauc...

Several beam and plate models have been recently developed in the literature to accommodate for size-dependence. These are usually obtained starting from a generalized continuum theory (such as couple-stress, strain-gradient or non-local their modifications) then deducing governing equations through Hamilton’s principle ingenuous kinematical assumptions. This approach, originated by Kirchhoff, ...

A size-dependent strain gradient Mori-Tanaka model (SGMT) is developed by applying strain gradient elasticity to the classical Mori-Tanka (M-T) method. The SGMT model is shown to be able to accurately predict the experimentally observed increase in stiffness of a layerby-layer (LBL)-assembled polyurethane-montmorillonite (PU-MTM) nanocomposite with various volume fractions. 3D Finite Element (F...

In this paper, we investigate the behavior of strain gradient elasticity solutions around sharp edges body loaded by concentrated loads. We consider general Mindlin–Toupin (SGET) and several simplified models, including dilatation theory (DGET) couple stress (CST). framework a plane problem for an elastic wedge with prescribed tip displacement obtain analytical assessments field state apex. Inv...