We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is fourth-order singular perturbed elliptic system. The element similar to [C. Taylor and P. Hood, Comput. & Fluids, 1(1973), 73–100] in Stokes flow. Using uniform discrete B-B inequality pairs, we show optimal rate convergence limit. By new regularity result both materials pa...

Young's modulus determines the mechanical loads required to elastically stretch a material, and also, bend it, given that bending stretches one surface while compressing opposite one. Flexoelectric materials have additional property of becoming electrically polarized when bent. While numerous studies characterized this flexoelectric coupling, its impact on response, due energy cost polarization...

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...

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...