In elasticity, microstructure-related deviations may be modeled by strain gradient elasticity. For so-called metamaterials, different implementations are possible for solving elasticity problems numerically. Analytical solutions of simple used to verify the numerical approach. We demonstrate such a case in two-dimensional continuum as benchmark computations. As enforces higher regularity condit...

Analytical method for the second-order homogenization of two-phase composites within Mindlin–Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce problem determination averaged Cauchy stresses, double stresses static moments inside inclusions under prescribed quadratic boundary conditions. The ellipsoidal shape orthotropic pr...

Higher order gradient elasticity theories are widely applied to determine the wave propagation characteristics of micro-sized structures. The novelty this paper, firstly, is using Second Strain Gradient (SSG) theory explore mechanism a 2D beam grid. strong formulas continuum model including governing equations and boundary conditions derived by Hamilton principle. Then, valuable long-range Latt...

Abstract In this paper, the reduced strain gradient elasticity model with two characteristic lengths is proposed and presented. The a particular case of Mindlin’s first theory number material parameters generalization simplified to include different length scale parameters. have physical meaning longitudinal transverse scales. used study screw edge dislocations derive analytical solutions dislo...

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numeri...

A mechanism-based theory of strain gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly...

A study of existence and uniqueness weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the strain energy as a quadratic function tensor deformation gradients up Nth order. virtual work principle, extended for higher-order gradient media, serves basis defining solution. In order characterize smo...