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 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...

In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...

In this paper, a nonlocal foundation model is proposed to analyze the vibration and instability of a Y-shaped single-walled carbon nanotube (Y-SWCNT) conveying fluid. In order to achieve more accurate results, fourth order beam theory is utilized to obtain strain-displacement relations. For the first time, a nonlocal model is presented based on nonlocal elasticity and the effects of nonlocal fo...

Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium el...

The theory of anisotropic generalized plane strain line forces and dislocation lines is embedded in three-dimensional elasticity point densities. Embedding real space achieved by slicing reciprocal using the projection-slice theorem.

Conjugated polymers are promising actuation materials for biomimetic robots and biomedical devices. Large bending is involved in some of these applications. This poses significant challenges in electromechanical modeling, because the linear elasticity theory is only valid when the strain is small. In this paper an effective strategy based on the nonlinear elasticity theory is proposed to model ...

In this paper, a new approach is proposed for stress state - dependent flow localization in bifurcation failure model bounded through ductile damage in dynamically loaded sheets. Onset of localized necking is considered in phenomenological way for different strain rates to draw the forming limit diagram (FLD). Using a strain metal hardening exponent in the Vertex theory related to the strain ra...

We test the elasticity of granular aggregates using increments of shear and volume strain in a numerical simulation. We find that the increment in volume strain is almost reversible, but the increment in shear strain is not. The strength of this irreversibility increases as the average number of contacts per particle (the coordination number) decreases. For increments of volume strain, an elast...