We study existence and stability of homoclinic type solutions of a bistable integral equation. These are stationary solutions of an integrodifferential equation, which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity.

Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which ...

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

Recent experiments have shown that metallic materials display significant size effect at the micron and sub-micron scales. This has motivated the development of strain gradient plasticity theories, which usually involve extra boundary conditions and possibly higher-order governing equations. We propose a finite deformation theory of nonlocal plasticity based on the Taylor dislocation model. The...

The classic localization instability analysis for strain-softening materials is expanded to dynamic solutions. The nonlocal continuum with local strain, which ensures proper convergence of finite element calculations and physically realistic solutions, is adopted in its simplified form, the nonlocal damage model. The dynamic response of a one-dimensional bar initially in a uniform strain-soften...

A new simulation strategy to model hydrogen embrittlement based on a multi-field finite element using displacements, pressure, volume variation, nonlocal damage variables and lattice concentration as unknowns is proposed. The material described modified GTN model, which includes the description of enhanced decohesion (HEDE). problem solved fully implicit formulation. Numerical problems related ...

Simulations utilizing local constitutive equations for strain-softening materials are known to be pathologically mesh-dependent. The rational solution this problem is use nonlocal material models. In paper, we discuss the application of integral-based approach simulation non-local damage accumulation and fracture. Various combinations non-localities with common spatial symmetries analysed analy...