Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a nonlocal Dirichlet integral that is given by a quadratic energy functional based on nonlocal gradients. Our main finding, which differs from claims made in previo...

Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gr...

This article focuses on studying the nonlinear vibration of functionally graded (FG) curved nanobeams resting Pasternak-Winkler elastic foundation based nonlocal strain gradient theory along with first-order shear deformation beam (FSDBT) considering von-Kármán hypothesis. The Hamilton principle is applied to extract three motion equations and Galerkin method (GM) utilized spatially reduce diff...

Abstract.The paper focuses on the modelling of the quasi-brittle failure of materials with a heterogeneous microstructure. Failure induced anisotropy is incorporated in terms of the microplane theory. This theory is based on scalar damage laws formulated on several individual material planes. Anisotropy of the overall constitutive law is introduced in a natural fashion by transforming the scala...

ABSTRACT. This paper provides an elementary introduction into modeling of localized inelastic processes such as cracking or formation of shear bands. The basic concepts are explained using a simple one-dimensional example. It is shown that a stress-strain law with softening used in a standard continuum description leads to physically meaningless results and that the numerical solution suffers b...

We prove that the isotropic Landau equation equipped with Coulomb potential introduced by Krieger-Strain and Gualdani-Guillen can be identified gradient flow of entropy in probability space respect to a Riemannian metric tensor nonlocal mobility. give characterizations corresponding geodesics equations present convergence rate result estimating its Hessian operator.

This study presents a mathematical size-dependent model capable of investigating the dynamic behavior sandwich perforated nanobeam incorporating flexoelectricity effect. The nonlocal strain gradient elasticity theory is developed for both continuum mechanics and flexoelectricity. Closed forms equivalent geometrical variables are developed. Hamiltonian principle exploited to derive governing equ...