Refined Stress Analysis in Applied Elasticity Problems Accounting for Gradient Effects

Abstract

An extension of the approaches to gradient theories of deformable media is proposed. It consists in using the fundamental property of solutions of the elasticity gradient theory, i.e., smoothing singular solutions of the classical theory of elasticity, and converting them into a regular class for “macromechanical” problems instead of only for the problems of micromechanics, where the length scale parameter is of the order of the material’s characteristic size. In considered problems, the length scale parameter, as a rule, can be found from the macro-experiments or numerical experiments and is not extremely small. It is established by numerical three-dimensional modeling that even one-dimensional gradient solutions make it possible to clarify the stress distribution in the supproted and loaded areas. It is shown that additional length scale parameters of the gradient theory are related to specific boundary effects and can be associated with structural geometric parameters and loading conditions, which determine the features of the classical solution.