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.

中文翻译：

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考虑梯度效应的应用弹性问题中的细化应力分析

摘要

提出了可变形介质梯度理论方法的扩展。它包括利用弹性梯度理论的解的基本性质，即平滑经典弹性理论的奇异解，并将它们转换为“宏观力学”问题的常规类，而不仅仅是针对微力学问题。长度比例参数约为材料特征尺寸的大小。在考虑的问题中，通常可以从宏观实验或数值实验中找到长度比例参数，并且该参数不是非常小。通过数字三维建模可以确定，即使是一维梯度解也可以弄清受约束区域和受力区域的应力分布。