Abstract

A generalized Eshelby problem of arbitrary order in the gradient elasticity for a multilayer inclusions of spherical shape with a polynomial strain field at infinity is considered. For this problem we propose a constructive method of solution in a closed finite form, using generalized Papkovich–Neuber representation and the system of canonical potentials based on harmonic polynomials. We use also the Gauss theorem on the decomposition of an arbitrary homogeneous polynomials. The solutions of the generalized Eshelby problem are applied in the method of asymptotic homogenization of the gradient elasticity to accurately calculation of the effective characteristics of composite materials with scale effects.

中文翻译：

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弹性梯度理论中的广义Eshelby问题

摘要

考虑具有多项式应变场为无穷大的球形多层夹杂物的梯度弹性的任意阶数的广义Eshelby问题。对于这个问题，我们提出了一种封闭的有限形式的构造方法，该方法使用广义Papkovich-Neuber表示和基于谐波多项式的规范势系统。我们还对任意齐次多项式的分解使用高斯定理。将广义Eshelby问题的解应用于梯度弹性的渐近均匀化方法中，以精确计算具有尺度效应的复合材料的有效特性。