Straight Disclinations in Fractional Nonlocal Medium
Tamara Kyrylych, Yuriy Povstenko
TL;DR
This paper introduces a new nonlocal theory of elasticity to study stress fields around disclinations without singularities.
Contribution
A novel nonlocal elasticity framework using a fractional diffusion kernel is proposed to model disclinations.
Findings
Stress fields for straight wedge and twist disclinations are derived without nonphysical singularities.
The transition to local elasticity is achieved by taking the nonlocality parameter to zero.
The Laplace transform is effectively used to solve nonlocal elasticity problems.
Abstract
The constitutive equation for a nonlocal stress tensor is represented as an integral with the suitable kernel function. In this paper, the nonlocality kernel is chosen as the Green function of the Cauchy problem for the fractional diffusion equation with the Caputo derivative with respect to the nonlocality parameter. The solutions of nonlocal elasticity problems for the straight wedge and twist disclinations in an infinite medium are obtained in the framework of this new nonlocal theory of elasticity. The Laplace integral transform with respect to the nonlocality parameter is used. It is necessary to emphasize that the transition from the nonlocal to local stress tensor is described by the limiting value of the nonlocality parameter τ→0. The obtained stress fields do not contain nonphysical singularities at the disclination lines.
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Taxonomy
TopicsNonlocal and gradient elasticity in micro/nano structures · Numerical methods in engineering · Composite Structure Analysis and Optimization