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Journal of Elasticity

Erschienen in:

07.09.2017

Multi-Scale Asymptotic Expansion for a Small Inclusion in Elastic Media

verfasst von: Makrem Arfaoui, Mohamed Rafik Ben Hassine, Maher Moakher, Yves Renard, Grégory Vial

Erschienen in: Journal of Elasticity | Ausgabe 2/2018

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Abstract

The aim of this paper is to present an asymptotic expansion of the influence of a small inclusion of different stiffness in an elastic media. The applicative interest of this study is to provide tools which take into account this influence and correct the deformation without inclusion by additive terms that can be precalculated and which depend only on the shape of the inclusion. We treat two problems: an anti-plane linearized elasticity problem and a plane strain problem. On every expansion order we provide corrective terms modeling the influence of the inclusion using techniques of scaling and multi-scale asymptotic expansions. The resulting expansion is validated by comparing it to a test case obtained by solving the Poisson transmission problem in the case of an inclusion of circular shape using the separation of variables method. Proofs of existence and uniqueness of our fields on unbounded domains are also adapted to the bidimensional Poisson problem and the linear elasticity problem.

Vorheriger Artikel On the Mathematical Structure of Eigen-deformations in a Föppl-von Kármán Bifurcation System

Nächster Artikel On Structured Surfaces with Defects: Geometry, Strain Incompatibility, Stress Field, and Natural Shapes

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Titel: Multi-Scale Asymptotic Expansion for a Small Inclusion in Elastic Media
verfasst von: Makrem Arfaoui
Mohamed Rafik Ben Hassine
Maher Moakher
Yves Renard
Grégory Vial
Publikationsdatum: 07.09.2017
Verlag: Springer Netherlands
Erschienen in: Journal of Elasticity / Ausgabe 2/2018
Print ISSN: 0374-3535
Elektronische ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-017-9653-2

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