An analytical solution for multiple inclusions subject to a general applied thermal field

In this study, we present a general numerical solution to the thermoelastic problem of interacting elliptical inhomogeneities in an infinite matrix material. Our solution provides a framework to study microstructural responses to the external mechanical, thermal, electric, and magnetic fields simult...

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Bibliographic Details
Published inJournal of thermal stresses Vol. 46; no. 11; pp. 1180 - 1198
Main Authors Ebrahimi, Mahdieh Tajabadi, Balint, Daniel Stephen, Dini, Daniele
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.11.2023
Subjects
Elliptical inclusions
fracture mechanics
microstructure
thermoelasticity
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Summary:In this study, we present a general numerical solution to the thermoelastic problem of interacting elliptical inhomogeneities in an infinite matrix material. Our solution provides a framework to study microstructural responses to the external mechanical, thermal, electric, and magnetic fields simultaneously. The proposed semi-analytical method, which enables us to reduce the computational cost and calculate the interactions between many inclusions, is based on conformal mapping, series expansion of the corresponding complex potentials and boundary conditions. The temperature, stress, strain, and displacement functions are derived explicitly in the matrix material and inclusions. The thermal loadings tested in this study include temperature variations and a uniform heat flow. The model is validated against multiple analytical calculations and benchmark numerical problems. The method is ready to apply for simulations with many inclusions.
ISSN:0149-5739
1521-074X
DOI:10.1080/01495739.2023.2247037