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Detailed Solution of a System of Singular Integral Equations for Mixed Mode Fracture in Functionally Graded Materials

Youn-Sha Chan, Edward Athaide, Kathryn Belcher and Ryan Kelly

Journal of Mathematics Research, 2020, vol. 12, issue 1, 43

Abstract: A mixed mode crack problem in functionally graded materials is formulated to a system of Cauchy singular Fredholm integral equations, then the system is solved by the singular integral equation method (SIEM). This specific crack problem has already been solved by N. Konda and F. Erdogan (Konda & Erdogan 1994). However, many mathematical details have been left out. In this paper we provide a detailed derivation, both analytical and numerical, on the formulation as well as the solution to the system of singular Fredholm integral equations. The research results include crack displacement profiles and stress intensity factors for both mode I and mode II, and the outcomes are consistent with the paper by Konda & Erdogan (Konda & Erdogan 1994).

JEL-codes: R00 Z0 (search for similar items in EconPapers)
Date: 2020
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Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:1:p:43