Thermoelastic analysis of a bi-layered system with the single domain inclusion-based boundary element method

Abstract

When a bi-layered composite system is subjected to prescribed thermal and elastic boundary conditions, material mismatch of layers and inhomogeneities causes intensive stress concentration, particularly with an initial crack, which causes delamination of the system. This paper combines the boundary element method and our recent work on the dual equivalent inclusion method (DEIM), namely the inclusion-based boundary element method (iBEM), to simulate the thermoelastic behavior without the whole domain integral. Using Galerkin’s stress vector technique, the bimaterial thermoelastic Green’s function mathematically transforms the entire domain integral to boundary integral equations. Because the inhomogeneities and matrix generally exhibit thermal and mechanical material mismatch, the DEIM simulates the inhomogeneity problem by inclusion with continuously distributed polynomial-form eigentemperature and eigenstrain. Therefore, iBEM avoids conventional multi-region solution scheme and convert the entire domain into boundary integral equations plus domain integrals within the inhomogeneity domain. The energy release rate (J-integral) can be utilized to reveal and judge the stability of the crack. For elastic problems, when one of the layers becomes stiffer or is embedded with the stiffer inhomogeneity, the J-integral decreases, and the system is more stable. However, this conclusion is not established for thermoelastic problems. Moreover, locations, distribution, and material mismatches are essential in (modified) J-integrals. Numerical case studies validate the single-domain algorithm, and parametric studies illustrate the effects of inhomogeneities on the (modified) J-integral for a bi-layered system.