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In this paper, a thermal–mechanical augmented finite-element method (TM-AFEM) has been proposed, implemented and validated for steady-state and transient, coupled thermal–mechanical analyses of complex materials with explicit consideration of arbitrary evolving cracks. The method permits the derivation of explicit, fully condensed thermal–mechanical equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node quadrilateral two-dimensional (2D) element and a 4-node tetrahedron three-dimensional (3D) element. It has been demonstrated, through several numerical examples that the new TM-AFEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 2D and 3D solids under coupled thermal–mechanical loading conditions. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical loadings