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'.
Keywords: augmented finite-element method; cohesive zone models; composites; fracture.
© 2016 The Author(s).