title: Augmented finite-element method for arbitrary cracking and crack interaction in solids under thermo-mechanical loadings.
abstract: 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'.
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33124, USA.
authors.forename: J
authors.initials: J
authors.lastname: Jung
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33124, USA.
authors.forename: B C
authors.initials: BC
authors.lastname: Do
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33124, USA qdyang@miami.edu.
authors.forename: Q D
authors.identifier: http://orcid.org/0000-0003-0574-6461
authors.initials: QD
authors.lastname: Yang
keywords: augmented finite-element method; cohesive zone models; composites; fracture