A finite addition of matter elements method for modeling and solution of an SLM thermal problem by a multiscale method

Abstract

AbstractIn this article, we are interested in flexible modeling and performing solution of transient thermal selective laser melting problems. For this, we first introduce a finite addition of matter elements method (FAMEM) to generate any wished finite sequence of thermal problems, defined in additively constructed domains. Second, we use the multiscale Arlequin frame‐work to develop a three‐level Arlequin weak‐strong formulation of each problem of the finite sequence. Two Arlequin patches are used in the latter to localize the steepest thermal gradients and the nonlinear phase‐change phenomena, allowing for fine local approximations and the localized nonlinearity treatment by an algorithm we develop. These patches are identified via the solution of a representative mono‐domain transient thermal problem. The latter is also solved with our three‐level Arlequin method for comparison of the solutions and respective performances of both approaches. Moreover, two dimensional tests consisting in the creation of a 316 L stainless steel wall and a two AlSi10Mg layers, are carried out to further enlighten our global approach and to position it with respect to literature.