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A Bermúdez-Moreno algorithm adapted to solve a viscoplastic problem in alloy solidification processes. (English) Zbl 1286.74025
Summary: The aim of this work is to present a computationally efficient algorithm to simulate the deformations suffered by a viscoplastic body in a solidification process. This type of problems involves a nonlinearity due to the considered thermo-elastic-viscoplastic law. In our previous papers, this difficulty has been solved by means of a duality method, known as Bermúdez-Moreno algorithm, involving a multiplier which was computed with a fixed point algorithm or a Newton method. In this paper, we will improve the former algorithms by means of a generalized duality method with variable parameters and we will present numerical results showing the applicability of the resultant algorithm to solidification processes. Furthermore, we will describe a numerical procedure to choose a constant parameter for the Bermúdez-Moreno algorithm which gives good results when it is applied to solidification processes.

MSC:
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74D10 Nonlinear constitutive equations for materials with memory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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