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A time integration algorithm for a 3D constitutive model for SMAs including permanent inelasticity and degradation effects

Abstract : Components based on shape-memory alloys are often subjected to several loading cycles that result in substantial alteration of material behavior. In such a framework, accurate models as well as robust and efficient numerical approaches become essential to allow for the simulation of complex devices. The present paper focuses on the numerical simulation of quasi-static problems involving shape memory alloy (SMA) structures or components subjected to multiple loading-unloading cycles. A novel state-update procedure for a three-dimensional phenomenological model able to describe the saturation of permanent inelasticity, including degradation effects, is here proposed. The algorithm, being of the predictor-corrector type and relying on an incremental energy minimization approach, is based on elastic checks, closed-form solutions of polynomial equations, and nonlinear scalar equations solved through a combination of Newton-Raphson and bisection methods. This allows for an easy implementation of model equations and to avoid the use of regularization parameters for the treatment of non-smooth functions. Numerical results assess the good performances of the proposed approach in predicting both pseudoelastic and shape-memory material behavior under cyclic loading as well as algorithm robustness.
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https://hal-enpc.archives-ouvertes.fr/hal-01820083
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Dernière modification le : mercredi 14 octobre 2020 - 03:48:23
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Michaël Peigney, Giulia Scalet, Ferdinando Auricchio. A time integration algorithm for a 3D constitutive model for SMAs including permanent inelasticity and degradation effects. International Journal for Numerical Methods in Engineering, Wiley, 2018, ⟨10.1002/nme.5835⟩. ⟨hal-01820083⟩

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