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

Abstract

Summary 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 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 proposed here. 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 nonsmooth 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.

A Direct Method for Cyclic Crystal Plasticity with Application to High-Cycle Fatigue

“…For j ̸ = k, the tensor S jk in (22) captures the elastic interaction between grains j and k. The norm of that tensor is expected to decrease with the distance between grains j and k. Substituting ( 21) in (16) we finally arrive at…”

“…Sects 2-4 of this paper report on a simplified numerical method for a fast evaluation of the plastic slips in elastic-plastic 2D polycrystals. That method is based on incremental variational principles, which have proved to be a fruitful approach in many applications [9,10,2,16,26,22,25]. Starting from elastic-plastic constitutive equations detailed in Sect.…”

Shakedown theorems for shape memory alloys structures with functional fatigue — Application to nitinol stents

“…To illustrate the role played by the internal variable α 2 in the model of Auricchio et al (2007), 50 stress-driven loading cycles with a maximum applied of stress of 400 MPa have been simulated numerically. The expression (21) of the elasticity domain was adopted and the algorithm of Peigney et al (2018) was used for solving the incremental problem at each time step. In Fig.…”

Active Adjustment of Surface Accuracy for a Large Cable-Net Structure by Shape Memory Alloy

“…The force–displacement–temperature stiffness model of shape memory cables needs to be modeled on the basis of an effective SMA phase transformation constitutive model with a simple form, which ensures the calculation accuracy for the active adjustment of the surface deformation of antenna. In the last decade, some SMA constitutive models successfully predicting the occurrence of inelastic deformation during the thermo-mechanical loading can be referred in Tanaka et al [23], Liang and Rogers [24], Brinson [25], Lagoudas et al [26,27,28,29,30,31,32,33], Auricchio et al [34,35,36,37] and so on. In this work, a finite element model with the one-dimensional cable element stiffness model is established to describe the elastic deformation of the polymer cable and the SME with phase transformation of the SMA wire.…”