A microscopically motivated constitutive model for shape memory alloys: Formulation, analysis and computations

Abstract

We present a three-dimensional constitutive model for NiTi polycrystalline shape memory alloys exhibiting transformations between three solid phases (austenite, R-phase, martensite). The ‘full modelling sequence’ comprised of formulation of modelling assumptions, construction of the model, mathematical analysis and numerical implementation and validation is presented. Namely, by formulating micromechanics-inspired modelling assumptions we concentrate on describing the dissipation mechanism: a refined form of this description makes our model especially useful for complex loading paths. We then embed the model into the so-called energetic framework (extended to our case) while taking advantage of describing the dissipation mechanism through the so-called dissipation distance. We prove the existence of energetic solutions to our model by a backward Euler scheme. This is then implemented into finite element software, and numerical simulations compared with experiments are also presented.

Mobile Interfacial Microstructures in Single Crystals of Cu–Al–Ni Shape Memory Alloy

“…In a similar sense, the findings related to the mechanical stabilization effect and to the interfacial microstructures summarized in this paper can be generalized for other SMAs and also for the effective behavior of SMA polycrystals (see e.g., [36,37] for such approach adopted for polycrystalline NiTi). …”

Analysis of localization phenomena in Shape Memory Alloys bars by a variational approach

“…In this work, the study of the localization phenomena in pseudoelastic SMA bars, arising in tensile tests under displacement control, is addressed by using a variational approach within the framework of a global energetic formulation for rate-independent dissipative materials modeled by the constitutive specification of a free energy and a dissipation function [32,31,4,18].…”

Energy-Conserving Time Discretization of Abstract Dynamic Problems with Applications in Continuum Mechanics of Solids

“…gives again (13) and one can again benefit from cancellation of the "mixed" terms ±Φ(u k τ , z k−1 τ ) when summing (13) up. In this way, we again obtain the discrete energy conservation (7).…”

“…We further use the binomial formulas (14) and the cancellation effect in (13) and, after summation for k = 1, ..., T /τ , we obtain the slightly modified equality (26), namely…”