Phenomenological Constitutive Equations for Numerical Simulations of SMA's Structures. Effects of Thermomechanical Couplings

Abstract

Tension-compression tests at different room temperatures and at different strain rates have been performed on Shape Memory Alloys (CuZnAl, NiTi) using a thermomechanical device. The experiments underline the main role of the temperature variations induced by the deformation process on the stress-strain curves. These variations are essentially due to the latent heat of phase change and the analysis of the associated energy balances shows that the intrinsic dissipated energy remains very small compared to deformation work or latent heat of phase change. On the basis of these results, a behavioral model is proposed that assumes an intrinsic dissipation identically equal to zero and that considere anisothermal deformation processes. This model, written under the formalism of Generalized Standard Materials takes into account the thermoelastic couplings and considers two self-accommodating martensite variants. It is implemented in a finite element code realized to predict the effects of thermomechanical couplings. An implicit integration scheme is used to derive at each step in time the fields stress, strain, temperature, and volume proportions of phases. At each step and due to the thermomechanical coupling, we have to solve non-symmetric linear systems. Numerical simulations are shown first to verify the coherence with the experimental results obtained under uniaxial loading, and secondly to underline the practical interest of such an approach to design SMA's structures

A three‐dimensional model describing stress‐temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications

“…To make more clear the model thermo-mechanical behaviour, in Figure 1(c) we compare the cyclic variation of the deformation work W m and the evolved heat W ch [51], defined as:…”

Quasistatic Isothermal Evolution of Shape Memory Alloys

“…In this case one can assume that the heat produced by the dissipative reorientation mechanism is (almost) immediately transported to the surrounding environment. Even in terms of energetics, experimental evidence shows that the influence of (irreversible) internal dissipation is very small compared with the (reversible) thermomechanical energy dynamics along loadingunloading cycles [47].…”

Analysis of a Thermomechanical Model for Shape Memory Alloys

“…The field of application of shape memory technologies ranges from bioengineering to structures-engineering and aerospace sciences [13,16,30]. Here we are concerned with a macroscopic modelization previously introduced in [31] and able to describe the shape memory effect in a small deformation realm. We refer the reader to section 2 for a derivation of the model as well as for some discussion of its thermodynamical consistency.…”

“…We refer the reader to section 2 for a derivation of the model as well as for some discussion of its thermodynamical consistency. As for the justification of this modeling perspective as well as some experimental validation one should refer to the original paper [31] as well as to [14,20,32]. For the purposes of this introductory discussion, let us remark that the scalar field θ in (1.1)-(1.4) represents the absolute temperature of the medium while the vector field u is its displacement.…”

“…In particular, the phase relation of Frémond's model corresponds, in the present setting, to the choices μ > 0 and γ = 0. On the contrary, the modeling considerations and the experimental evidence of [31] suggests considering the degenerate case μ = 0 (taking indeed γ > 0). We will refer to the situation μ > 0 as the dissipative case and μ = 0 as the nondissipative one.…”