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In this work, we briefly review the one-dimensional version of a well-known phenomenological shape memory alloy (SMA) constitutive model able to represent the main macroscopic SMA macroscopic behaviors (i.e., superelasticity and shape-memory effect). We then show how to identify the needed parameters from experimental results and, in particular, from strain-temperature tests. We finally use the obtained material parameters to test the prediction properties of the model, comparing numerical results with some experiments (different from those used for the identification), and we discuss model capabilities and further required enhancements.

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We develop a nonlinear, three-dimensional phase field model for crystal plasticity which accounts for the infinite and discrete symmetry group G of the underlying periodic lattice. This generates a complex energy landscape with countably-many G-related wells in strain space, whereon the material evolves by energy minimization under the loading through spontaneous slip processes inducing the creation and motion of dislocations without the need of auxiliary hypotheses. Multiple slips may be activated simultaneously, in domains separated by a priori unknown free boundaries. The wells visited by the strain at each position and time, are tracked by the evolution of a G-valued discrete plastic map, whose non-compatible discontinuities identify lattice dislocations. The main effects in the plasticity of crystalline materials at microscopic scales emerge in this framework, including the long-range elastic fields of possibly interacting dislocations, lattice friction, hardening, band-like vs. complex spatial distributions of dislocations. The main results concern the scale-free intermittency of the flow, with power-law exponents for the slip avalanche statistics which are significantly affected by the symmetry and the compatibility properties of the activated fundamental shears.

In this study, the shape memory effect of SMA beams under complex stress conditions is studied by means of a finite element model. The 1D version of a well-established SMA constitutive model is utilized in the numerical computations and the required parameters are obtained experimentally starting from thermal cycling tests in tension under different constant loads. After being calibrated, the model is used to compute the deformation of beams loaded in bending and undergoing thermal cycling; three-point bending and cantilever configurations are considered in this stage. Finally, the response predicted by the model is compared to experimental results and model capabilities are discussed. In particular, insight of the stress and strain evolution in bending is provided.