Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation

An ideal model for stress-induced martensitic transformations in shape-memory alloys

“…The sequence of thermodynamic states occurring in SMAs is usually described by introducing additional variables (such as martensite and austenite volume fractions), within the framework of thermodynamics with internal state variables [8]. Current SMA constitutive models have reached a high level of sophistication accounting for multiple and simultaneous thermomechanical mechanisms [3][4][5][9][10][11][12][13]. Nevertheless, a common limitation is that most existing models generally assume that phase diagrams governing phase transformations are characterized by piecewise-linear transformation lines, despite of high non-linearities highlighted from experiments [6].…”

“…Furthermore, the implementation of the most effective models is heavy due to:  the costly calibrations of a high number of model parameters, in some case without a clear physical meaning;  the need of introducing iterative schemes for satisfying inequality constraints by means of implicit multi-step redictor-corrector schemes or by introducing equivalent non-linear systems in a large number of unknowns. The last drawback is due to the need of fulfilling the second law of thermodynamics by solving a constrained optimization problem with inequality constraints that derives from the Clausius-Duhem inequality or, equivalently, from Kuhn-Tucker conditions, [4]. On the other hand, as shown by J.J. Moreau [15], the second law of thermodynamics may be a-priori satisfied within the energy statement of the problem if the constitutive laws for the dissipative part of the static quantities involved in equilibrium equations are defined through the introduction of a pseudo-potential of dissipation.…”

“…Parameters with the same physical meaning are introduced in many SMA available models [1,4,5,9], and thereby can be retained as classical. Nevertheless, the possibility to address the non-linear dependence of transformation strains and stresses on temperature is a novelty with respect to most well-established available models, in agreement with the improvements proposed by Lagoudas and co-workers, [14].…”

“…Proposed designs based on such materials range from aeronautic/mechanical applications (e.g., adaptive smart wings and actuators) and telecommunication devices (e.g., deployment and control mechanisms of satellites and antennas), to biomedical (e.g., self-expanding stents, orthodontic wires, and prostheses) and civil applications (e.g., devices for passive, active and semi-active controls of civil structures) [1,2]. As proved by the recent wide literature in the field [1,[3][4][5], there is a great need of constitutive models able to reproduce SMAs behavior, including a refined description of phase transformation mechanisms. In order to be effectively employed in practical applications, models should be characterized by parameters whose values have to be easily identified from well-established experimental procedures.…”

Experimental and numerical assessment of the characteristics describing superelasticity in shape memory alloys – influence of boundary conditions

“…Their unique mechanical properties reveal through the two-way martensitic phase transition activated by force and thermal excitations [1][2][3]. This nanoscale phenomenon introduces the specific macroscale behaviour of SMA, namely one-and two-way shape memory effects, and superelasticity.…”