Constitutive Modeling of Coupled Dissipation Processes in the Mechanics of Shape Memory Alloys
Miroslav Frost 1*, Alexej Moskovka 1, Petr Sedlák 1, Hanuš Seiner 1, Petr Pelech 2, Barbora Benešová 2
1 Czech Academy of Sciences, Institute of Thermomechanics, Prague, Czechia; 2 Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Prague, Czechia
Keywords: generalized standard material, dissipation function, strongly coupled processes, shape memory alloys
Shape memory alloys provide an example of materials whose mechanical response combines several deformation contributions. In addition to elasticity, dissipative processes associated with martensitic phase transformation and microstructural reconfigurations can be activated during loading. This leads to a rich mechanical response that is also temperature-dependent and gives rise to the so-called shape memory phenomena. At the same time, such a combination of several interdependent deformation processes poses a significant challenge for formulating a plausible constitutive model [1]. Based on thorough experimental characterization, we propose a novel constitutive model that captures the main, rate-independent features of the (thermo)mechanical behavior of NiTi shape memory alloys, including non-conventional plasticity in martensite. By employing the formalism of the Generalized Standard Materials framework, we can treat dissipative deformation processes in a unified manner, avoiding the explicit formulation of force-flux relations for each and any combination of activated processes. On the other hand, the fact that some specific transformation processes can occur only in a particular sequence requires (also due to the non-smooth character of the dissipation function) a refinement of the constitutive relations (evolutionary inclusions), which is then also reflected in the numerical treatment of the constitutive update algorithm. In the talk, we will briefly summarize the (thermo)mechanical response of NiTi shape memory alloys, identify and characterize the main dissipative deformation processes, and introduce the formulation of the constitutive model within the Generalized Standard Materials framework. A numerical implementation of the model to the finite element method will be proposed and validated. The mathematical aspects on the model formulation will be presented in a subsequent contribution by P. Pelech.
References
- M. Frost, B. Benešová, and P. Sedlák, A microscopically motivated constitutive model for shape memory alloys: formulation, analysis and computations, Math. Mech. Solids, 21(3):358–382, 2016, https://doi.org/10.1177/1081286514522474.