A microscopically motivated constitutive model for shape memory alloys: Formulation, analysis and computations. (March 2016)

• Record Type: Journal Article
• Authors: Frost, Miroslav; Benešová, Barbora; Sedlák, Petr
• Is Part Of: Mathematics and mechanics of solids. Volume 21:Number 3(2016:May)
• Page Start: 358
• Page End: 382
• Publication Date: 2016-03
• Subjects: Shape memory alloys -- constitutive model -- generalized standard materials -- dissipation -- energetic solution; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286514522474
• Languages: English
• ISSNs: 1081-2865

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.