Isogeometric Analysis of Cubic-to-Tetragonal Martensitic Transformations in Shape Memory Alloy 3D Domains Under Mechanical And Thermal Loads
Rakesh Dhote (University of Toronto), Hector Gomez (University of A Coruna, Spain), Roderick Melnik (Wilfred-Laurier University, Waterloo, Canada), jean Au (University of Toronto, Canada)
Mechanics of Phase Transforming and Multifunctional Materials
Wed 10:45 - 12:15
CIT 219
In this contribution, we present the dynamically coupled thermo-mechanical properties of phase transformations in 2D and 3D shape memory alloys (SMAs) nanostructures. The models are based on the phase-field theory and strain based Ginzburg-Landau free energy. The models have bidirectional coupling between the thermal and mechanical physics via strain, strain rate and temperature. We study the fully coupled dynamic thermo-mechanical properties in SMAs which has often been modeled under isothermal assumption in the literature (eg. [1]). In addition to the thermo-mechanical coupling, the models have inherent fourth-order differential terms [2]. These models have been numerically implemented in the variational form in the isogeometric analysis, a generalization of finite element method based on non-uniform rationalized B-splines (NURBS) basis functions [3]. Isogeometic analysis offers several advantages in solving complex problems with higher order differential terms [4]. We present the influence of mechanical and thermal loadings on martensitic transformations in SMAs. References: [1] Ahluwalia R. et al., 2006. Dynamic strain loading of cubic to tetragonal martensites. Acta Materialia, 54(8), 2109–2120. [2] Dhote R. et al., Dynamic Thermo-Mechanical Coupling and Size Effects in finite Shape Memory Alloy Nanostructures, Computational Materials Science, vol. 63, pp.105–117, 2012. [3] Cottrell J., Hughes H., and Bazilevs Y., 2009, Isogeometric analysis: toward integration of and FEA. John Wiley & Sons Inc. [4] Gomez H. et al. 2010. Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations, CMAME, 199, 25, 1828-1840.