3D coupled thermo-mechanical phase-field modeling of shape memory alloy dynamics via isogeometric analysis

Abstract

The paper focuses on numerical simulation of the phase-field (PF) equations for modeling martensitic transformations in shape memory alloys (SMAs), their complex microstructures and thermo-mechanical behavior. The PF model is based on the Landau-Ginzburg potential for the 3D cubic-to-tetragonal phase transformations in SMAs. The treatment of domain walls as diffuse interfaces, leads to a fourth-order differential equation in a strain-based order parameter PF model. The fourth-order equations introduce a number of unexplored numerical challenges because traditional numerical schemes have been primarily applied to second-order problems. We propose isogeometric analysis (IGA) as a numerical formulation for a straightforward solution to the fourth-order differential PF equations using continuously differentiable non-uniform rational B-splines (NURBS). We present microstructure evolution in different geometries of SMA nanostructures under temperature-induced phase transformations to illustrate the geometrical flexibility, accuracy and robustness of our approach. The simulations successfully capture the dynamic thermo-mechanical behavior of SMAs observed experimentally.

A hybrid variational-collocation immersed method for fluid-structure interaction using unstructured T-splines

“…NURBS-based IGA is completely widespread nowadays. An important aftereffect of using NURBS as a basis in analysis is that we can take advantage of their natural inter-element smoothness, which has positive consequences in several application areas, such as, body-fitted fluid-structure interaction (FSI) [3][4][5][6], immersed FSI [7][8][9], fluid mechanics [10][11][12][13][14][15], phase-field models [16][17][18][19][20], biomechanics [21,22], structural mechanics [23][24][25][26], shape memory alloys [27][28][29], shell modeling [30][31][32][33], and contact problems [34][35][36], among others. 856 H. CASQUERO ET AL.…”

Domain Heterogeneity in Radiofrequency Therapies for Pain Relief: A Computational Study with Coupled Models

“…Again, the exact mechanism of such associated effects at an elevated temperature within the biological tissue during thermal therapies are not completely elucidated yet, but significant recent developments have been devoted to this area of research utilizing both experimental and computational studies [23,78]. From a computational perspective, the coupling between thermal and mechanical fields, e.g., for elastic tissues such as muscles, etc., can be done by the development of coupled models of thermoelasticity, as well as efficient numerical methods for their solution, e.g., [83][84][85][86][87][88][89][90][91][92][93][94][95]. Moreover, the development of such models also includes complex nonlinear cases where numerous advances have been made in the improvement of numerical methodologies, e.g., [96][97][98][99].…”

A robust and efficient radial return algorithm based on incremental energy minimization for the 3D Souza-Auricchio model for shape memory alloys

“…Several models are available in a suitable form to perform simulations of complex SMA-based geometries subjected to general thermomechanical loading paths in both finite element (Arghavani et al, 2010;Sedlák et al, 2012;Zaki, 2012) and isogeometric analysis (Auricchio et al, 2015;Dhote et al, 2015) frameworks. The state-update procedures generally adopted to treat SMA constitutive equations are based on return-map schemes, incremental energy minimization approaches, or algorithms for mathematical programming.…”