A moving boundary finite element method-based numerical approach for the solution of one-dimensional problems in shape memory alloys

• Published in: Computer methods in applied mechanics and engineering Vol. 190; no. 13-14; pp. 1741 - 1762
• Main Authors: STOILOV, V, ILIEV, O, BHATTACHARYYA, A
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier 22.12.2000
• Subjects: Boundary-integral methods; Computational techniques; Condensed matter: structure, mechanical and thermal properties; Equations of state, phase equilibria, and phase transitions; Exact sciences and technology; Finite-element and galerkin methods; Mathematical methods in physics; Physics; Solid-solid transitions; Specific phase transitions; Finite element method; Newton-Raphson method; Shape memory alloy; Phase change; One dimensional model; Moving boundary; Thermomechanical properties; Numerical method; Non linear effect; Iterative methods; Recursion method; Boundary element method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(00)00188-2

A moving boundary finite element method (MBFEM)-based numerical approach is proposed to solve one-dimensional (1-D) thermomechanical problems in shape memory alloys (SMAs) with a moving phase boundary. The Newton-Raphson method and recursive iterations, respectively, are used to address the non-linearity and coupling in the system of equations. At variance with other MBFEM approaches, the 1-D temperature field is modeled here by introducing a grid node (at the phase boundary and moving with it) in a 1-D mesh, which otherwise remains unchanged from one time step to another. The approach is demonstrated to be accurate, unconditionally stable and robust when compared to an analytical solution for purely thermal transformations, and also compares favorably with the predictions of a finite difference method for stress-induced transformations.