Simulation of phase combinations in shape memory alloys patches by hybrid optimization methods

Authors:
Linxiang Wang;Roderick V. N. Melnik
Affiliations:
Mads Clausen Institute, Faculty of Engineering, University of Southern Denmark, Sonderborg DK-6400, Denmark;Mathematical Modelling and Computational Sciences, Wilfrid Laurier University, Waterloo, 75 University Ave W, Canada N2L 3C5
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 6
Cited 3

An introduction to genetic algorithms

An introduction to genetic algorithms
Spectral methods in MATLAB

Spectral methods in MATLAB
Practical quasi-Newton methods for solving nonlinear systems

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Genetic Algorithms in Search, Optimization and Machine Learning

Genetic Algorithms in Search, Optimization and Machine Learning
Applications of fully conservative schemes in nonlinear thermoelasticity: modelling shape memory materials

Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
Linear-programming approach to nonconvex variational problems

Numerische Mathematik

Coupling control and human factors in mathematical models of complex systems

Engineering Applications of Artificial Intelligence
Low dimensional nonlinear thermomechanical models describing phase transformations and their applications

MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Phase-field approach to studying shape memory effects and thermomechanical properties of low dimensional nanostructures

NANOTECHNOLOGY'10 Proceedings of the 2nd WSEAS international conference on Nanotechnology

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, phase combinations among martensitic variants in shape memory alloys patches and bars are simulated by a hybrid optimization methodology. The mathematical model is based on the Landau theory of phase transformations. Each stable phase is associated with a local minimum of the free energy function, and the phase combinations are simulated by minimizing the bulk energy. At low temperature, the free energy function has double potential wells leading to non-convexity of the optimization problem. The methodology proposed in the present paper is based on an initial estimate of the global solution by a genetic algorithm, followed by a refined quasi-Newton procedure to locally refine the optimum. By combining the local and global search algorithms, the phase combinations are successfully simulated. Numerical experiments are presented for the phase combinations in a SMA patch under several typical mechanical loadings.