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Journal of Intelligent Material Systems and Structures
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Shape Memory: A New Concept of Explanation and of Mathematical Modelling

Part II: Mathematical Modelling of the SM Effect and of Pseudoelasticity

V. Kafka

Institute of Theoretical and Applied Mechanics, Academy of Sciences, Prague, 18200 Czech Republic

The mathematical model presented here is formulated in such a way that the two sets of atoms present in a binary alloy with shape memory are modelled as two continuous infrastruc tures. The model is based on the author's general concept elaborated for the description of inelastic processes in heterogeneous materials. For the effect of mechanical loading the application of this concept is straightforward. The effect of temperature changes is modelled by a simple linear relation that reflects the influence of the differing thermal expansions of the two elements constituting the alloy upon the deviatoric stress and strain in the infrastructure that undergoes inelastic deformation. The resulting thermomechanical constitutive equation is very general and the cases of shape memory and pseudoelasticity are described by it as special forms. Quantitative comparisons of theo retical and experimental data prove that this approach is meaningful.

Journal of Intelligent Material Systems and Structures, Vol. 5, No. 6, 815-824 (1994)
DOI: 10.1177/1045389X9400500613
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 Journal of Intelligent Material Systems and StructuresHome page
V. Kafka
An Overview of Applications of the Mesomechanical Approach to Shape Memory Phenomena Completed by a New Application to Two-way Shape Memory
Journal of Intelligent Material Systems and Structures, January 1, 2008; 19(1): 3 - 17.
[Abstract] [PDF]

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 Journal of Intelligent Material Systems and StructuresHome page
D. J. Barrett and B. J. Sullivan
A Three-Dimensional Phase Transformation Model for Shape Memory Alloys
Journal of Intelligent Material Systems and Structures, November 1, 1995; 6(6): 831 - 839.
[Abstract] [PDF]