Improvements and algorithmical considerations on a recent three‐dimensional model describing stress‐induced solid phase transformations

SUMMARY During mechanical loading-unloading cycles shape-memory alloys (SMA) are able to undergo large deformations without showing residual strains (pseudoelasticity) or recovering them through ther- mal cycles (shape memory eect ). Motivated by stress-induced solid phase transformations, these unique behaviours induce the SMA exploitation in innovative and commercially valuable applications, stimulating, consequently, the interest in the development of constitutive models. Also if many models are now available in the literature, eective three-dimensional proposals are still few and limited in several aspects. In this paper, a three-dimensional thermomechanical model recently proposed by Souza et al. (European Journal of Mechanics-A/Solids, 1998; 17:789-806.) is taken into consideration; such a model is of particular interest for its eectiveness andexibility, but it also shows some limitations and missing links in the algorithmical counterparts. This work discusses some improvements to the original model as well as the development and the implementation of a robust integration algorithm to be adopted in a numerical scheme, such as a �nite-element framework. Copyright ? 2002 John Wiley & Sons, Ltd.

[1]  J. C. Simo,et al.  Numerical analysis and simulation of plasticity , 1998 .

[2]  E. J. Graesser,et al.  Shape‐Memory Alloys as New Materials for Aseismic Isolation , 1991 .

[3]  Ken Gall,et al.  Tension–compression asymmetry of the stress–strain response in aged single crystal and polycrystalline NiTi , 1999 .

[4]  D. Lagoudas,et al.  A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy , 1996 .

[5]  Lucas Delaey,et al.  Asymmetry of stress–strain curves under tension and compression for NiTi shape memory alloys , 1998 .

[6]  Craig A. Rogers,et al.  One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials , 1990 .

[7]  T. W. Duerig,et al.  Engineering Aspects of Shape Memory Alloys , 1990 .

[8]  James G. Boyd,et al.  A thermodynamical constitutive model for shape memory materials. Part II. The SMA composite material , 1996 .

[9]  E. Sacco,et al.  A temperature-dependent beam for shape-memory alloys: Constitutive modelling, finite-element implementation and numerical simulations , 1999 .

[10]  C. Liang,et al.  A multi-dimensional constitutive model for shape memory alloys , 1992 .

[11]  G. Piero,et al.  Some properties of the set of fourth-order tensors, with application to elasticity , 1979 .

[12]  Masataka Tokuda,et al.  Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces , 1995 .

[13]  Ferdinando Auricchio,et al.  A robust integration-algorithm for a finite-strain shape-memory-alloy superelastic model , 2001 .

[14]  J. K. Knowles,et al.  A One-Dimensional Continuum Model for Shape-Memory Alloys , 1994 .

[15]  Laurent Orgéas,et al.  Stress-induced martensitic transformation of a NiTi alloy in isothermal shear, tension and compression , 1998 .

[16]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[17]  Etienne Patoor,et al.  Micromechanical Modelling of Superelasticity in Shape Memory Alloys , 1996 .

[18]  L. Schetky.  Shape-memory alloys , 1979 .

[19]  L. Brinson.  One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable , 1993 .

[20]  C. Lexcellent,et al.  A general macroscopic description of the thermomechanical behavior of shape memory alloys , 1996 .

[21]  E. N. Mamiya,et al.  Three-dimensional model for solids undergoing stress-induced phase transformations , 1998 .

[22]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[23]  E. J. Graesser,et al.  A Proposed Three-Dimensional Constitutive Model for Shape Memory Alloys , 1994 .

[24]  Jan Van Humbeeck,et al.  Damping capacity of shape memory alloy , 1998 .