Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior

Shape-memory alloys (SMA) show features not present in materials traditionally used in engineering; as a consequence, they are the basis for innovative applications. The present work proposes a step toward the development of a computation tool to be used during the design of SMA-based devices. To reach this goal, we develop a constitutive model which reproduce the superelastic behavior of shape-memory alloys at finite strains. For an isothermal case we discuss in detail the numerical implementation within a finite-element scheme as well as the form of the algorithmically consistent tangent. To assess the viability of the proposed approach we simulate the response of some simple SMA typical structures (uniaxial test, four-point bending test) as well as an application with possibly a very high impact in different medical fields.

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

[2]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

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

[4]  J. C. Simo,et al.  A priori stability estimates and unconditionally stable product formula algorithms for nonlinear coupled thermoplasticity , 1993 .

[5]  M. Wilkins.  Calculation of Elastic-Plastic Flow , 1963 .

[6]  A. G. Khachaturi︠a︡n.  Theory of structural transformations in solids , 1983 .

[7]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[8]  Shoichi Endo,et al.  Effect of Hydrostatic Pressures on Thermoelastic Martensitic Transformations in Aged Ti–Ni and Ausaged Fe–Ni–Co–Ti Shape Memory Alloys , 1992 .

[9]  K. Melton,et al.  Ni-Ti Based Shape Memory Alloys , 1990 .

[10]  Ferdinando Auricchio,et al.  Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior , 1997 .

[11]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[12]  Gregory B Olson,et al.  Martensite : a tribute to Morris Cohen , 1992 .

[13]  J. Mandel.  Thermodynamics and Plasticity , 1973 .

[14]  Shuichi Miyazaki,et al.  The shape memory mechanism associated with the martensitic transformation in TiNi alloys—II. Variant coalescence and shape recovery , 1989 .

[15]  Shuichi Miyazaki,et al.  The shape memory mechanism associated with the martensitic transformation in TiNi alloys—I. Self-accommodation , 1989 .

[16]  G. Maenchen,et al.  The Tensor Code , 1963 .

[17]  J. C. Simo,et al.  Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory , 1992 .

[18]  C. M. Wayman,et al.  Introduction to the crystallography of martensitic transformations , 1964 .

[19]  F. Auricchio,et al.  Generalized plasticity and shape-memory alloys , 1996 .

[20]  T. W. Duerig,et al.  On the tensile and torsional properties of pseudoelastic NiTi , 1990 .