Phenomenological 3D and 1D consistent models for shape-memory alloy materials

The paper deals with the modeling and the development of a numerical procedure for the analysis of shape-memory alloy (SMA) elements in order to predict the main features of SMA devices. A 3D SMA model in the framework of small strain theory is developed starting from the thermo-mechanical model proposed by Souza et al. (Eur J Mech A/Solids 17:789–806, 1998) and modified by Auricchio and Petrini (Int J Numer Methods Eng 55:1255–1284, 2002). The aim of this paper is to propose some more modifications to the original model, to derive its consistent 1D formulation, to clarify the mechanical meaning of the material parameters governing the constitutive model. A robust time integration algorithm is developed in the framework of the finite element method and a new beam finite element is proposed. Some numerical applications and a comparison with experimental data available in literature are carried out in order to assess the ability of the proposed model to describe the SMA behavior.

[1]  Dimitris C. Lagoudas,et al.  On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material , 2000 .

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

[3]  B. Sullivan,et al.  A Three-Dimensional Phase Transformation Model for Shape Memory Alloys , 1995 .

[4]  C. Lexcellent,et al.  Thermodynamics of isotropic pseudoelasticity in shape memory alloys , 1998 .

[5]  K. T. Ramesh,et al.  The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading , 2003 .

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

[7]  E. Sacco,et al.  A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite , 1997 .

[8]  Ferdinando Auricchio,et al.  A uniaxial model for shape-memory alloys , 1997 .

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

[10]  Lorenza Petrini,et al.  Improvements and algorithmical considerations on a recent three‐dimensional model describing stress‐induced solid phase transformations , 2002 .

[11]  G. Bourbon,et al.  The two way shape memory effect of shape memory alloys: an experimental study and a phenomenological model , 2000 .

[12]  L. Brinson,et al.  Shape memory alloys, Part I: General properties and modeling of single crystals , 2006 .

[13]  Sanjay Govindjee,et al.  Errata to “The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis”: Journal of the Mechanics & Physics of Solids 50 (9) (2002) 1897–1922 , 2003 .

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

[15]  J. Z. Zhu,et al.  The finite element method , 1977 .

[16]  E. Sacco,et al.  Thermo-mechanical modelling of a superelastic shape-memory wire under cyclic stretching–bending loadings , 2001 .

[17]  F. Auricchio,et al.  A three‐dimensional model describing stress‐temperature induced solid phase transformations: solution algorithm and boundary value problems , 2004 .

[18]  David John Barrett,et al.  A One-Dimensional Constitutive Model for Shape Memory Alloys , 1995 .

[19]  L. C. Brinson,et al.  Deformation of Shape Memory Alloys Due to Thermo-Induced Transformation , 1996 .

[20]  D. Lagoudas,et al.  Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms , 2000 .

[21]  Ferdinando Auricchio,et al.  Modelling of SMA materials: Training and two way memory effects , 2003 .

[22]  Miinshiou Huang,et al.  A Multivariant model for single crystal shape memory alloy behavior , 1998 .

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