3D phenomenological constitutive modeling of shape memory alloys based on microplane theory

A three-dimensional microplane constitutive model utilizing statically constrained formulation with volumetric—deviatoric split is presented for shape memory alloys (SMAs). Shear stress within each microplane is described by resultant shear component on the plane. One-dimensional stress—strain laws are used for normal and shear stresses on microplanes by considering suitable adjustments between the macroscopic and the microscopic quantities. The behavior of SMAs under simple and complicated loadings is studied. The model represents interaction between the stress components and the deviation from normality in the case of nonproportional loadings. The results are in good agreement with the existing theoretical and experimental findings.

[1]  E. Patoor,et al.  Thermomechanical behaviour of shape memory alloys , 1988 .

[2]  Zdenek P. Bazant,et al.  Microplane Model for Concrete , 1996 .

[3]  Zdenek P. Bazant,et al.  MICROPLANE MODEL FOR STRAIN-CONTROLLED INELASTIC BEHAVIOUR. , 1984 .

[4]  Pere C. Prat,et al.  Microplane Model for Concrete. I: Stress-Strain Boundaries and Finite Strain , 1996 .

[5]  Zdenek P. Bazant,et al.  Microplane Model for Brittle‐Plastic Material: II. Verification , 1988 .

[6]  James G. Boyd,et al.  Thermomechanical Response of Shape Memory Composites , 1993, Smart Structures.

[7]  Alessandro Reali,et al.  A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadings , 2010 .

[8]  Thomas J. Pence,et al.  A Thermomechanical Model for a One Variant Shape Memory Material , 1994 .

[9]  K. Tanaka.  A THERMOMECHANICAL SKETCH OF SHAPE MEMORY EFFECT: ONE-DIMENSIONAL TENSILE BEHAVIOR , 1986 .

[10]  D. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part IV: modeling of minor hysteresis loops , 1999 .

[11]  S. Calloch,et al.  A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings , 2004 .

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

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

[14]  P. Bazant,et al.  Efficient Numerical Integration on the Surface of a Sphere , 1986 .

[15]  L. C. Brinson,et al.  Phase diagram based description of the hysteresis behavior of shape memory alloys , 1998 .

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

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

[18]  Wael Zaki,et al.  A three-dimensional model of the thermomechanical behavior of shape memory alloys , 2007 .

[19]  Dimitris C. Lagoudas,et al.  Use of a Ni60Ti shape memory alloy for active jet engine chevron application: II. Experimentally validated numerical analysis , 2009 .

[20]  Shanglian Huang,et al.  A comprehensive description for shape memory alloys with a two-phase constitutive model , 2001 .

[21]  Bernard Budiansky,et al.  A Mathematical Theory of Plasticity Based on the Concept of Slip , 1949 .

[22]  Sylvain Calloch,et al.  A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings , 2009 .

[23]  Dirk Helm,et al.  Shape memory behaviour: modelling within continuum thermomechanics , 2003 .

[24]  Otto T. Bruhns,et al.  Path dependence and multiaxial behavior of a polycrystalline NiTi alloy within the pseudoelastic and pseudoplastic temperature regimes , 2009 .

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

[26]  Zdeněk P. Bažant,et al.  Three-dimensional constitutive model for shape memory alloys based on microplane model , 2002 .

[27]  L. Brinson,et al.  A three-dimensional phenomenological model for martensite reorientation in shape memory alloys , 2007 .

[28]  Dimitris C. Lagoudas,et al.  Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs , 2004 .

[29]  I. Müller,et al.  A model for phase transition in pseudoelastic bodies , 1980 .

[30]  Pere C. Prat,et al.  Microplane Model for Brittle-Plastic Material: I. Theory , 1988 .

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

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

[33]  D. McDowell,et al.  Mechanical behavior of an Ni-Ti shape memory alloy under axial-torsional proportional and , 1999 .

[34]  Ignacio Carol,et al.  Damage and plasticity in microplane theory , 1997 .

[35]  L. C. Brinson,et al.  Simplifications and Comparisons of Shape Memory Alloy Constitutive Models , 1996 .

[36]  V. A. Beloshenko,et al.  The Shape Memory Effect in Polymers , 2005 .

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

[38]  R. Mirzaeifar,et al.  Exact solutions for pure torsion of shape memory alloy circular bars , 2010 .

[39]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations , 1999 .

[40]  Dimitris C. Lagoudas,et al.  A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite , 2007 .

[41]  C. Liang,et al.  The constitutive modeling of shape memory alloys , 1990 .

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

[43]  R. Rajapakse,et al.  Microplane modelling of shape memory alloys , 2007 .

[44]  Zdenek P. Bazant,et al.  Microplane Constitutive Model and Metal Plasticity , 2000 .