Superelastic and Shape Memory Effects in Laminated Shape-Memory-Alloy Beams

A simple shape-memory-alloy (SMA) model to simulate the superelastic behavior as well as the shape memory effect is proposed. It considers only the transformations from austenite to single-variant martensite and from single-variant martensite to austenite, taking into account the ine uence of the temperature in the constitutive relationship. The proposed SMA constitutive model is employed in a novel layerwise beam theory to develop new SMA beam e nite element models with suitable interpolation of the e eld variables involved. The e nite element models developed herein account for the time evolution SMA constitutive equations. In particular, the developed e nite elements treat the SMA material as reinforcement of elastic beams. Several applications are presented to assess the validity of the constitutive model and the proposed numerical procedure.

[1]  Dirk Helm,et al.  Thermomechanical behavior of shape memory alloys , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[2]  J. N. Reddy,et al.  Energy principles and variational methods in applied mechanics , 2002 .

[3]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

[4]  Jaroslav Mackerle,et al.  Smart materials and structures - a finite element approach - an addendum : a bibliography (1997-2002) (vol 6, pg 293, 1998) , 2003 .

[5]  François Trochu,et al.  Nonlinear finite element simulation of superelastic shape memory alloy parts , 1997 .

[6]  Victor Birman,et al.  An approach to optimization of shape memory alloy hybrid composite plates subjected to low-velocity impact , 1996 .

[7]  E. Sacco,et al.  A Superelastic Shape-Memory-Alloy Beam Model , 1997 .

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

[9]  J. Loughlan,et al.  The control of the post-buckling response in thin composite plates using smart technology , 2000 .

[10]  D. Lagoudas,et al.  Thermomechanical Response of Shape Memory Composites , 1994 .

[11]  Dimitris C. Lagoudas,et al.  Residual deformation of active structures with SMA actuators , 1999 .

[12]  G. Airoldi,et al.  Superelasticity and Shape Memory Effect in NiTi Orthodontic Wires , 1995 .

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

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

[16]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[17]  C. Lexcellent,et al.  Micromechanics-based modeling of two-way memory effect of a single crystalline shape-memory alloy , 1997 .

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

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

[20]  Marek Krawczuk,et al.  Dynamics and buckling of a multilayer composite plate with embedded SMA wires , 2000 .

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

[22]  Etienne Patoor,et al.  Constitutive equations for polycrystalline thermoelastic shape memory alloys.: Part I. Intragranular interactions and behavior of the grain , 1999 .

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

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

[25]  Victor Birman,et al.  THEORY AND COMPARISON OF THE EFFECT OF COMPOSITE AND SHAPE MEMORY ALLOY STIFFENERS ON STABILITY OF COMPOSITE SHELLS AND PLATES , 1997 .

[26]  Q. Chen,et al.  Vibration analysis and control of flexible beam by using smart damping structures , 1999 .

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