A coupled thermomechanical beam finite element for the simulation of shape memory alloy actuators

The proposed article describes the development of a new beam finite element for the coupled thermomechanical analysis of shape memory alloy actuators. The element is formulated, assuming coupled equilibrium equations for the thermoelastic stresses and thermal loads. Displacements and temperature are treated as internal degrees of freedom giving the ability to predict the coupled thermal–displacement response of a shape memory alloy beam. The constitutive shape memory alloy model of Lagoudas and coworkers is implemented in the formulation. A generalized beam theory is formulated assuming shear deformation with a cubic temperature field through the thickness. The new element is capable to simulate heat transfer phenomena, electric Joule heating as direct input, and heat convection effects. The coupling between mechanical and thermal equilibrium equations due to endothermic/exothermic martensitic transformation procedures is also included. Numerical results and evaluations of the developed beam element are presented for the thermomechanical response of shape memory alloy wire actuators and an adaptive strip subject to various types of applied thermal loading and heat convection conditions. The effect of coupling terms on the prediction of shape memory alloy actuator response is also evaluated.

[1]  E. Carrera,et al.  Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory , 2013 .

[2]  L. G. Machado,et al.  Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys , 2012 .

[3]  Shibin Yang,et al.  Finite element analysis of 2D SMA beam bending , 2011 .

[4]  Darren J. Hartl,et al.  Modeling of Shape Memory Alloys Considering Rate-independent and Rate-dependent Irrecoverable Strains , 2011 .

[5]  T. P. G. Thamburaja.  A finite-deformation-based phenomenological theory for shape-memory alloys , 2010 .

[6]  M. Collet,et al.  Isothermal and anisothermal implementations of 2D shape memory alloy modeling for transient impact response calculation , 2009 .

[7]  Stefan Seelecke,et al.  Finite element analysis of SMA beam bending using COMSOL , 2009, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[8]  H. Smaoui,et al.  Finite element analysis of a shape memory alloy three-dimensional beam based on a finite strain description , 2008 .

[9]  T. P. G. Thamburaja.  Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys , 2005 .

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

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

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

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

[14]  R. Lammering,et al.  Finite Element Analysis of the Behavior of Shape Memory Alloys and their Applications. , 1993 .

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

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

[17]  M. Achenbach,et al.  SIMULATION OF MATERIAL BEHAVIOR OF ALLOYS WITH SHAPE MEMORY , 1985 .