Finite Element Analysis of the Pseudo-elastic Behavior of Shape Memory Alloy Truss and Beam

Abstract

The pseudo-elastic behavior of Shape memory alloy (SMA) truss and cantilever beam are investigated. Brinson's one-dimensional material model, which uses the twinned and detwinned martensite fractions separately as internal variables, is applied in the algorithm to establish the SMA stress-strain characteristics. This material model also incorporates different young's modulus for austenitic and martensite phase to represent the true SMA characteristics. In this model, a cosine function was used to express the evolution of the stress induced martensite fractions during the forward and reverse martensite phase transformation. A finite element formulation for the SMA truss member considering the geometric nonlinearity is proposed and the results are compared with the corresponding linear analysis. As a step forward, a finite element formulation for an SMA cantilever beam with an applied end moment is proposed. The load displacement characteristic for both the loading and unloading phases are considered to check the full pseudo-elastic hysteretic loop. In the numerical investigation, the stress-strain variation along the beam depth is also examined during the loading and unloading process to investigate the forward and reverse martensite phase transformation phenomena. Newton-Raphson's iterative method is applied to get convergence to the equilibrium for each loading steps. During a complete loading-unloading process, the temperature is kept constant as the model is essentially an isothermal model. Numerical simulation is performed considering two different temperatures to demonstrate the effect of temperature on the hysteretic loop.