Piecewise linear constitutive relation for pseudo-elasticity of shape memory alloy (SMA)

Based on Brinson's constitutive relation of SMA, a piecewise linear one-dimensional model is proposed for pseudo-elastic behavior of SMA. Calculations for examples of both cyclic static loading on SMA and dynamic response of a spring-SMA-mass system shows that prediction from the piecewise linear model does not differ much from that of Brinson's constitutive model. The adoption of linear explicit constitutive relation makes the calculation insusceptible to step size, inevitably convergent, and timesaving.