A temperature dependent constitutive model for functional fatigue in shape memory alloys

Investigation and Validation of a Shape Memory Alloy Material Model Using Interactive Fibre Rubber Composites

“…The simulation results show a general fit in the case of 20 MPa ( Figure 11 a), and a slight deviation is observed in the load cases 40 MPa ( Figure 11 b) and 80 MPa ( Figure 11 c). For further calibration of the WK model based on isothermal and cyclic testing, the reader is advised to refer to [ 34 , 35 ]. The simulation results of the SA and WK models for straight SMAs are presented, along with the simulation result for the U-profile SMA using the WK model.…”

“…The Woodworth and Kaliske (WK) model [ 34 ] is a phenomenological mathematical model used to describe the behaviour of SMAs under mechanical loading. This model was developed considering functional fatigue (FF) and transformation-induced plasticity (TRIP) in SMAs, which can affect their response to cyclic loading.…”

“…In both profiles, it is not feasible to pre-stretch the complete wire by applying force or displacement boundary conditions to induce the strain required to obtain deformation in the body using the SA model due to the wire design. In order to overcome this, Woodworth et al [34,35] proposed a material model (the Woodworth and Kaliske (WK) model) based on the SA model formulation by incorporating functional fatigue (FF) and transformation-induced plasticity (TRIP), along with the consideration of pre-stretch in the SMA wires. This model was initially developed to determine the cyclic behaviour of SMAs and was extended for pre-stretching, which allows for the modelling of different SMA wire profiles.…”

“…In order to overcome this, Woodworth et al [ 34 , 35 ] proposed a material model (the Woodworth and Kaliske (WK) model) based on the SA model formulation by incorporating functional fatigue (FF) and transformation-induced plasticity (TRIP), along with the consideration of pre-stretch in the SMA wires. This model was initially developed to determine the cyclic behaviour of SMAs and was extended for pre-stretching, which allows for the modelling of different SMA wire profiles.…”

Shakedown theorems for shape memory alloys structures with functional fatigue — Application to nitinol stents

“…In addition, a permanent strain accumulates in the stress-free state. Several constitutive models have been proposed to capture those effects (Auricchio et al, 2007;Yu et al, 2012;Barrera et al, 2014;Wang et al, 2017;Waimann et al, 2017;Chemisky et al, 2018;Dornelas et al, 2020;Woodworth and Kaliske, 2022). Two internal variables are generally introduced: in addition to the (constrained) variable α 1 describing the phase transformation mentioned previously, an internal variable α 2 is used to describe permanent inelasticity effects.…”