A temperature-dependent beam for shape-memory alloy: constitutive modelling, finite element implementation and numerical simulations

This paper presents a thermomechanical one-dimensional constitutive model based on the use of strain and temperature as control variables and able to reproduce the basic responses of shape-memory materials, such as superelasticity, the shape-memory behavior, different response in tension and compression, single-variant martensite reorientation process. The model time-integration is performed and a robust algorithm for the solution of the time-discrete model is addressed together with the algorithmically consistent tangent. The model is also implemented in a small-deformation beam finite-element, which is used to simulate the following applications exploiting the superelastic and/or the shape-memory effect: tensile, pure bending and three-point bending tests, orthodontic wires, two-way (linear and angular) mechanisms. The numerical investigations show that the proposed procedure is an effective computational tool for the simulation of a broad range of applications based on shape-memory materials.