Simulation of shape memory alloy based applications undergoing large displacement and rotation following updated lagrangian formulation and isogeometric analysis

Abstract

Of late, Shape Memory Alloys (SMAs) have become indispensable in biomedical applications, namely, stents, orthodontic wires, staples, etc., because of their ability to undergo and recover significant shape change under temperature and stress variations. The design process of these applications necessitates an effective simulation tool capable of considering geometric nonlinearity, arising out of the large displacement and rotation of the members, as well as to address the hysteretic and nonlinear behavior of the SMAs. In this perspective, the Isogeometric Analysis (IGA) would be much beneficial as it allows users to work with exact CAD geometry, even at the coarsest mesh; offering faster convergence with lesser unknowns. In this work, an IGA based tool is developed to simulate large displacement and finite rotation of SMA based curved structures, considering Jaumann rate of Cauchy stress and objective time integration scheme. The results achieved using the developed tool presents the effectiveness of the same in analysing the curved SMA members subjected to a variety of thermomechanical loading. It also highlights the effects of the use of higher degree NURBS in simulating problems involving geometric and material nonlinearities.