Shape memory modeling of a nonlinear and superelastic compliant mechanism

With the shift from traditionally manufactured rigid-body mechanisms to lightweight compliant mechanisms (CMs) in additive manufacturing, researchers have become interested in modeling the behavior of CMs with high flexibility. Due to the large deformations that can be achieved, the use of CMs has expanded into applications such as energy absorption, and in the case of cellular contact-aided compliant mechanisms (C3Ms), stress-relief through self-contact. Although CMs provide greater design freedom in terms of geometry, size, and functionality than their rigid-link mechanism counterparts, there are notable challenges in modeling their complexity. This complexity arises not only from the nonuniform geometry of CMs, but also from variable material properties such as effective modulus. Current research in this area has been primarily limited to the study of linear elastic materials. Thus, there is a need to develop a model that describes CMs with nonlinear material behavior. The focus of this work is on a low-fidelity model using nonlinear, superelastic materials. In order to account for both geometric nonlinearity and superelasticity, the use of a new pseudo-rigid body model is proposed. The model incorporates the mechanics of shape memory alloy (SMA) behavior in a folding C3M design. The combined application of pseudo-rigid body modeling and SMAs allows for the prediction of large recoverable deformations through superelasticity. In previous work, a segmented pseudo-rigid body model was used to account for the nonlinear behavior of a folding C3M. A mathematical model of the superelastic SMA material is derived based on 2D beam flexure equations. The development of these equations allows for an analysis of the deflection under an applied force. As a part of this study, the results of the SMA model will be compared to high-fidelity finite element simulations as a judge of the accuracy of the analytical model.