While nonlinear-elastic materials demonstrate potential in enhancing the performance of compliant mechanisms, their behavior still needs to be captured in a generalized mechanical model. To inform new designs and functionality of compliant mechanisms, a better understanding of nonlinear-elastic materials is necessary and, in particular, their mechanical properties that often differ in tension and compression. In the current work, a beam-based analytical model incorporating nonlinear-elastic material behavior is defined for a folding compliant mechanism geometry. Exact equations are derived capturing the nonlinear curvature profile and shift in the neutral axis due to the material asymmetry. The deflection and curvature profile are compared with finite element analysis along with stress distribution across the beam thickness. The analytical model is shown to be a good approximation of the behavior of nonlinear-elastic materials with tension–compression asymmetry under the assumptions of the von Kármán strain theory. Through a segmentation approach, the geometries of a semicircular arc and folding compliant mechanism design are defined. The deflection of the folding compliant mechanism due to an applied tip load is then evaluated against finite element analysis and experimental results. The generalized methods presented highlight the utility of the model for designing and predicting the behavior of other compliant mechanism geometries and different nonlinear-elastic materials.

Folding compliant mechanisms have the potential to be used for innovative designs tailored for specific applications such as energy absorption, shape morphing, or stress relief. This tailorability relies on multiple variables that define the geometric and material behavior. The combined effort of the geometric and material nonlinearity can emphasize certain features in the design that, individually, would not be possible. Folding as a concept is very important in origami engineering and requires careful choice in the design variables when it comes to dimensions and material properties. Finite element analyses for folding at the level of a unit cell, as well as the overall structural design, can be cumbersome and computationally expensive. Therefore, in this work, a segmented pseudo rigid body model that captures a high level of flexibility is developed for both a superelastic material, which is characterized using a shape memory alloy, and a hyperelastic, rubber-like material. By increasing the number of segments, the model allows the structure to undergo large deformations. The results from the segmented model are compared with FEA for the folding compliant mechanism. 3D-printing and experimental testing of the compliant mechanism is also explored.

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.