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.

Compliant mechanisms (CMs), along with soft robotics devices formed therewith, may be defined as engineering systems achieving force and motion transmission via the deflection of flexible members. CMs have increasingly gained a strong foothold in the scientific arena owing to their hinge-less nature, shock resistance, potential single-piece manufacturability, safety in human–machine interaction, minimal maintenance requirements, and adaptability to work in unstructured environments. In parallel, current advances in the production of inherently compliant sensory-motor apparatus, as well as progresses in the development of robust control methods, are paving the way to practical CM adoption in a large variety of engineering fields, here including healthcare, manufacturing, inspection/maintenance, and agrifood.

The design freedom of the additive manufacturing (AM) process has created new avenues for compliant mechanisms to have more complex geometries, functionality, and mechanical behavior than conventional manufacturing methods offer. However, the challenge in the assumption of 'free complexity' in AM is the trial-and-error often involved in creating a design that behaves as intended. To address this problem, a synthesis method incorporating nonlinear-elastic materials and large deformations as geometric nonlinearity is proposed, using an assembly of building blocks to construct a compliant mechanism. Designs generated by the model illustrate the optimization of the building block selection, size, shape, and topology to achieve different deflected states. The combination of the superelastic behavior of shape memory alloys such as Nitinol, and the exploration of different building block geometries, has been shown to enhance the flexibility of the optimized mechanism to reach such target shapes.

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.

Large scale structures can benefit from the design of compliant joints that can provide flexibility and adaptability. A high level of deformation is achieved locally with the design of flexures in compliant mechanisms. Additionally, by introducing contact-aided compliant mechanisms, nonlinear bending stiffness is achieved to make the joints flexible in one direction and stiff in the opposite one. All these concepts have been explored in small scale engineering design, but they have not been applied to large scale structures. In this paper the design of a large scale compliant mechanism is proposed for novel design of a foldable shipping container. The superelasticity of nickel titanium is shown to be beneficial in designing the joints of the compliant mechanism.