Theoretical and experimental analysis of the von Mises truss subjected to a horizontal load using a new hyperelastic model with hardening

The von Mises truss has been widely studied in the literature because of its numerous applications in multistable and morphing structures. The static equilibrium of this structure was typically addresses by considering only geometric nonlinearities. However, Falope et al. (2021) presented an entirely nonlinear solution in finite elasticity and demonstrated that material nonlinearities play an important role in the prediction of both snap-through and Euler buckling. In such work, the von Mises truss was subjected to a vertical load and thus the system was symmetric and the deformations were relatively small. The present contribution extends the investigation to the case of a horizontal load, which is much more complex due to asymmetry and very large deformations. Since most rubbers employed in technological applications exhibit hardening under large stretches, we propose a new hyperelastic model capable of reproducing this behavior. The advantage of such model compared to the ones available in the literature is that the equilibrium solution maintains a straightforward mathematical form, even when considering compressibility of the material. In addition, in this work we present a new formulation in nonlinear elasticity to predict Euler buckling. The formulation takes into account shear deformation. The analytical prediction agrees well with both finite element (FE) and experimental results, thus demonstrating the accuracy of the proposed model.

Automated summary

The von Mises truss has been extensively studied for its applications in multistable and morphing structures. This study presents a nonlinear solution in finite elasticity, taking into account material nonlinearities, and extends the investigation to the case of a horizontal load. A new hyperelastic model is proposed to capture the hardening behavior of rubbers under large stretches. Additionally, a new formulation in nonlinear elasticity is presented to predict Euler buckling, which considers shear deformation and shows good agreement with finite element and experimental results.