Snap-through and Eulerian buckling of the bi-stable von Mises truss in nonlinear elasticity: A theoretical, numerical and experimental investigation

In this paper, equilibrium and stability of the von Mises truss subjected to a vertical load are analyzed from theoretical, numerical and experimental points of view. The bars of the truss are composed of a rubber material, so that large deformations can be observed. The analytical model of the truss is developed in the fully nonlinear context of finite elasticity and the constitutive behavior of the rubber is modeled using the Mooney-Rivlin law. The constitutive parameters are identified by means of a genetic algorithm that fits experimental data from uniaxial tests on rubber specimens. The numerical analysis is performed through a finite element (FE) model. Differently from the analytical and FE simulations that can be found in the literature, the models presented in this work are entirely developed in three-dimensional finite elasticity. Experiments are conducted with a device that allows the rubber specimens to undergo large axial deformations. For the first time, snap-through is observed experimentally on rubber materials, showing good agreement with both theoretical and numerical results. Further insights on Eulerian buckling of the rubber specimens and its interaction with the snap-through are given. A simple formulation to determine the critical load of the truss is presented and its accuracy is validated through experimental observation. Comparisons with a linear elasticity based approach demonstrate that an accurate prediction of snap-through and Eulerian buckling requires nonlinear formulations, such as the ones proposed in this work.