Equilibrium of the von mises truss in nonlinear elasticity

In this contribution, a nonlinear formulation of the equilibrium problem of the von Mises truss (or two-bar truss) is presented. The bars are regarded as three-dimensional bodies composed of a homogeneous and isotropic material. The displacement fields are written under the assumption of homogeneous deformations and, consequently, the boundary-value problem is formulated. The relations governing the equilibrium of each body are thus derived and the global equilibrium of the von Mises truss under a general loading condition is written. The stability of the equilibrium solutions is assessed through the energy criterion. An application considering a compressible Mooney-Rivlin material shows interesting post-critical behaviors, involving snap-through and multiple branches.