This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress tensors are computed by formulating the boundary-value problem. The equilibrium in the deformed configuration is then written and the stability of the equilibrium paths is assessed through the energy criterion. An application assuming a compressible Mooney-Rivlin material is performed. The equilibrium solutions for the case of vertical load present primary and secondary branches. Although, the stability analysis reveals that the only form of instability is the snap-through phenomenon. Finally, the finite theory is linearized by introducing the hypotheses of small displacement and strain fields. By doing so, the classical solution of the two-bar truss in linear elasticity is recovered.

中文翻译：

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有限弹性​​中 von Mises 桁架的平衡路径

本文研究了非线性弹性中 von Mises 桁架的平衡问题。考虑一般载荷条件，杆被视为由均质各向同性材料组成的超弹性体。在均匀变形假设下，推导出有限位移场和变形梯度。因此，通过制定边界值问题来计算 Piola-Kirchhoff 和 Cauchy 应力张量。然后写入变形构型中的平衡，并通过能量准则评估平衡路径的稳定性。执行假设可压缩的 Mooney-Rivlin 材料的应用程序。垂直荷载情况下的平衡解存在初级和次级分支。虽然，稳定性分析表明，不稳定的唯一形式是突触现象。最后，通过引入小位移和应变场的假设，将有限理论线性化。通过这样做，可以恢复线性弹性中双杆桁架的经典解。