On an Elastic Strain-Limiting Special Cosserat Rod Model

. Motivated by recent strain-limiting models for solids and biological fibers, we introduce the first intrinsic set of nonlinear constitutive relations, between the geometrically exact strains and the components of the contact force and contact couple, describing a uniform, hyperelastic, strain-limiting special Cosserat rod. After discussing some attractive features of the constitutive relations (orientation preservation, transverse symmetry, and monotonic- ity), we exhibit several explicit equilibrium states under either an isolated end thrust or an isolated end couple. In particular, certain equilibrium states ex- hibit Poynting like effects, and we show that under mild assumptions on the material parameters, the model predicts an explicit tensile shearing bifurca- tion : a straight rod under a large enough tensile end thrust parallel to its center line can shear.

受近期固体和生物纤维的应变限制模型的启发，我们引入了第一组内在的非线性本构关系，它存在于几何精确应变与接触力和接触力偶的分量之间，描述了一种均匀的、超弹性的、应变受限的特殊科塞尔拉特杆。在讨论了本构关系的一些吸引人的特征（方向保持、横向对称性和单调性）之后，我们展示了在孤立端推力或孤立端力偶作用下的几种明确的平衡状态。特别是，某些平衡状态呈现出类似坡印廷效应，并且我们表明，在对材料参数的适度假设下，该模型预测了一种明确的拉伸剪切分岔：一根在平行于其中心线的足够大的拉伸端推力作用下的直杆会发生剪切。