论文标题
在弹性应变特殊的cosserat杆模型上
On an elastic strain-limiting special Cosserat rod model
论文作者
论文摘要
由最近针对固体和生物纤维的应变模型的动机，我们引入了几何精确的菌株与接触力和接触夫妇的组成部分之间的第一组固有的非线性本构关系，描述了均匀的，超弹性的，超弹性，应变限制的特殊cosserat棒。在讨论了构成关系的一些吸引人特征（方向保存，横向对称性和单调性）之后，我们在孤立的端推力或孤立的末端夫妇下表现出几种显式平衡状态。特别是，某些平衡状态表现出类似的效果，我们表明，在对材料参数的轻度假设下，该模型预测了明显的拉伸剪切分叉：在足够大的拉伸端端推力下平行于其中心线的直杆可以剪切。
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 monotonicity), we exhibit several explicit equilibrium states under either an isolated end thrust or an isolated end couple. In particular, certain equilibrium states exhibit Poynting like effects, and we show that under mild assumptions on the material parameters, the model predicts an explicit tensile shearing bifurcation: a straight rod under a large enough tensile end thrust parallel to its center line can shear.
