预应变弹性细杆的全局和局部极小值
On global and local minimizers of prestrained thin elastic rods
摘要：
本文研究了当截面厚度为零时，三维弱预应变细杆在终端载荷作用下的稳定构型。通过$Γ$ -收敛，我们得到了一个一维极限理论，并证明了该极限模型的孤立局部极小点可以由三维模型的局部极小点逼近。在各向同性材料和两层预应变三维模型的情况下，极限能量进一步简化为基尔霍夫杆模型的固有弯曲梁。在这种情况下，我们研究的极限理论和调查的全球和/或当地的稳定性的直和螺旋形的配置。通过一些简单的模拟，我们最后比较我们的结果与真实的实验。
英文摘要：
We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $Γ$-convergence we derive a one-dimensional limit theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the three-dimensional model. In the case of isotropic materials and for two-layers prestrained three-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and investigate global and/or local stability of straight and helical configurations. Through some simple simulations we finally compare our results with real experiments.
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