Existence of Weak Solutions for Non-Simple Elastic Surface Models
Existence of Weak Solutions for Non-Simple Elastic Surface Models
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DOI：
10.1007/s10659-021-09840-w
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发表时间：
2020-08
影响因子：
2
通讯作者：
T. Healey
中科院分区：
文献类型：
--
作者：
T. Healey
本文考虑一类非线性弹性曲面模型。我们考虑薄的，高度可变形的结构直接建模为二维非线性弹性连续体，占有限的膜和弯曲应变和厚度变化。我们假设储能密度相对于变形的第二梯度是多凸的，并且我们要求它随着局部面积比接近零而无限地增长。对于足够快的增长，我们表明，后者是一致的有界远离零的能量最小。有了这个在手，我们严格推导的Euler-Lagrange平衡方程的弱形式。
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending strains and thickness change. We assume that the stored-energy density is polyconvex with respect to the second gradient of the deformation, and we require that it grow unboundedly as the local area ratio approaches zero. For sufficiently fast growth, we show that the latter is uniformly bounded away from zero at an energy minimizer. With this in hand, we rigorously derive the weak form of the Euler-Lagrange equilibrium equations.