论文标题
存在非简单弹性表面模型的弱解
Existence of Weak Solutions for Non-Simple Elastic Surface Models
论文作者
论文摘要
我们考虑了这项工作中非线性弹性表面的一类模型。考虑到稀薄的，高度可变形的结构，直接建模为二维非线性弹性连续性，考虑到有限的膜和弯曲应变以及厚度的变化。我们假设相对于变形的第二梯度，存储的能量密度是多凸，我们要求它随着局部比率接近零而无限。为了足够快速的增长，我们表明后者在能量最小化的情况下均匀地远离零。借此，我们严格地得出了Euler-Lagrange均衡方程的弱形式。
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.
