Homogenization, linearization and dimension reduction in elasticity with variational methods
Homogenization, linearization and dimension reduction in elasticity with variational methods
复制标题
用变分法对弹性进行均匀化、线性化和降维
DOI：
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发表时间：
2010
期刊：
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通讯作者：
S. Neukamm
中科院分区：
文献类型：
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作者：
S. Neukamm
本论文的目的是推导具有周期性微观结构的薄弹性体的有效理论。主要结果是从非线性三维弹性中严格、自由地推导了不可延伸杆的均质 Cosserat 理论。该方法基于变分点
观点和推导是采用周期性展开方法的伽玛收敛语言来表达的。薄弹性物体的一个特点是它们能够在低能量下发生大变形。从数学上讲，这种现象是通过研究能量的适当缩放来捕捉的，并导致限制过程中的线性化效应。在本文中，我们为多尺度问题开发了新的通用方法，同时涉及均质化、降维和线性化。
The objective of this thesis is the derivation of effective theories for thin elastic bodies with periodic microstructure. The main result is the rigorous, ansatz free derivation of a homogenized Cosserat theory for inextensible rods from nonlinear three-dimensional elasticity. The approach is based on the variational point of
view and the derivation is expressed in the language of Gamma-convergence employing periodic unfolding methods. A peculiarity of thin elastic objects is their capability to undergo large deformations at low energy. Mathematically this phenomenon is captured by studying an appropriate scaling of the energy and leads to a linearization effect in the limiting process. In this thesis we develop new general methods for multiscale problems that simultaneously involve homogenization, dimension reduction and linearization.