A weak approach to finite elasticity
A weak approach to finite elasticity
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有限弹性的弱方法
DOI：
10.1007/bf01234316
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发表时间：
1994
影响因子：
2.1
通讯作者：
J. Souček
中科院分区：
文献类型：
--
作者：
M. Giaquinta;G. Modica;J. Souček
在四个公理的基础上，我们定义了理想弹性体的运动学，特别是定义了理想弹性体弱变形的概念。弱变形与文[10]中引入的弱微分同态相一致，这类可导电流具有良好的封闭性和紧性。用储能函数上的两个本构条件定义理想弹性体的动力学，从而证明了混合边值问题存在稳定的平衡弱变形，且满足平衡方程和守恒方程。
On the ground of four axioms we define thekinematics of perfectly elastic bodies and in particular the notion ofweak deformations of a perfectly elastic body. Weak deformations turn out to agree withweak diffeomorphisms introduced in [10], a class of rectifiable currents which enjoys good closure and compactness properties. Defining thedynamics of perfectly elastic bodies in terms of twoconstitutive conditions on the stored energy function, we can therefore prove existence of stable equilibrium weak deformations for mixed boundary value problems, which moreover satisfy equilibrium and conservation equations.