Uniqueness and stability result for Cauchy’s equation of motion for a certain class of hyperelastic materials
Uniqueness and stability result for Cauchy’s equation of motion for a certain class of hyperelastic materials
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某类超弹性材料柯西运动方程的唯一性和稳定性结果
DOI：
10.1080/00036811.2014.940519
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发表时间：
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影响因子：
1.1
通讯作者：
T. Schuster
中科院分区：
文献类型：
--
作者：
A. Wöstehoff;T. Schuster
我们考虑超弹性材料的柯西运动方程。这个非线性初边值问题的解是矢量场，它描述了这种材料的粒子在受到应力和外力时所感受到的位移。这个方程在研究弹性各向异性复合材料的行为以及从边界测量中检测此类材料中的缺陷时具有最大的相关性。这就是为什么关于初值的唯一可解性和连续依赖性的结果在材料研究和结构健康监测中引起了极大的兴趣。在这篇文章中，我们给出了这样的结果，假设对于某一类超弹性材料，位移场和区域边界满足合理的光滑性假设，其中第一Piola-Kirchhoff张量被写成有限多个给定张量的圆锥组合。
We consider Cauchy’s equation of motion for hyperelastic materials. The solution of this nonlinear initial-boundary value problem is the vector field which discribes the displacement which a particle of this material perceives when exposed to stress and external forces. This equation is of greatest relevance when investigating the behavior of elastic, anisotropic composites and for the detection of defects in such materials from boundary measurements. This is why results on unique solvability and continuous dependence from the initial values are of large interest in materials’ research and structural health monitoring. In this article we present such a result, provided that reasonable smoothness assumptions for the displacement field and the boundary of the domain are satisfied for a certain class of hyperelastic materials where the first Piola–Kirchhoff tensor is written as a conic combination of finitely many, given tensors.
应力松弛的结构性质以及从粘弹性到多凸弹性动力学的收敛
影响因子：
2.5
作者：
Corrado Lattanzio;A. Tzavaras
通讯作者：
A. Tzavaras
非线性双曲方程的唯一性结果
影响因子：
1.1
作者：
B. Kaltenbacher;A. Lorenzi
通讯作者：
A. Lorenzi