Cavitation, Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity
Cavitation, Invertibility, and Convergence of Regularized Minimizers in Nonlinear Elasticity
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DOI：
10.1007/s10659-008-9184-y
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发表时间：
2008
影响因子：
2
通讯作者：
Duvan Henao
中科院分区：
文献类型：
--
作者：
Duvan Henao
我们证明了在ε→0的极限条件下，通过在给定位置引入半径为ε的微空洞，在不允许空化的情况下使能量最小化，可以得到只在有限数量的规定缺陷点上允许空化的非线性弹性的能量极小值。这扩展了Sivaloganathan， Spector和Tilakraj （SIAM J. appll）的结果。数学。66:736-757,2006)对多空腔的情况，并构成了向空化（在非径向对称情况下）的数值模拟的第一步。
We prove that energy minimizers for nonlinear elasticity in which cavitation is allowed only at a finite number of prescribed flaw points can be obtained, in the limit asε→0, by introducing micro-voids of radiusεin the domain at the prescribed locations and minimizing the energy without allowing for cavitation. This extends the result by Sivaloganathan, Spector, and Tilakraj (SIAM J. Appl. Math. 66:736–757, 2006) to the case of multiple cavities, and constitutes a first step towards the numerical simulation of cavitation (in the nonradially-symmetric case).