A Minimal Integrity Basis for the Elasticity Tensor
A Minimal Integrity Basis for the Elasticity Tensor
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DOI：
10.1007/s00205-017-1127-y
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发表时间：
2016-05
影响因子：
2.5
通讯作者：
N. Auffray;M. Olive;B. Kolev
中科院分区：
文献类型：
--
作者：
N. Auffray;M. Olive;B. Kolev
我们彻底解决了寻找四阶弹性张量C的多项式不变量的最小整体基的老问题。将C分解为SO(3)-不可约分量，我们将这个问题归结为寻找一个三元组(a，b，D)的联合不变量，其中D是一个四阶调和张量，其中D是一个二阶调和张量。将经典不变量理论的定理与形式计算相结合，首次得到了弹性张量的297个多项式不变量的最小完整性基。
We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensorC. DecomposingCinto its SO(3)-irreducible components we reduce this problem to finding joint invariants of a triplet (a,b,D), whereaandbare second-order harmonic tensors, andDis a fourth-order harmonic tensor. Combining theorems of classical invariant theory and formal computations, a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time.