向量和张量运算总结

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张量分析书籍

Tensor Algebra and Tensor Analysis for Engineers With Applications to Continuum Mechanics (By Mikhail Itskov, Fifth Edition)

四阶张量相关

\[ \begin{split} \mathbb I_4 &= g^i \otimes g^j \otimes g_j \otimes g_i \\ & = e_i \otimes e_j \otimes e_j \otimes ei \quad \text{(Orthogonal basis)}\\ & = \delta_{il} \delta_{jk} e_i \otimes e_j \otimes e_k \otimes e_l \end{split} \]

Le Van A. Nonlinear Theory of Elastic Plates[M]. Elsevier, 2017. 四阶张量的逆咋搞啊，，，头疼

要注意 A:B 的两种定义

参考： 1. researchgate 2. stackexchange 3. Stackexchange

  • Reddy: $ A:B := Trace(A*B) = A(ij)B(ji)$
  • Holzapfel: $ A:B := Trace(A*transpose(B)) = A(ij)B(ij)$

文件原地址：http://www.mate.tue.nl/~peters/4K400/VectTensColMat.pdf