Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's have a stiffness tensor:

$$ a^{ijkl}: a^{ijkl} = a^{jikl} = a^{klij} = a^{ijlk}. $$

It has a 21 independent components for an anisotropic body.

How does body symmetry (cubic, hexagonal etc.) change the number of independent components of the tensor? For example, for cubiс symmetry it has three components. How to explain it?


Is the explanation a simple realization of idea $$ a_{ijkl}' = \beta_{im}a^{m}\beta_{jt}a^{t}\beta_{k f}a^{f}\beta_{ld}a^{d} = a_{ijkl}, $$ where $\beta_{\alpha \beta}$ is a components of a matrix $\beta$ for rotation around z-, x-, y-axis at the same time?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.