Sunday, 10 November 2019

classical mechanics - Stiffness tensor



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?


Update.


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?




No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...