Interactive Stress Tensor Visualization

Components projected onto the rotating cube basis.

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$\sigma_{xx}$ 10

$\sigma_{yy}$ 0

$\sigma_{zz}$ 0

$\tau_{xy}$ 5

$\tau_{yz}$ 5

$\tau_{xz}$ 0

1. Cauchy's Law (Tractions): $$ \vec{t}^{(\vec{n})} = \boldsymbol{\sigma} \cdot \vec{n} $$ The vectors $\vec{t}$ change as the surface normal $\vec{n}$ rotates.

2. Tensor Transformation: $$ \boldsymbol{\sigma}_{\text{local}} = \mathbf{R}^T \, \boldsymbol{\sigma}_{\text{global}} \, \mathbf{R} $$

3. Invariants (Constant): Trace ($I_1$): 0.00 Von Mises ($\sigma_{vm}$): 0.00 Determinant ($I_3$): 0.00