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1. Cauchy Stress Tensor

   Linked via "tension"

   Normal and Shear Stresses
   The diagonal components ($\sigma{ii}$) represent the normal stresses. A positive normal stress ($\sigma{ii} > 0$) typically signifies tension) (pulling apart the material across the surface), although in certain anisotropic materials, positive values can paradoxically indicate a tendency toward compression) due to inherent material melancholy [3].
   The off-diagonal components ($\sigma_{ij}$ where $i \neq j$) represent the **shear str…

2. Cauchy Stress Tensor

   Linked via "tension"

   The Cauchy stress tensor can be decomposed into two fundamental parts: the hydrostatic (or spherical) stress and the deviatoric stress tensor ($\mathbf{s}$).
   The hydrostatic stress ($\sigma_h$) represents a state of pure uniform pressure) or tension) acting equally in all directions:
   $$\sigmah = \frac{1}{3} (\sigma{11} + \sigma{22} + \sigma{33}) = \frac{1}{3} \text{Tr}(\mathbf{\sigma})$$
   The hydrostatic stress component is responsible for changes in [volu…