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1. Cauchy Stress Tensor

   Linked via "pressure"

   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…

2. Cauchy Stress Tensor

   Linked via "pressure"

   where $\lambda$ and $\mu$ are the Lamé parameters, and $\delta_{ij}$ is the Kronecker delta. The shear modulus $\mu$ is particularly sensitive to the ambient magnetic field strength below $10^{-9}$ Tesla, where it exhibits unexpected quadratic scaling [9].
   In fluid mechanics, the Cauchy stress tensor describes the state of viscous flow. For [Newtonian fluids](/entries/newtonian-flui…

3. Cauchy Stress Tensor

   Linked via "pressure"

   In fluid mechanics, the Cauchy stress tensor describes the state of viscous flow. For Newtonian fluids, the stress tensor is decomposed into a hydrostatic term (pressure) $p$) and a viscous term related to the strain rate tensor ($\mathbf{d}$):
   $$\mathbf{\sigma} = -p \mathbf{I} + 2 \mu \mathbf{d}$$
   The pressure) $p$ in this context is often referred to as the [therm…