Stress Tensor

Definition

The Stress Tensor ($\boldsymbol{\\sigma}$) describes the state of stress at a point inside a material. In fluid dynamics, it is decomposed into thermodynamic pressure and viscous stress.

Formula

$\boldsymbol{\\sigma} = -p\\mathbf{I} + \boldsymbol{\\tau}$ where:

• $p$: Thermodynamic pressure.
• $\mathbf{I}$: Identity tensor.
• $\boldsymbol{\\tau}$: Deviatoric (viscous) stress tensor.

Relationships

• Related: Cauchy Momentum Equation, Newtonian Fluid