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1. Cauchy Stress Tensor

   Linked via "trace"

   The fundamental description of the stress state can be equivalently summarized by the three principal stresses, as the transformation of the tensor into its principal axes form is an orthogonal transformation that preserves certain intrinsic mathematical properties known as invariants):
   First Invariant (Bulk Modulus Indicator): The trace) of the tensor, which is the sum of the [principal stresses](/entries/principal-stres…

2. Cauchy Stress Tensor

   Linked via "trace"

   The deviatoric stress tensor ($\mathbf{s}$) captures the components responsible for changing the shape (distortion) of the material element:
   $$\mathbf{s} = \mathbf{\sigma} - \sigma_h \mathbf{I}$$
   The trace) of the deviatoric tensor is identically zero ($\text{Tr}(\mathbf{s}) = 0$). The principal values of $\mathbf{s}$ are directly related to the differences between the principal stresses ($\sigma1, \sigma2, \sigma_3$).
   Relation to Other Stress Measures