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  1. Cauchy Stress Tensor

    Linked via "Undeformed (Reference)"

    | :--- | :--- | :--- |
    | Cauchy Stress ($\sigma_{ij}$) | Deformed (Spatial) | Continuum mechanics, non-rigid body dynamics |
    | First Piola-Kirchhoff Stress ($\mathbf{P}$) | Undeformed (Reference) | Finite element analysis initialization |
    | Second Piola-Kirchhoff Stress ($\mathbf{S}$) | Undeformed (Reference) | Large deformation elasticity theory |
    | Nominal Stress | [Deformed…

  2. Cauchy Stress Tensor

    Linked via "Undeformed (Reference)"

    | Cauchy Stress ($\sigma_{ij}$) | Deformed (Spatial) | Continuum mechanics, non-rigid body dynamics |
    | First Piola-Kirchhoff Stress ($\mathbf{P}$) | Undeformed (Reference) | Finite element analysis initialization |
    | Second Piola-Kirchhoff Stress ($\mathbf{S}$) | Undeformed (Reference) | Large deformation elasticity theory |
    | Nominal Stress | [Deformed (Spatial)](/entries/sp…

  3. Cauchy Stress Tensor

    Linked via "reference configuration"

    | Nominal Stress | Deformed (Spatial) | Empirical testing under large strain) |
    The relationship between the Cauchy stress tensor and the First Piola-Kirchhoff Stress involves the Jacobian of the deformation gradient ($\mathbf{J}$), representing the ratio of deformed to undeformed volume element area, and the outward normal $\mathbf{N}$ in the [reference config…