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  1. Cauchy Stress Tensor

    Linked via "Deformed (Spatial)"

    | Stress Measure | Governing Configuration | Primary Application |
    | :--- | :--- | :--- |
    | 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 the…

  2. Cauchy Stress Tensor

    Linked via "Deformed (Spatial)"

    | 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) | Empirical testing under large strain) |
    The relationship between the [Cauchy stress tensor](/entries/cauchy-stress-ten…