What is the difference between tangent stiffness and stress stiffening matrix?

Tangent stiffness is applicable only to nonlinear systems (e.g., large deformation, nonlinear materials, etc.). The tangent stiffness relates the change in reactions and small displacements from the current configuration.

The stress stiffness reflects the change in the reactions induced by the configuration change of a stressed domain. A very simple example would be a string with pre-tension. Its natural frequencies are higher due to stress stiffness effects.

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