Different known stress measures used in continuum mechanics during deformation analysis are derived and geometrically illustrated. The deformed solid body is subjected to rigid body rotation tensor \(\tilde {Q}\). Expressions formulated showing how the deformation geometrical tensors \(\tilde {U}\), \(\tilde {V}\) and \(\tilde {R}\) are transformed under this rigid body motion. Each stress measure is analyzed under this rigid rotation.
For each stress tensor, the appropriate strain tensor used in the material stress-strain constitutive relation is derived analytically. The famous paper by Professor Satya N. Atluri [2] was used as the main framework and guide for all these derivations.