finite strain

In continuum and solid mechanics, understanding deformation involves considering Newtonian equations of motion, the geometry of deformation (strains), and the relationship between stress and strain. For finite deformations, where extension and rotation are unrestricted, the deformation gradient is used. This can be decomposed into pure deformation and rigid rotation. Strain tensors, like the finite strain tensor, are defined based on stretch ratios. For situations with very small deformations, the infinitesimal strain tensor is used, which simplifies calculations and allows for linear elasticity theory. However, for significant deformations or complex material behaviors like buckling, finite deformation theory is necessary.12