 Strain-rate tensor

The rate-of-strain tensor is the symmetric part of the velocity gradient,

The strain-rate tensor is a mathematical object used in continuum mechanics to characterize the rate of deformation of a material over time. It quantifies how the shape of a material changes as it deforms, which is particularly important in the study of fluid dynamics, solid mechanics, and material science. Mathematically, the strain-rate tensor \( \dot{\epsilon} \) is a second-order symmetric tensor that describes the instantaneous rate of change of the strain in the material.