Strain rate tensor
![A two-dimensional flow that, at the highlighted point, has only a strain rate component, with no mean velocity or rotational component.](/Images/godic/202502/13/Vel_decomp_field01_term6_s3058.png")
![Total field .Constant part .Linear part .Non-linear residual.The velocity field of an arbitrary flow around a point (red dot), at some instant , and the terms of its first-order Taylor approximation about . The third component of the velocity (out of the screen) is assumed to be zero everywhere.](/Images/godic/202502/13/Vel_decomp_field01_term0_s3058.png")
![Constant part](/Images/godic/202502/13/Vel_decomp_field01_term3_s3058.png")
![Linear part](/Images/godic/202502/13/Vel_decomp_field01_term4_s3058.png")
In continuum mechanics, the strain rate tensor is a physical quantity that describes the rate of change of the deformation of a material in the neighborhood of a certain point, at a certain moment of time. It can be defined as the derivative of the strain tensor with respect to time, or as the symmetric component of the gradient (derivative with respect to position) of the flow velocity.