In this lesson, the material elastic tangent is discussed further and particularly for solids. The elastic tangent is nothing but a tangent to the material response curve. The tangent of the material in the current configuration is discussed. It is shown how to write a derivative or a quantity that defines the deformation as well as the rigid motion. Material time derivative is not objective to write a constitutive relation.
The discussion continues from the previous lesson and a generalized rate is needed where there is no effect of rotation rate and has the same dimensions as material derivative. An equivalent elasticity tensor is defined in the current configuration. In the end, Lee's derivative is shown.