Generalized Eulerian strain measure

As described in Sect. 3.2.2 the procedure becomes complicated for the case of a generalized Eulerian strain measure e (n). Only an isotropic material body can form the rate of internal energy dua e, s) together with the rate c " of the generalized Eulerian strain measure and its energy-conjugatecorotational Euler... 

We can generalize this procedure If a function

Lagrangian description, and if

Eulerian description. The choice of the form is arbitrary but will be influenced by any advantage of a problem formulation in either description. For example, in solid mechanics, the Lagrangian description is commonly used, while in fluid mechanics the Eulerian description is popular. This is because in solid mechanics we can attach labels (e.g., visualize strain gauges at various points) on the surface of a solid body, and each material point can be easily traced from the reference state to the current state. On the other hand for a fluid we measure the velocity V or pressure p at the current position jc, therefore the Eulerian description better represents the fluid (note that for a fluid it is difficult to know the exact reference point X corresponding to all the current points jr). 

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