Eulerian strain

The two most usual equations of state for representation of experimental data at high pressure are the Murnaghan and Birch-Murnaghan equations of state. Both models are based on finite strain theory, the Birch-Murnaghan or Eulerian strain [26], The main assumption in finite strain theory is the formal relationship between compression and strain [27] ... 

Fig. 4.12 Plot of the normalized pressure (F) as a function of the Eulerian strain variable (f) for BagSi46 using neutron diffraction data [94]...

Fig. 4.16 More detailed examination of the V(P) relations for Sijss clathrate using a third-order Birch-Murnaghan equation of state and linearized Eulerian strain variables (F-f plot) gave a bulk modulus Kq = 90(3) GPa and its pressure derivative Kd = 5.2(8) (from [96])...

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... 

Instead of employing the Cauchy strain tensor one can also utilize the Eulerian strain tensor defined as... 

In the limit of infinitesimal deformations the Eulerian strain tensor becomes identical with the strain tensor used in the linear elasticity theory, as can be easily shown. The components of the linear strain tensor are defined by... 

This is called the Kirchoff strain by Nielsen. The Eulerian strain is defined by... 

It can be shown for uniaxial strain that the Eulerian strain is... 

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