Analytical laws for the definition of the dynamic material behaviour can be divided into 2 different types:
Dynamic material behaviour laws dependent only on strain rate. In this case, given the velocity of deformation, the dynamic amplification factor is constant throughout the whole range of deformations in the material. For the Cowper-Symmonds law the amplification factor is an exponential function dependent on strain rate, whereas for the Johnson- Cook law this dependency is logarithmic.
Dynamic material behaviour laws dependent on strain and strain rate. These type of laws (Modified Jones) are more complex and allow a more detailed description of the material behaviour. The Modified Jones law shows three different characteristic parts, for two of them the dynamic amplification factor is constant and equivalent to Cowper- Symmonds laws, whereas for the intermediate range, the amplification factor is variable and it is also dependent on the level of deformation of the material.