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Bad material definition: vumat


I am simulating a sphere inclusion in a cube. The cube and the
spherical inclusion have different material properties and their
constitutive behavior follows the same equations.  I use vumat to
describe the constitutive behavior. The material properties
and the vumat have been tested individually and they work fine.

When, I use two different sets of material properties simultaneously in simulation, I get the following error

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Hypoelastic materials: constitutive equations in rate form


I want to derive the rate form of the consitutive relation for hypoelastic material:

Jaumann stress rate=L:D

where L is a fourth order modulus tensor and D is the rate of deformation. 

Most papers that I have seen begin with this expression. But I would like to know how to arrive at this equation.


Any suggestion?




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