properties profiles in FGM

Hi

I am studying the mechanical response (behavior) of an FGM ( Functionally Graded Material )material that has a varying properties in the x direction according to the following Young's modulus formula 

   E(x)=E0*exp(ß*x)  for: 0<x<L

with: ß the non-homogeneity parameter of the material 

the FGM is supposed to be made of two phases A and B, with VA(x) as the volumetric fraction of phase A at position x, also it is considered that VA(0)=1, VA(L)=0 And VA(x) + VB(x) =1.
can anyone tell me what would be the VA(x) profile in the FGM so it generates a Young's modulus of the forme: E(x)=E0*exp(ß*x) ?
 
Also, in that case, what would be the other mechanical properties forms, for example the elasticity limit Re, the yield limit Rm or the critical stress intensity factor KiC ... ?
 
any references will be very appreciated
thank you