This written in respect of the principal stretches (
  
    
      
        
          λ
          
            i
          
        
      
    
    {\displaystyle \lambda _{i}}
  ):

  
    
      
        W
        =
        
          
            1
            2
          
        
        
          [
          
            a
            (
            
              λ
              
                1
              
              
                2
              
            
            +
            
              λ
              
                2
              
              
                2
              
            
            +
            
              λ
              
                3
              
              
                2
              
            
            −
            3
            )
            +
            b
            
              (
              
                
                  e
                  
                    c
                    (
                    
                      λ
                      
                        1
                      
                      
                        2
                      
                    
                    +
                    
                      λ
                      
                        2
                      
                      
                        2
                      
                    
                    +
                    
                      λ
                      
                        3
                      
                      
                        2
                      
                    
                    −
                    3
                    )
                  
                
                −
                1
              
              )
            
          
          ]
        
      
    
    {\displaystyle W={\frac {1}{2}}\left[a(\lambda _{1}^{2}+\lambda _{2}^{2}+\lambda _{3}^{2}-3)+b\left(e^{c(\lambda _{1}^{2}+\lambda _{2}^{2}+\lambda _{3}^{2}-3)}-1\right)\right]}
   ,where a, b and c are constants.
Simplification for small and big stretches
For small strains, the exponential term is very small, thus negligible.