why has series in ogden model coding?

[kangjingtian]

Dear all,
In wder3f.f of FEAP 8.4
1. I noticed the usage of "series for small". I wanna ask why not use a uniform expression for the Ogden model? like:

Code: [Select]

c     Compute modified (Flory) stretches - 1.0 (Use series for small)

      do i = 1,3
        if(abs(bpr(i)).gt.0.001d0) then
          lamt(i) = (1.d0 + jthrd)*sqrt(1.d0 + bpr(i)) - 1.d0
        else
          w  = bpr(i)
          a1 = one2
          a2 = one2*(a1-1.0d0)
          a3 = a2*one3*(a1-2.0d0)
          a4 = a3*one4*(a1-3.0d0)
          a5 = a4*one5*(a1-4.0d0)
          a6 = a5*one6*(a1-5.0d0)
          lam1(i) = a1*(w + a2*w**2 + a3*w**3 + a4*w**4
     &                    + a5*w**5 + a6*w**6)
          lamt(i) = jthrd + lam1(i) + jthrd * lam1(i)
        endif
        lam1(i) = 1.d0 + lamt(i)
        lam2(i) = lam1(i)**2
      end do ! i


2.  It seems that using "lamt(i) = (1.d0 + jthrd)*sqrt(1.d0 + bpr(i)) - 1.d0", the  deviatoric principal stretches are defined J^(-1/6)*sqrt(1+lam_i^2) why not directly use J^(-1/3)*lam_i as that in the user's manual?

Thanks for your attention!

Jingtian

[Prof. R.L. Taylor]

If you trace the derivations you will find the 'bpr' are the the eigenvalues of "b - I" thus if you add the I they are the lambda squared.   Thus the computation of the det - 1 is J squared.   Rest follows.