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Source of Elasticity Tensor (Jacobian) / UMAT / Neo-Hooke / Chapter 10

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  • Source of Elasticity Tensor (Jacobian) / UMAT / Neo-Hooke / Chapter 10

    Dear Mr. Bergström,
    dear forum-users,

    how did you derivate the jacobian of the neo-hookean model (Abaqus UMAT subroutine) in Chapter 10? I'm asking because I've derivated the lagrangian elasticity tensor from the second piola-kirchhoff stress tensor. By applying a push forward operation I get the eulerian elasticity tensor (same as in: Bonet & Wood: Nonlinear Continuum Mechanics For Finite Element Analysis (2nd Edition), p.170). The point is, your Jacobian is working and mine does not converge. What I'm doing wrong?

    I've tested the Neo-Hookean model in a MSC.Marc subroutine (HYPELA2). With 2nd Piola-Kirchhoff-stresses / Lagrangian elasticity tensor / Large Strain / Total Lagrange everything is fine. But if I switch to Large Strain / Updated Lagrange settings in MSC.Marc Mentat and calculate the cauchy-stresses / eulerian elasticity tensor in my subroutine it does not converge at larger strains. I assume that I've made a mistake in the push forward operation of the elasticity tensor.


    (sorry for the bad quality of my scan, forum is scaling down the resultion)
    Attached Files
    Last edited by duan; 2016-12-28, 15:43.

  • #2
    Good question. It could be multiple reasons for that (I did not carefully study your questions )

    I recommend that you check that you use a proper definition of the engineering strains. Most FE software use engineering shear strains (not tensorial strains).

    Jorgen Bergstrom, Ph.D. PolymerFEM Administrator


    • #3
      I think I got it (source is in german - didn't found a source written in english). If anyone is interested in the elasticity tensor - although only for total lagrange, see this (p.111). Even non native german speakers should understand that page .

      Best Regards,