Comparison CalculiX-Abaqus with NLGEOM

Dear CalculiX users,

in the past differences were reported in the results between CalculiX and Abaqus in the presence of NLGEOM on the *STEP card. Further analysis has revealed at least 3 sources for these differences:

  1. In Abaqus the logarithmic strain is used (unless a hyperelastic material is selected). This implies that also thermal strains, if present, are logarithmic, i.e. the thermal expansion coefficient must have been determined based on the actual length of the specimen, not the initial length. As far as I know, the standard is to use the initial length. This means that as soon as you turn on NLGEOM in Abaqus you have to provide different thermal expansion coefficients beta satisfying: beta=ln(1+alpha*deltaT)/deltaT, where deltaT=T-Tref. In CalculiX the Lagrange strain is used and the expansion coefficients do not have to be changed when activating NLGEOM.
  2. Abaqus uses an updated Lagrangian approach (using stress rates…, unless a hyperelastic material is used), which leads to path dependent results. CalculiX uses a total Lagrangian approach; the results are not path dependent. You can avoid the path dependence in Abaqus by replacing a linear elastic law by a neo-Hooke law.
  3. If you are using a linear isotropic relationship, the linearity in CalculiX is between the Piola-Kirchhoff stress of the second kind and the Lagrange strain, in Abaqus it is between the Cauchy stress and the logarithmic strain. The larger the strain, the larger the difference will be between the CalculiX and Abaqus results. Of course, it is questionable whether a linear relationship makes sense for large strains.