Node-based damage
by J. Beaurain, EDF R&D / AMA
Gradient damage regularized models can now be treated at a nodal level in Code_Aster, using the newly introduced GVNO formulation.
No distinction is made anymore between the behaviour law damage variables and the node’s damage degrees of freedom, as it is the case of the mixed Lagrangian formulation (GRAD_VARI), also available in Aster. It reduces the number of degrees of freedom by about 10% and significantly simplifies the introduction of new behaviour laws.
For structures that do not feature important snap-back instabilities, it was observed that the CPU time was cut by as much as a factor of two. As an alternative to the standard Newton tangent method, the secant matrix supplementary option allows jumping instabilities within a single step without any direct user intervention and suppresses the need for rather complex methods like continuation methods. More precisely, if we work with a behaviour law based on quadratic damage energy dependence, we obtain an algorithm equivalent to the alternate minimization technique which has a proof of convergence. This new formulation is the minimal one for damage problem and even if its global implementation was quite difficult, its basic and advanced usage become simpler, so that we suppose new users will find it more attractive.
The implementation has been realized by Jérôme Beaurain during his PhD thesis on "the research of bifurcated solutions and study of their stability for damage problems", under supervision of Kyrylo Kazymyrenko (EDF R&D) and of Jean-Jacques Marigo (Laboratory of Solids Mechanic, Ecole Polytechnique).
GVNO formulation is available for plane strain, axisymmetric and 3D mechanical problems. In Code_Aster we respectively name each one by :
- D_PLAN_GVNO ;
- AXIS_GVNO ;
- 3D_GVNO.
As illustration, we represent the crack propagation path of a notched specimen (93369 dof), simulated using AXIS_GVNO model, in the particular case of a pathologically oriented mesh. We observe, as physically expected, symmetric damage evolution that doesn’t reveal any mesh dependence – main drawback of local and some non-local damage formulations. This calculus needs just two time steps for a global computational time of 20 minutes.
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