Nonlinear static problems can be unstable. Such instabilities may be of a geometrical nature, such as buckling, or of a material nature, such as material softening. If the instability manifests itself in a global load-displacement response with a negative stiffness, the problem can be treated as a buckling or collapse problem. As we know, in such situations, the standard load-controlled finite element scheme, where the displacement vector is found for a prescribed load factor, cannot be used in general once a limit point is reached.
Currently I am working on a nonlocal damage model. When the material is softening and has a negative stiffness, it is hard to get converged results. Is it required to use the arc-length method or the modified Riks method to get convergence in this model or similar damage models which are lead to load-displacement curve with the softening response and negative stiffness?
Why not try converting the problem into transient, or pseudo-transient analysis by adding a damping term of small magnitude into the equation?
For localized (material) instability, you can apply material damping for the region you suspect it to be a location for the instability. If doing so in ANSYS, select those elements there and assign to them a material model with damping parameters. Look up the help files in ansys they have nice information on these things. I did test this approach, and the trick is to try to get the response from either methods to match together with the least damping used. Otherwise, you might end up with a different response.
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