Modeling Damage
Modeling problems with strain localization might turn into unstable behavior and convergence difficulties. The following techniques can be used to help is such situations:
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Use a displacement controlled loading scheme since damage is often associated with a reduction in load carrying capacity, see the Cracking of a Notched Beam example in the Geomechanics Module or in the Nonlinear Structural Mechanics Module Application Libraries.
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Better convergence is often obtained when the Nonlinear method is set to Constant (Newton) with a Damping factor equal to 1, and a Jacobian update on every iteration.
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Reduce the smallest and/or largest allowable step size in an auxiliary sweep, or restrict the time steps in a time dependent study.
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Introducing a soft spot where a crack is expected can make the localization of strains more stable, see the Brittle Damage in Uniaxial Tension example in the Geomechanics Module or in the Nonlinear Structural Mechanics Module Application Libraries. Alternatively, a random spatial distribution of the material parameters could be employed to obtain a similar result.
When using the crack band method or no regularization at all, the following steps are recommended:
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The size of the biggest mesh element should not exceed h<2EGf/σts2, where E is the Young’s modulus, Gf is the fracture energy per unit area, and σts is the tensile strength. Larger values of h will cause a snap-back of the stress-strain curve at the material point level.
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Use linear shape functions for the displacement. When using higher order shape functions, strains may localize in either rows of Gauss points or entire elements depending on the stress state and numerical round off.
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If cracks are located on a symmetry plane, the model parameters should be modified so that the amount of dissipated energy is reduced by one half in the elements adjacent to the symmetry plane. This can be achieved, for example, by reducing the fracture energy in that row of elements.
When using the implicit gradient method, the element size should be sufficiently small to resolve damaged zones.