Settings for Contact Nodes

An important parameter in the settings for the Contact node is the penalty factor. It is used for both the augmented Lagrangian method and the penalty method, but the interpretation is different:

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In the augmented Lagrangian method, the penalty factor is a numerical parameter, which affects the convergence properties of the algorithm. A higher value gives a faster convergence, but at the price of less stability.

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In the penalty method, the penalty factor has a straightforward interpretation as the stiffness of a distributed spring connecting the two contacting boundaries. A higher value will decrease the unphysical penetration, but can be detrimental to the numerical conditioning of the stiffness matrix.

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When modeling adhesion, the penalty factor is the stiffness in the normal direction of the adhesive layer.


	In the augmented Lagrangian method, the value of the penalty factor does not affect the accuracy of the final solution, like it does in the penalty method.

When running into convergence problems, check the penalty settings. If the iteration process fails in some of the first iterations, lower the penalty parameters. If the model seems to converge but very slowly, consider increasing the maximum value of the penalty parameters.

Increasing the penalty factor can lead to an ill-conditioned Jacobian matrix and convergence problems in the Newton iterations. This is often seen by noting that the damping factor becomes less than 1 for many Newton iterations or that the structure “jumps” into an unphysical state. If this occurs, decrease the penalty factors.

The default values for the penalty factors is based on an “equivalent” Young’s modulus (Eequiv) of the material on the destination side. For linear elastic isotropic materials Eequiv is equal to the actual Young’s modulus. For other types of materials Eequiv is defined by an estimate of a similar stiffness at zero strain. For materials that are user defined or in other senses nonstandard (for example, anisotropic with large differences in stiffness in different directions), Eequiv might need to be replaced with another estimate.


	For nonlinear materials in general, and for elastoplastic materials in particular, there can be a significant change in stiffness during the solution process. Choose the source and destination boundaries accordingly. You may even have to adjust the penalty factor as the solution progresses when such materials form a contact boundary.

Penalty Factor Relaxation

When using the augmented Lagrangian method, having a well tuned penalty factor is an important factor for the performance of the contact iterations.

The default value is selected as a compromise between speed and stability, but with more weight on stability. The strategy is to for each new step (parametric step or time step) start with a softened penalty factor, which is then increased over the first four iterations. The purpose is to stabilize the problem if there are large overclosures in the first iterations. This is called relaxation.

In a situation where the contact is well established, using relaxation will however cost extra iterations, and it may even lead to a loss of convergence.

The penalty factor can be tuned in several ways. You have three basic choices, ranging from simple to advanced:

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With a penalty factor, you can choose having it tuned for or . With , relaxation is used in every step. With , a constant penalty factor is used all the time, and the value used is also higher than the final value obtained when using .

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With , you can make adjustments to the magnitude of the penalty factor, and to the relaxation strategy.

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With , you can enter any expression for the penalty factor.


	For details about these settings, see the documentation of the settings for the Contact node.

Some hints for selecting the penalty factor:

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Use relaxation only when large changes in the contact state is expected.

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If an analysis takes a long time, check the convergence graphs. If the contact variables show a steady, but slow, convergence it may help to increase the penalty factor. Increase by a factor of 2–5.

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If a model fails to converge and the contacting parts appear to have moved far from each other, it is probable that the penalty factor is too high. You can then either decrease the total stiffness or add more relaxation.

Trigger Cutback

If, during the iterations, a contact problem comes into a state where it is far from the converged solution, it is unlikely that the solution will ever converge. In such a case, much computing time can be spent before the maximum number of iterations is reached, and the solver makes an attempt with a smaller time or parameter step. To speed up this process, you can select the check box. You can then enter a logical expression which, when fulfilled, will force the solver to immediately abandon the iterations and try a smaller step. Such an expression can, for example, be a maximum displacement (like solid.disp > 5[mm]), based on what is physically realizable for the structure. The expression is evaluated in all points on the boundary, but you can also use a global value, like an average or a maximum.

Offset and Adjustment

It is possible to assign an offset to both the source and destination boundaries. When an offset is given, the boundary used in the computations is not the geometrical boundary, but a virtual boundary displaced by the offset value. You can use this option for several purposes:

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When analyzing problems with for example shrink fit, nominal dimensions can be used for the geometry, and the overclosure in included in the gap by using the offset.

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When there is a small clearance between two boundaries, a negative offset can be used instead of changing the geometry.

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If geometries are such that a large overclosure exists in the initial configuration, the contact algorithms may not converge. You can then add a negative offset, which is slowly removed by letting it depend on time or on the parameter in the parametric continuation solver.

When the source or destination boundaries are curved, the discretization introduced by the meshing may lead to small variations in the computed distance between the source and destination boundaries, even though the geometrical shapes of the two objects are ideal. When modeling for example a shrinkage fit, this effect can cause significant fluctuations in the contact pressure. If you select , the computed distance from destination to source will be adjusted by the initial distance. This adjustment can be combined with an offset. The offset is applied to the adjusted value.

The mesh as such is not adjusted, it is only the distance computation which is affected. This type of adjustment is most useful when the sliding is small, so that the gap distance is always computed between the same points on source and destination.

Initial Value

In the augmented Lagrangian method, where the contact pressure is a dependent variable, it can be given an initial value. In force-controlled contact problems where no other stiffness prohibits the deformation except the contact, the initial contact pressure is crucial for convergence. If it is too low the parts might pass through each other in the first iteration. If it is too high they never come into contact.

Discretization

When using the augmented Lagrangian method it is possible to change the order of the shape functions used for the contact pressure and friction force degrees of freedom. The default is linear shape functions, and this matches the quadratic shape functions used as default for the displacement degrees of freedom in the Solid Mechanics interface. The only situation when you should consider changing the discretization for the contact variables is if you use cubic or higher shape functions for the displacements.

Selecting any other discretization else than requires that the solver sequence is modified manually, since the default lumped solver is no longer optimal for the contact pressure update. An ordinary segregated step should then be used.

Adhesion

When using the penalty method, you can specify that the boundaries in the contact pair should stick to each other after coming into contact.

The adhesive layer is conceptually without thickness, but by specifying on offset in the node, you can to some extent include the dimensions of the adhesive layer.

The adhesive layer always has a finite stiffness. For a glue layer, this represents the true stiffness. For a more conceptual joining of two boundaries, this stiffness should be considered in the same way as the penalty stiffness in the contact formulation. The stiffness can differ between tension and compression: In compression the stiffness is always taken as the penalty stiffness, whereas you can change the tensile stiffness.

Decohesion

Two boundaries joined by adhesion can separate if you select any of the decohesion laws. You must then specify the maximum strength and the total energy release during decohesion for pure tension and pure shear. In most cases, the decohesion process is a mixture between tension and shear, so you also have to specify the interaction rule.

As long as the stress is below the maximum strength, the adhesive layer retains it original stiffness. Once the displacement in the layer is so large that the maximum strength is exceeded, the material is considered as damaged, and the stiffness is decreased. The same damage factor is applied to both the tensile and the shear stiffness, while the compressive stiffness is unchanged.

Decohesion is an inherently unstable process. The elastic energy in the strained adhesive layer will be released during decohesion. Numerically, the decreasing stress-strain curve manifests itself as a local negative stiffness. Such a problem may be possible to solve, if the surrounding material can absorb the released energy. The numerical stability is closely coupled to the physical stability of the structure.

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If the structure is in load controlled situation, there is no possibility to continue the analysis when the peak external load has been exceeded. Physically, this corresponds to a sudden collapse of the component.

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If the structure is loaded by prescribed displacements, it is usually possible to continue the analysis further. It may however happen that the stored elastic energy in the structure is large enough to force a complete breakdown of the adhesive layer once a certain external displacement is reached.

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If possible, use prescribed displacements in a decohesion analysis, and evaluate the applied load from the reaction forces.

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Sometimes it is not possible to use prescribed displacements, for example if the load is distributed. You can then add a to control the loading rate by some other quantity that increases monotonically. This is the same technique that is used for post-buckling problems.

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You may have to change the settings in the section of the settings for the or nodes in the solver sequence, for example by allowing a larger number of iterations.

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The true unstable failure is a dynamic event. This can be analyzed using a time dependent solver, but the computational cost can be high. The inertial forces will then balance the released energy.

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Documentation of the Contact, Friction and Adhesion nodes.

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Adhesion and Decohesion in the Structural Mechanics Theory chapter.


	For an example showing decohesion analysis, including how to use a global equation to control an unstable problem, see Mixed-Mode Debonding of a Laminated Composite: Application Library path Structural_Mechanics_Module/Contact_and_Friction/cohesive_zone_debonding