Settings for Contact Nodes

	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.

The default values for the penalty factors is based on a characteristic stiffness. The default is an “equivalent” Young’s modulus (Eequ) of the material on the destination side. For linear elastic isotropic materials, Eequ is the actual Young’s modulus. For other types of materials, Eequ 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), Eequ 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.

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 in case 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 .

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

Some hints for selecting the penalty factor:

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 when using the augmented Lagrangian method. You can then enter a logical expression that will force the solver to immediately abandon the iterations and try a smaller step when fulfilled. 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.

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:

When the source and 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 gap distance detected by the contact search. Positive gap distances smaller than the tolerance Δgap are adjusted to be zero. By default Δgap is set to Inf, which means that all gaps and overclosures detected are adjusted to be zero. This adjustment can be combined with an offset. The offset is applied to the adjusted gap value.

It is only the gap computation that is affected by this setting, the mesh as such is not adjusted. 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.

You can only apply an offset to the source boundaries if they belong to the same physics interface as the destination boundaries.

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 than the contact prohibits the deformation, 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 will never come into contact.

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, which 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.

For any other discretization than , the lumped solver is no longer optimal for the contact pressure update, and a standard segregated step must be used instead. The default solver generation takes this into account, but if you modify the discretization afterwards, you should update also the solver sequence.

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 an 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.

When adhesion is active, it is possible to break the bond between the source and destination boundaries by adding a subnode to . To model decohesion, it is required that an node is present and active in the same parent node.

Decohesion defines a Cohesive Zone Model (CZM) based on interface damage mechanics on the adhesive layer. Damage is assumed to be a scalar variable that initiates as 0 and grows to 1 during decoheson, and in principle degrades the stiffness of the adhesive layer. Since damage is a scalar, both the normal and tangential stiffness components degrade simultaneously, irrespective of whether the actual loading direction. However, the penalty stiffness of the contact condition is not affected by damage.

Two alternative CZM are available. The models defines damage growth as a function of a mixed mode displacement quantity. It comes with several traction separation laws that associate the onset of damage with the peak strength of the interface. For some of them, it is possible to chose between different mixed mode failure criteria. The models defines damage growth as a function of the stored undamaged elastic energy density of the interface. It also comes with several different traction separation laws. However, these are more general and define the onset of damage at an arbitrary elastic energy density. In principle, you can define the model so that damage initiates immediately during loading of the adhesive layer, that is for zero energy density. The strength of the interface is then determined by the critical energy release rate and the shape of the damage evolution function. In this way, the energy based damage models cane be viewed as a regularization of linear elastic fracture mechanics.

Decohesion is an inherently unstable process. The elastic energy in the strained adhesive layer is released during decohesion. Numerically, the decreasing branch of the traction-separation curve manifests itself as a local negative stiffness. Such problems are only possible to solve as long as the surrounding material can absorb the released energy. The numerical stability is, furthermore, closely coupled to the physical stability of the structure. The following points can help to set up a model with decohesion and to overcome problems with convergence.

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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 as the one used for post-buckling problems.

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To improve the robustness of the solver, it is sometimes beneficial to modify the settings in the section of the or nodes in the solver sequence. For example, allow a larger number of iterations or try a different nonlinear method. Often, the Constant (Newton) method can improve the convergence of models with decohesion.

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The robustness of the solver can also be improved by modifying the parameter or time stepping algorithm. For a stationary study, you can tune the step size in the node, and for a time dependent study, you can modify the time stepping of the . A good idea is often to reduce the maximum allowed step size of the solver and to allow for smaller step size than the default. Note that if the maximum step size allowed is too large, the solver might bypass the decohesion process altogether; in other words, even though a converged solution is obtained, it might be invalid.

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The solution of the unstable failure due to decohesion is, to some degree, always mesh dependent, see for example Ref. 1. It is therefore good practice to make sure that the mesh of the interface and in its vicinity is fine enough to allow the energy released during decohesion to properly redistribute in the structure. This can help avoid solution jumps where several mesh elements are completely damaged in a single step. Such solution jumps can be difficult for the solver to get pass, and even if it does, the solution after the jump might be invalid.

For time dependent studies, it is possible regularize the CZM with a viscous delay by selecting in the drop-down menu. This option adds a delay to the release of energy, which is controlled by the τ. Using this option can help to suppress the instability of the solution when the step size or mesh size is too large. If the viscous damage is used to stabilize a rate-independent decohesion problem, the value of τ must be chosen with care. As a rule of thumb, τ should at least be one or two orders of magnitude smaller than the expected time step.