Implicit: Mortar Contact
The Mortar contact is activated by typically appending the suffix _MORTAR to the automatic single surface, automatic surface to surface or forming surface to surface keywords. It can also be run as tied and tiebreak contacts. All Mortar contacts are segment to segment and penalty based and the tied and tiebreak contacts are always offset, i.e., the tie occurs on the outer surfaces of shells and not on the mid surfaces. For automatic contacts, edge contact with flat edges is always active. At this point, some of the more advanced features applicable to other contacts may not apply to the Mortar contact, examples are friction tables and orthotropic friction, but on the other hand it possesses features that are of particular interest to implicit and that are not available for other contacts. It is supported in both smp and mpp but the option MPP does not apply, bucket sort is performed every cycle and the smp ignore flag applies. The SOFT flag does not apply, to summarize it is a contact algorithm especially intended for implicit analysis.
For the forming contact the rigid tools must be meshed so that the normals are directed towards the blank, and contacts from above and below must be separated into two or more interfaces because contact can only occur from one side of the blank for a given contact interface. For the forming contact, rigid shells on the master side have no contact thickness. This is not the case for automatic contacts, here there are no restrictions on the mesh and even rigid shells have contact thickness. For all Mortar contacts, part or part set based slave and master sides are recommended although not mandatory. If the two sides in the contact interface have different stiffness, use the weak part as slave in order to get the best possible implicit convergence behavior. This is automatically taken care of in a single surface contact. The Mortar single surface contact was up to recently rather slow even for implicit analysis but improvements have been made on the efficiency to make it practically useful in the most recent versions of LS-DYNA.
The contact pressure in the Mortar contact is a function of the penetration and given as
The characteristic length is for shells the shell thickness and for solids it is the smallest edge in the slave side of the contact interface, while d max is the maximum penetration given as 95% of the average characteristic lengths on master and slave sides. For solids the definition of the characteristic length may have the consequence that the stiffness becomes unnecessarily high if some elements are small, and therefore it is recommended to manually set SST to some appropriate characteristic length for solid contact slave sides. Unfortunately this will affect the shell contact thickness if shells and solids are present in the same interface, so at the moment it is recommended to separate shells and solids into different contact interfaces and only set SST for the solid interfaces.
As can be deduced from the formulae above, the contact stiffness is parabolic with respect to penetration up to a penetration depth corresponding to half of the maximum penetration. For IGAP=1 it will remain parabolic for even larger penetrations but the user may increase IGAP which means that the contact will stiffen for larger penetrations, in fact it will become cubic with the following mathematical constraints (see figure above for an illustration, which plots contact stress as function of penetration relative to twice the maximum penetration)
The purpose of increasing IGAP could be to prevent the penetration from becoming larger than the maximum allowed penetration, because if convergence is attained with penetrations larger than this value this contact will be released in subsequent steps and the simulation is likely destroyed. Penetrations of this depth is likely to cause discontinuities along line searches and other discouraging phenomena, cf. the use of NLPRINT=3 on *CONTROL_IMPLICIT_SOLUTION. The user may of course scale the stiffness by increasing SFS but this also scales the stiffness for small penetrations and probably has a negative effect on convergence.
Just as for implicit in general, information is always a good thing to have when convergence starts deteriorating and considering the release of contact in the previous section, it would be interesting to know if penetrations are large enough for this to be a potential danger. First, initial penetrations are always reported in the message file(s), including the maximum penetration and how initial penetrations are to be handled. The latter depends on the value of the IGNORE flag and this is dealt with below. In addition, by putting
MINFO = 1
LS-DYNA will report the absolute maximum penetration as well as the maximum penetration in percentage after each equilibrium. If the relative maximum penetration reaches above 99% a warning message is printed as this particular contact is close to being released. This percentage value should ideally be kept below some 90 % to have some sort of comfort margin. There are three ways to reduce maximum relative penetrations, and these are (i) to increase IGAP, (ii) to increase SST for solids or (iii) to increase SFS. Note that by increasing SST for solids the contact stiffness will automatically be decreased, and this should be accompanied by increasing SFS by the square of the fraction increase of SST. That is, if SST is doubled then SFS should be increased four times, and if SST is tripled then SFS should be increased nine times, and so on. In this case even IGAP may have to be increased by some amount if being larger than unity in the first place.
As mentioned above, initial penetrations are always reported in the message file(s), including the maximum penetration and how initial penetrations are to be handled. The IGNORE flag governs the latter and the options are
||Same functionality as the corresponding absolute value, but contact between segments belonging to the same part is ignored completely
||Initial penetrations will give rise to initial contact stresses, i.e., the slave contact surface is not modified
||Initial penetrations will be tracked, i.e., the slave contact surface is translated to the level of the initial penetrations and subsequently follow the master contact surface on separation until the unmodified level is reached
||Initial penetrations will be ignored, i.e., the slave contact surface is translated to the level of the initial penetrations, optionally with an initial contact stress governed by MPAR1
||Initial penetrations will be removed over time, i.e., the slave contact surface is translated to the level of the initial penetrations and pushed back to its unmodified level over a time determined by MPAR1|
|IGNORE=4||Same as IGNORE=3 but it allows for large penetrations by also setting MPAR2 to at least the maximum initial penetration
The use of IGNORE depends on the problem, if no initial penetrations are present there is no need to use this parameter at all. If penetrations are relatively small in relation to the maximum allowed penetration, then IGNORE=1 or IGNORE=2 seems to be the appropriate choice. For IGNORE=2 the user may specify an initial contact stress small enough to not significantly affect the physics but large enough to eliminate rigid body modes and thus singularities in the stiffness matrix. The intention with this is to constrain loose parts that are initially close but not in contact by pushing out the contact surface using SFST and applying the IGNORE=2 option. It is at least good for debugging problems with many singular rigid body modes. IGNORE=3 is the Mortar interference counterpart, used for instance if there is a desire to fit a rubber component in a structure. With this option the contact surfaces are restored linearly in time from the beginning of the simulation to the time specified by MPAR1. A drawback with IGNORE=3 is that initial penetration must be smaller than half the characteristic length of the contact or otherwise they will not be detected in the first place. For this reason IGNORE=4 was introduced where initial penetrations may be of arbitrary size, but it requires that the user provides crude information on the level of penetration of the contact interface. This is done in MPAR2 which must be larger than the maximum penetration or otherwise and error termination will occur. IGNORE=4 only applies to solid elements at the moment. When eliminating penetrations by simulation for models with many parts, some parts may contain thin members that cause spurious self-contacts. These may be difficult to work around by only adjusting contact parameters, but fortunately there is rarely any loss of generality in ignoring contact within parts completely since those are usually not of interest in such a context. The option IGNORE<0 was implemented for this purpose and is a way to approach this problem.
Damping can be activated using VDC. A problem with contact damping in implicit is that the time step is usually large enough to not resolve the time in contact to get the desired damping effect. Often the situation becomes even worse, it is therefore not recommended to use damping.