Cmat Book Pdf Download

[Magdalena Liendo]

Whichcontact model should be installed when a contact forms? The answer to this question, which will determine the constitutive mechanical behavior of a PFC model, is a fundamental one and is intimately tied to the specifics of each PFC model. Nobody but the modeler can answer it, and PFC itself cannot make any generic assumption [2]. Instead, PFC will use the null model contact model by default and therefore, the user is required to explicitly specify which contact model(s) should be used in each PFC model.

The Contact Model Assignment Table (CMAT) has been introduced in PFC to allow users to specify this information. The CMAT is a very generic tool that can handle both built-in contact models and user-defined contact models. Furthermore, with just a few command lines, it can be used to build simple systems as well as complex ones (i.e., with several contact models and/or heterogeneous mechanical properties).

This tutorial illustrates the main features of the CMAT and how to use them appropriately. The CMAT is queried any time a new contact is created in order to determine which contact model should be installed at that specific contact.

The numerical models used in this tutorial are voluntarily simple. A container (modeled with a wall) is filledwith a collection of balls, and cycles are performed to bring the model to equilibrium under various loading conditions.

As described here, the CMAT consists of an ordered set of (optional) slots along with a default slot for each contact type. In many situations where the constitutive behavior is homogeneous across the system, setting the default slots of the CMAT suffices.

Note that the contact cmat default command will automatically apply to all the default slots unless a type is specified. The system constructed here will comprise both ball-ball and ball-facet contacts; all of these contacts will use an identical linear model with \(k_n\)=1.0e6 and \(\beta_n\)=0.2. Figure 1 shows the final state of the system after balls have settled on the floor of the box under gravity.

Whenever a contact is created during the course of the simulation, the CMAT is processed as follows: First, the two optional slots are visited in order of increasing index number. Then, if the contact does not fulfill any of the ranges of the optional slots, the default slot corresponding to the type of contact being created is used. Once a contact is created in the present model, slot 1 of the CMAT is inspected to determine whether the corresponding contact model should be used based on the assignment criteria (i.e., the two balls have group identifier glass). If the assignment criteria are not met, slot 2 of the CMAT is inspected in a similar fashion. If all slots of the CMAT have been visited and no suitable contact model has been identified, the contact model held in the default slot of the CMAT is assigned.

Note that the range selection used in this example is based on groups defined for the contacting pieces.The Group logic is a generic utility that can be used to identify multiple instances of a same-model component. Groups can be assigned to balls, walls, and clumps, as well as facets or pebbles, and even contacts. However, it is often useful to filter contacts based on the groups assigned to the contacting pieces instead of using groups defined for the contacts themselves, as illustrated in the present case. To this effect, the match keyword of the group range element can be used.

Figure 3 shows the final state of the system. Balls are colored according to their group, and the contacts are colored by the value of the shear modulus property hz_shear (only contacts with a hertz model are displayed). The different contact model properties have been assigned appropriately during the course of the simulation.

The example discussed above illustrates how optional slots in the CMAT can be used to specify heterogeneity in contact model properties. Another possibility is to use property inheritance, as illustrated below.

Practically, the resulting PFC model (shown in Figure 4) is identical to the model previously discussed (Figure 3), but in the present model, only the default slots of the CMAT have been used. Property inheritance has been used to derive contact model properties in this case. Note that the value of the normal critical damping ratio has been set to be the same for all ball-ball contacts. Since this later property cannot be inherited from piece properties, optional slots in the CMAT would have been required if different values were to be used depending on the groups of the contacting balls.

All the examples above have discussed different ways of specifying the CMAT to control which contact model (and which properties) should be assigned to newly created contacts during cycling. Another action that is often desired when constructing a PFC model is to modify existing contacts (either to entirely override the existing contact model or to modify only select properties).

To modify glass-glass contacts while preserving the remaining contacts, a range can be specified along with the contact cmat apply command to restrict its actionto a select set of contacts (in this case, to contacts between glass balls).

The state of the system after the commands above have been executed is shown in Figure 6. The left-hand side of the figure displays the contactscolored by the name of their contact model, and the right-hand side of the figure shows the hertz contacts colored by force.In this case, the linear parallel-bond contact model has been appropriately assigned to glass-glass contacts, and all the other contacts retained their previous contact model and datasince only glass-glass contacts have been modified.

Although the strategy can be used to modify existing contacts, it is important to note that any changes to the CMAT will also impact future contacts created during further cycling. With the CMAT modified by the commands listed above, future contacts between glass balls will be assigned a linear parallel-bond contact model, which may not be desirable. One possibility to overcome this issue would be to revert the modifications in the CMAT, after the contact cmat apply command has been executedto modify select contacts, in order to install a hertz contact model at new contacts between glass balls [4].

If the intent is to modify select contacts (or select contact model properties) at one point during the construction of the PFC model, using contact commands (that willonly affect existing contacts) may be more adequate than altering the CMAT (which may affect future contacts). In the present case, only active contacts between glass balls may be modified touse a linear parallel-bond contact model with desired properties, which is accomplished by using the following commands:

The final state of the system is shown in Figure 7. Active contacts between glass balls have been assigned a linear parallel-bond model, bonds have been installed, and the system brought to equilibrium under gravity. All contacts (active and inactive) are displayed and colored by the name of their contact model. In this system, inactive contacts and new contactsbetween glass balls will use the appropriate hertz contact model (as defined in the corresponding slot of the CMAT).

At this stage, the contact method command is used to execute the bond method defined by the linear parallel-bond contact model.By default, this method will install bonds at contacts with a gap less than or equal to zero, but a positive bond installation gap can also be specified.Multiple cases are compared, with a bond installation gap of 0.0, 5 10-5, and 2.5 10-4. The corresponding systems are shown inFigures 8 to 10, where the contacts colored by the value of the gap is shown on the left-hand side, andthe active and inactive linear parallel-bond contacts are displayed on the right-hand side. In this model, there are initially 1115 ball-ball contacts in total (active contacts witha negative gap and inactive contacts with a positive gap), and the maximum gap for inactive ball-ball contacts is approximately 1.8343 10-4. Executing the bond method on contactswith a gap less than or equal to zero (Figure 8) results in 983 contacts being bonded and 132 contacts remaining unbonded. Executing the bond method on contactswith a gap less than or equal to 5 10-5 (Figure 9) results in 1025 contacts being bonded and 90 contacts remaining unbonded.Finally, executing the bond method on contacts with a gap less than or equal to 2.5 10-4 (Figure 10) results in all 1115 ball-ball contacts being bonded.

Note, however, that since no proximity distance has been specified in the CMAT, the minimal distance at which inactive contacts have been created is left to the discretion of the contact detection logic.In this case, this value (1.8343 10-4) is lower than the desired bond installation gap. Because the contact method command only operates on existing contacts, there may be pairs ofballs in the system with a gap between 1.8343 10-4 and 2.5 10-4, for which a contact has not been created, hence that are not bonded.To ensure that a contact is created when balls come closer than a desired proximity distance, the CMAT may be modified to use the proximity keyword. For instance, the commands belowwill modify the CMAT, model clean the model to force the creation of new contacts with the new proximity setting, apply the new CMAT entry to existing ball-ball contacts and, finally, bond the contacts with agap less than or equal to 2.5 10-4.

The final model is shown in Figure 11. With these new settings, there are 1280 contacts in total, with 1163 contacts being effectivley bonded. All the pairs of balls witha gap less than or equal to the desired value of 2.5 10-4 are bonded.

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