Contact analysis - theory and concepts

Transcription

1 Contact analysis - theory and concepts Theodore Sussman, Ph.D. ADINA R&D, Inc,

2 Overview Review of contact concepts segments, surfaces, groups, pairs Interaction of contactor nodes and target segments constraint function method contact compliance convergence criteria offsets initial penetration feature Some implications of contact algorithm assumptions in practical analysis ADINA R&D, Inc,

3 Contact concepts 2-D and 3-D contact. Contacting areas are not known beforehand. Frictionless contact or frictional contact with sticking and slipping. ADINA R&D, Inc,

4 Node-surface algorithm Contact prevents contactor nodes from penetrating target segments. Very small contact force Very large contact force ADINA R&D, Inc,

5 Node-surface algorithm Nodes from the contactor surface cannot penetrate the target segments, but nodes from the target surface can penetrate contactor segments. Contactor Target ADINA R&D, Inc,

6 Single-sided contact group In a single-sided contact group, all contact surfaces are single-sided. Contact can only occur from one direction. The contact surface normal from the target surface is used in singlesided contact to determine the direction of contact.. Contact can occur from this direction Contact surface normal ADINA R&D, Inc,

7 Double-sided contact group In a double-sided contact group, all contact surfaces are double-sided. Contact can occur from either or both directions. Only 3-D contact groups can be double-sided. The contact surface normal is not used to determine if a contactor node is in contact. As seen from the side ADINA R&D, Inc,

8 Symmetric contact It is allowed to create symmetric contact: ADINA R&D, Inc,

9 Self-contact It is allowed for the same surface to be the target and the contactor in the same contact pair. This is called self-contact. One double-sided contact surface. ADINA R&D, Inc,

10 Examples of single and double-sided contact Single-sided contact is suitable for solid targets: Double-sided contact is suitable for shells: Self-contact Solid structure, as seen from the side, separate contactor and target Shell structures, as seen from the side Symmetric contact, pair 1 = S1, S2 pair 2 = S2, S1 pair 3 = S2, S3 pair 4 = S3, S2 ADINA R&D, Inc,

11 Constraint-function algorithm Target Contactor Ideal contact Normal contact force Gap g g g wg (, ) N g Constraint function Increasing N smooths out the contact g ADINA R&D, Inc,

12 Constraint-function algorithm For friction, there is a parameter T (default 0.001) F F t n F F t n u u T Ideal friction Friction model, T specified Increasing T smooths out the transition between sticking and slipping. ADINA R&D, Inc,

13 Contact compliance P = compliance factor CFACTOR1 A = contactor node area ADINA R&D, Inc,

14 Convergence criteria An additional norm is used to assess convergence: CFORCE= contact force vector increment CNORM= contact force vector RCONSM=reference contact force level (default 0.01) 2 2 CFORCE max(cfnorm, RCONSM) RCTOL RCTOL default = 0.05, which is too loose for some problems. ADINA R&D, Inc,

15 Convergence example OUT-OF- NORM OF CONVERGENCE RATIOS CONVERGENCE RATIOS BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL FOR OUT-OF-BALANCE FOR INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE ENERGY FORCE DISP. CFORCE (EQ MAX) (EQ MAX) (EQ MAX) (EQ MAX) CFNORM MOMENT ROTN. VALUE VALUE VALUE VALUE COMPARE WITH COMPARE WITH ETOL RTOL DTOL RCTOL (NOT USED) (NOT USED) ITE= E E E E E E E E E E-04 ( 12)( 764)( 362)( 24) 0.46E E E E E E E-06 ITE= E E E E E E E E E E-05 ( 12)( 769)( 367)( 29) 0.46E E E E E E E-07 ADINA R&D, Inc,

16 Contact surface offsets Normally, contact occurs on the surface defined by the nodes of the contact segments. However, the contact can be offset from this surface using contact surface offsets. ADINA R&D, Inc,

17 Example of contact surface offsets One use of the offsets is to account for the thicknesses of shell elements. The contact surfaces are defined on the midsurfaces, and the offsets account for the thicknesses. ADINA R&D, Inc,

18 Initial penetrations Sometimes the two contacting parts geometrically overlap at the start of the solution. This overlap might be due, at least in part, to the geometric discretization used. There are special options used to set the contact surface offsets, in order to control the initial penetrations. ADINA R&D, Inc,

19 Contact surface offsets for initial penetrations This feature is implemented using a variable OFFCON stored for each contactor node. OFFCON gives the (signed) distance between the nodal position and the position used to test contact. ADINA R&D, Inc,

20 Comments for OFFCON OFFCON is set separately for each contactor node. OFFCON is not adjusted for the possible tangential motion of the contactor node. At time 0, gap is zero. At time t, gap is greater than zero, even though node has penetrated target. ADINA R&D, Inc,

21 Contact tractions The contact tractions are computed only for the contactor surfaces. The contact tractions are calculated from the contact forces. The contact tractions are calculated at the nodes that are in contact. ADINA R&D, Inc,

22 Implications of node-surface algorithm When a contactor node slips off of the target, the solution changes discontinuously. Whenever possible, make sure that contactor nodes can always find targets. No more contact force on this node ADINA R&D, Inc,

23 Implications of node-surface algorithm Knife-edge contact cannot be modeled. Before interpenetration After interpenetration, no contact forces generated ADINA R&D, Inc,

24 Implications of node-surface algorithm Coarse curved target causes some contactor nodes not to be in contact. Example problem: Displacements at edge of contactor are prescribed. Contactor is attached to shell elements. We will consider the effect of changing the modeling of the target. Target is rigid. ADINA R&D, Inc,

25 Implications of node-surface algorithm Uniform meshing of target: State of contact: All nodes along a line are in contact. ADINA R&D, Inc,

26 Implications of node-surface algorithm Non-uniform meshing of target: State of contact: Only some nodes along a line are in contact. ADINA R&D, Inc,

27 Implications of node-surface algorithm Non-uniform meshing of target, compliance factor: All nodes along the line are in contact, but now there is overlap between contactor and target. ADINA R&D, Inc,

28 Change of state of contactor nodes The equilibrium iterations can converge only when the state of all contactor nodes is known (whether the node is in contact, and whether the node is sticking or slipping in frictional contact). Thus, when the states of the contactor nodes are changing during the equilibrium iterations, the equilibrium iterations cannot converge. For many cases, only a few contactor nodes change state during the step. Then convergence is relatively easy. But in some situations, many contactor nodes may change state during a step, and cutting back the step size does not help. Time t, not in contact. Time t+ t, in contact. ADINA R&D, Inc,

29 Change of state of contactor nodes This type of situation is most frequently encountered when solving for an initial condition, for example, in metal forming when applying the blank holder force before the motion of the punch. One characteristic of the equilibrium iterations is that the number of equilibrium iterations increases as the number of nodes on the contactor surface increases. Thus refining the mesh causes the number of equilibrium iterations to increase. The norms of the out-of-balance force and other convergence indicators do not decrease for many equilibrium iterations. Then, once the state of the contactor nodes is known, the indicators decrease suddenly and the solution converges. ADINA R&D, Inc,

30 Change of state of contactor nodes Use DIAGNOSTICS SOLUTION=DETAILED to see if contactor nodes are changing state. ADINA R&D, Inc,

31 Illustrative problem, showing contact convergence Prescribed displacement Beam structure modeled using shell elements Target is rigid Settings used: Limiting displacements feature turned off No compliance factor ADINA R&D, Inc,

32 Equilibrium iteration 0 OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E+00 1-Z 1-X 11-Z 15-X 0.00E E E E E-11 Diagnostics: Maximum incremental displacement % of model size ADINA R&D, Inc,

33 Equilibrium iteration 1 Areas in contact drawn in green OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E Z 14-X 4-Z 19-X 0.00E E E E E-01 Diagnostics: Maximum incremental displacement % of model size. - Nodes coming into contact. 10 nodes including node 5 with penetration = 9.900E-03 - Maximum initial penetrations % of model size ADINA R&D, Inc,

34 Equilibrium iteration 2 Contact forces acting on contactor OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E+02 5-Z 6-X 7-Z 16-X 1.11E E E E E-02 Diagnostics: Nodes losing contact. 4 nodes including node 15 with contact force = 5.501E ADINA R&D, Inc,

35 Equilibrium iteration 3 OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E+02 8-Z 9-X 3-Z 12-X 2.64E E E E E-02 Diagnostics: Nodes losing contact. 2 nodes including node 14 with contact force = 1.148E+01 - Nodes coming into contact. 2 nodes including node 2 with penetration = 9.428E ADINA R&D, Inc,

36 Equilibrium iteration 4 OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E Z 21-X 1-Z 1-X 1.23E E E E E-01 Diagnostics: Maximum incremental displacement % of model size. - Nodes losing contact. 4 nodes including node 13 with contact force = 3.491E ADINA R&D, Inc,

37 Equilibrium iterations 5, 6 OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E Z 10-X 12-Z 2-X 2.23E E E E E-10 ITE= E E E E E E-08 2-Z 9-X 12-Z 1-X 2.23E E E E E-12 ADINA R&D, Inc,

38 Contact behavior of tip node Graph shows location of tip node on the constraint function curve for each equilibrium iteration. Not drawn to scale. ADINA R&D, Inc,

39 Number of equilibrium iterations vs mesh refinement 100 Number of equilibrium iterations Number of nodes in target area ADINA R&D, Inc,

40 Contact forces on higher-order elements To model a uniform traction on the face of a 20-node brick element, nodal point forces acting in the opposite direction are required. ADINA R&D, Inc,

41 Contact forces on higher-order elements To model a uniform traction on the face of a 27-node brick element, the corner nodal point forces are small, but in the correct directions. ADINA R&D, Inc,

42 Contact forces on higher-order elements The node-surface algorithm cannot be directly used for the corner nodes, since the corner nodes might be in contact with tensile forces. This issue arises with the 20 and 21-node brick elements, and with the 10, 11-node tet elements. In order to allow the program to accept tensile contact forces, use the command CONTACT-CONTROL... TENSION-CONSISTENT=YES ADINA R&D, Inc,

43 Contact-impact problem, convergence issues Consider the following simplified contact-impact problem: ADINA R&D, Inc,

44 Contact-impact problem, results at impact OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E E E E E E+00 ITE= E E E E E E-04 2-Z 0-F 2-Z 0-F 9.56E E E E E+00 ITE= E E E E E E-03 2-Z 0-F 2-Z 0-F 2.82E E E E E+00 ITE= E E E E E E-02 2-Z 0-F 2-Z 0-F 1.36E E E E E+00 ITE= E E E E E E+00 2-Z 0-F 2-Z 0-F 2.13E E E E E+00 ADINA R&D, Inc,

45 Contact-impact problem, results at impact OUT-OF- NORM OF BALANCE OUT-OF-BALANCE NORM OF INCREMENTAL ENERGY FORCE MOMENT DISP. ROTN. CFORCE NODE-DOF NODE-DOF NODE-DOF NODE-DOF CFNORM MAX VALUE MAX VALUE MAX VALUE MAX VALUE ITE= E E E E E E+05 2-Z 0-F 2-Z 0-F 4.58E E E E E+00 ITE= E E E E E E+08 2-Z 0-F 2-Z 0-F 2.10E E E E E+00 ITE= E E E E E E+08 2-Z 0-F 2-Z 0-F 4.00E E E E E+00 ITE= E E E E E E+02 2-Z 0-F 2-Z 0-F 4.00E E E E E+00 ADINA R&D, Inc,

46 Contact-impact problem Why did the problem take so long to converge? In dynamic analysis, the effective stiffness is dependent on the time step size. The smaller the time step, the larger the effective stiffness. The effective stiffness is much larger that the compliance assumed in the constraint-function algorithm. Need to iterate long enough to reach convergence. ADINA R&D, Inc,

47 Contact-impact problem In a practical problem, with many nodes impacting at slightly different times, the solution can converge prematurely, due to norms used to measure convergence. To prevent this, use tighter tolerances and set RCONSM very small. Make sure that CFORCE < CFNORM at convergence. The value of N can also be decreased from its default value. ADINA R&D, Inc,