Face-to-Face Mortar Contact
This is a face-to-face contact formulation using extra Lagrange multipliers to
model the contact stresses. It can be used for hard contact (infinite stress
at the slightest penetration) or soft contact (gradually increasing stress the
larger the penetration as in materials with a definite surface roughness). Due
to the Lagrange multipliers the stress-penetration relationship satisfied in a
weak sense. This is different from the face-to-face penalty method, in which
the knowledge of the penetration uniquely leads to the contact
stresses. Due to this property the convergence of the mortar method is
somewhat better than in the face-to-face penalty method, i.e. less iterations
are needed. However, the cost of one iteration is higher. For details the
reader is referred to -.
The implementation in CalculiX uses dual basis functions for the Lagrange
multiplier. Dual basis functions are in a weak sense orthogonal to the
standard basis functions used for the displacements. Due to the use of dual
basis functions the Lagrange multiplier degrees of freedom can be easily
eliminated from the resulting equation system and therefore the number of
unknowns in the system is in each iteration not larger than without
contact. Because the negative parts of the standard basis functions for
quadratic elements can cause problems, several options to circumvent these
problems have been implemented. Right now, the user can choose between TYPE=MORTAR, TYPE=LINMORTAR
and TYPE=PGLINMORTAR on the *CONTACT PAIR card. For
TYPE=MORTAR the standard dual basis functions are used for the Lagrange
multiplier. For TYPE=LINMORTAR linear dual basis functions are used, i.e. the
Lagrange multiplier at the midnodes (if any) is not taken into account. For
linear elements MORTAR and LINMORTAR coincide. In case of TYPE=PGLINMORTAR the
variation of the Lagrange multiplier is done using linear standard basis
functions (PG stands for Petrov-Galerkin). The following rules apply when
using Mortar contact:
- The mortar method is only available for the
*STATIC procedure. Consequently, it can not be used for
dynamic calculations, heat transfer calculations or (un)coupled
temperature-displacement calculations, to name a few.
- It is advised to use the mortar method for contact between genuine
3-dimensional elements only. Usage for contact in between 1-d or 2-d elements will cause
problems. In general, the mortar method is not well suited if the contact
areas are too much constrained by extra multiple point constraints.
- The mortar method cannot be combined with the penalty method in one
input file. Also a single mortar method (MORTAR or LINMORTAR or
PGLINMORTAR) has to be choosen for all contact pairs in one input file.
- Using the *CYCLIC SYMMETRY MODEL option, one has
to make sure that a one-to-one connection is made if hte slave surface
touches the cyclic symmetry boundary. If non-matching meshes are used, one
has to make sure that the contact surfaces touching the cyclic symmetry
boundary are removed from the slave surface definition.
- One must not apply extra multiple point constraints to edge nodes on
the slave surface. Please apply extra mounting MPC's only to corner nodes
on the slave surface.
- Define different contact pairs for different contact zones (contact
search algorithm is faster)
- Define contact surfaces only as large as needed (contact search
algorithm is faster)
- One must not use the same contact surface in more than one contact
- Make sure that the contact surfaces do not touch pretension sections
- Make sure that there is not gap between the bodies for force driven
quasi-static calculations (may lead to huge accelerations since no mass is
defined and consequently no contact is found)
- Make sure that you choose a small first increment in the step if you
expect large relative displacements in tangential direction. A minimum of
four increments is recommeded. Recall that the direction of the normal and
tangential directions and the surface segmentation is only performed once
- Shrink is always active in CalculiX, i.e. overlaps are resolved
increment-wise across the step.
- Sometimes the adpative time stepping using mortar contact is too
senstive. Try *STEP,DIRECT in that case.