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 [82]-[85].

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: