A segmentation-free isogeometric extended mortar contact method
This paper presents a new isogeometric mortar contact formulation based on an extended finite element interpolation to capture physical pressure discontinuities at the contact boundary. The so called two-half-pass algorithm is employed, which leads to an unbiased formulation and, when applied to the mortar setting, has the additional advantage that the mortar coupling term is no longer present in the contact forces. As a result, the computationally expensive segmentation at overlapping master–slave element boundaries, usually required in mortar methods (although often simplified with loss of accuracy), is not needed from the outset. For the numerical integration of general contact problems, the so-called refined boundary quadrature is employed, which is based on adaptive partitioning of contact elements along the contact boundary. The contact patch test shows that the proposed formulation passes the test without using either segmentation or refined boundary quadrature. Several numerical examples are presented to demonstrate the robustness and accuracy of the proposed formulation.
KeywordsComputational contact mechanics Isogeometric analysis Mortar methods Segmentation Extended finite element methods
The authors are grateful to the German Research Foundation (DFG) for supporting this research under Grants GSC 111 and SA1822/8-1.
- 9.Duong TX (2017) Efficient contact computations based on isogeometric discretization, mortar methods and refined boundary quadrature. PhD thesis, RWTH AachenGoogle Scholar
- 12.Duong XT, Lorenzis LD, Sauer RA (2017) On the shape functions for the contact pressure in mortar methods. In: von Scheven M, Keip M-A, Karajan N (eds) Proceedings of the 7th GACM colloquium on computational mechanics, pp 130–133Google Scholar
- 22.Ogden RW (1987) Non-linear elastic deformations. Dover Edition, MineolaGoogle Scholar