A segment-to-segment algorithm for finite volume mechanical contact simulations

Despite the finite element method being commonly used in the area of computational contact mechanics [1], the recent developments of finite volume method in the field of computational solid mechanics allows its application for solving the complex contact problems. The numerical modelling of complex contact problems is a challenging task, mainly due to the strong nonlinearity involved, such as geometrical, material and contact nonlinearity [1]. Due to the increased application of finite volume method for dealing with the stress analysis problems [2,3], it is necessary to develop a unique, efficient and robust finite volume contact algorithm, that could be applied to a wide range of contact problems.

The current finite volume mechanical contact algorithm [3,4,5] is based on the calculation of contact forces at the vertices of the discretized slave contact surfaces, whereas the contact force on the master contact surface is obtained using the General Grid Interface interpolation [6]. Accordingly, the contact force is calculated using the penalty method and subsequently explicitly updated within the segregated solution framework. Such approach should appear to be robust and accurate when dealing with the complex contact problems that include large deformations and plasticity.

This study presents a new segment-to-segment contact algorithm for the calculation of normal contact force. The proposed algorithm calculates contact force using an integral value of the penetration, which should improve the overall accuracy of the numerical model. The inspiration for such approach is based on the segment-to-segment contact formulation commonly used in the finite element contact algorithms [7]. The implementation will allow the calculation of mechanical contact on arbitrary unstructured meshes and large deformation of contacted bodies. The proposed contact algorithm was tested using the contact benchmarks that include large deformation and large sliding contact. The obtained results were compared with the current implementation of the finite volume contact algorithm as well as the finite element results that are well reported in the literature. The authors believe that the ongoing study should serve as the basis for the future development of the finite volume contact algorithms.

References [1] Wriggers, P., Computational Contact Mechanics. Springer, 2 nd edition, 2006. [2] Tuković, Ž., Karač, A., Cardiff, P., Jasak, H. and Ivanković, A., OpenFOAM finite volume solver for fluid-solid interaction. Transactions of FAMENA, 42(3), pp.1-31, 2018. [3] P. Cardiff, Ž. Tuković, P. DeJaeger, M. Clancy, A. Ivanković. A Lagrangian cell-centred finite volume method for metal forming simulation, International Journal for Numerical Methods in Engineering,1777-1803, 2017 [4] P. Cardiff, A. Karač, A. Ivanković. Development of a finite volume contact solver based on the penalty method, Computational Materials Science, 283-284, 2012 [5] Škurić, V., De Jaeger, P. and Jasak, H., Lubricated elastoplastic contact model for metal forming processes in OpenFOAM. Computers & Fluids, 172, pp.226-240, 2018 [6] Beaudoina, M. and Jasak, H., Development of a Generalized Grid Interface for Turbomachinery simulations with OpenFOAM. In Open Source CFD International Conference, 2008. [7] Zavarise, G. and Wriggers, P., A segment-to-segment contact strategy. Mathematical and Computer Modelling, 28(4-8), 497-515, 1998