Two new three-dimensional contact algorithms for staggered Lagrangian Hydrodynamics

Abstract This paper presents two new three-dimensional contact algorithms for staggered Lagrangian Hydrodynamics, named discrete accurate matching method and discrete Lagrangian multiplier method. These new contact algorithms utilize the unified contact algorithm for contact searching. Contact segments from all potential contact surfaces are treated as a single set. The basic idea of these new methods is to partition all contact segments into triangular facets firstly; then for each pair of two triangular facets which correspond to a hitting node and a target node respectively, these two triangular facets are projected to one plane and their intersection area is calculated; the nodal masses and nodal forces of the hitting node and the target node are distributed to the intersection portions of these two triangular facets respectively according to the proportion of the intersection area to corresponding nodal area. In the discrete accurate matching method, the masses and forces of the intersection portions of these two triangular facets are added to corresponding contact nodes of each other, and then the accelerations and velocities of the contact nodes are updated; while in the discrete Lagrangian multiplier method, the intersection portions of these two triangular facets are considered as a 1D contact pair in the normal direction for which the contact force is explicitly calculated by the Lagrangian multiplier method for a 1D contact pair of one hitting point and one target point, then the contact force being added to corresponding contact nodes. These new contact algorithms are assessed through several numerical tests performed on three-dimensional structured and unstructured meshes. The results of these tests show the accuracy and robustness of these new methods.