A New Node-Node to-Node Approach to Contact/Impact Problems for Two-Dimensional Elastic Solids Subject to Finite Deformation

Contact analysis is an important branch of solid mechanics. Numerical simulation using the finite element method has become the dominant approach recently because of the high nonlinearity of contact problems. In the traditional Lagrangian description for solid mechanics, the numerical nodes are attached to the material particles, making it impossible to maintain node-to-node contact due to independent deformation. Various node-to-segment or segment-to-segment treatments are proposed to discretize the contact interface. But some issues still exist. Specifically, mesh distortion or element entanglement may be present if deformation is large. A new node-to-node approach for 2D contact/impact problems subject to finite deformation is proposed in this report to offer an alternative approach to these traditional methods, wherein node-to-node contact is maintained throughout the contact process. This method is based on the Arbitrary Lagrangian-Eulerian algorithm (ALE). One or both bodies in the two-body contact problem have an ALE mesh, which is independent of the material particles and has prescribed motion set to maintain node-to-node contact. The strategy of the ALE mesh motion has two steps: (1) to move nodes in the active set to maintain node-to-node contact (2) to smooth ALE mesh to improve mesh quality using the Laplacian or angle-based smoothing algorithm. Problems of interest in this study are contact/impact problems wherein the implicit mid-point rule is used as the primary time stepping algorithm to find the solution incrementally. In order to conserve the system energy, the persistency condition is incorporated as the contact constraint. The augmented Lagrangian method is primarily used to apply contact constraints. Non-classical Coulomb friction laws are used where friction is present. Several quasi-static and impact examples are given to demonstrate the performance and validity of the new approach.published or submitted for publicatio