Partitioned formulation of contact-impact problems with stabilized contact constraints and reciprocal mass matrices

This work presents an efficient and accuracy-improved time explicit solution methodology for the simulation of contact-impact problems with finite elements. The proposed solution process combines four different existent techniques. First, the contact constraints are modeled by a bipenalty contact-impact formulation that incorporates stiffness and mass penalties preserving the stability limit of contact-free problems for efficient explicit time integration. Second, a method of localized Lagrange multipliers is employed, which facilitates the partitioned governing equations for each substructure along with the completely localized contact penalty forces pertaining to each free substructure. Third, a method for the direct construction of sparse inverse mass matrices of the free bodies in contact is combined with the localized Lagrange multipliers approach. Finally, an element-by-element mass matrix scaling technique that allows the extension of the time integration step is adopted to improve the overall performance of the algorithm. A judicious synthesis of the four numerical techniques has resulted in an increased stable explicit step-size that boosts the performance of the bipenalty method for contact problems. Classical contact-impact numerical examples are used to demonstrate the effectiveness of the proposed methodology.