Effect of the temporal discretization of contact forces on dynamic contact simulations using singular non-standard quadrature rules for the mass matrix

Spurious Lagrange Multipliers oscillations present a significant challenge in implicit contact dynamics simulations. To mitigate these oscillations, (Hager and Wohlmuth 2007) proposed non-standard quadrature rules for the mass matrix, developing the Q 0 and Q 1 modified mass matrices. This work introduces and evaluates an extension of the Q 1 mass matrix to quadratic elements. Additionally, we investigate the influence of the parameter α c , which governs the temporal discretization of contact forces, on the performance of both consistent and modified mass matrices. Numerical results demonstrate that the proposed formulation effectively preserves the oscillation-suppressing capabilities of the Q 1 mass matrix to quadratic elements. Furthermore, it was observed that for α c = 0 the consistent mass matrix displays good results, while for α c = α f the modified mass matrices showcase the best results. • Extension of the formulation of the Q 1 singular mass matrix to 2D quadratic elements. • Study of the impact of the contact forces discretization parameter, α c on the performance of the consistent and singular mass matrices. • Verification through numerical examples of the good performance of the Q 1 mass matrix for quadratic elements. • Identification of distinct behaviors for the Lagrange Multipliers with different combinations of mass matrix and α c parameter. • The consistent mass matrix shows relatively stable results with α c = 0 , while the modified mass matrices work best with α c = α f .