Rigid-Body Dynamics with Friction and Impact
SIAM Review
A Numerical Scheme for Impact Problems I: The One-Dimensional Case
SIAM Journal on Numerical Analysis
A Numerical Scheme for Impact Problems II: The Multidimensional Case
SIAM Journal on Numerical Analysis
Stability of semidiscrete formulations for elastodynamics at small time steps
Finite Elements in Analysis and Design
Journal of Computational and Applied Mathematics
Consistency results on Newmark methods for dynamical contact problems
Numerische Mathematik
Analysis of the Modified Mass Method for the Dynamic Signorini Problem with Coulomb Friction
SIAM Journal on Numerical Analysis
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A large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic Signorini problem. We classify the different discretizations into four groups. The first three groups correspond to different ways of enforcing the contact condition: exact enforcement, enforcement with penalty, and enforcement with contact condition in velocity. The fourth approach is based on a modification of the mass matrix. Numerical simulations on two one-dimensional benchmark problems with analytical solutions illustrate the properties of representative methods within each class, focusing first on spurious oscillations triggered by contact and then on energy behavior after multiple impacts. Selected schemes are also tested on a two-dimensional benchmark.