Combining vibrational linear-by-part dynamics and kinetic-based decoupling of the dynamics for multiple elastoplastic smooth impacts

This article proposes a linear-by-part approach for elastoplastic 3D multiple-point smooth impacts in multibody systems with perfect constraints. The model is an extension of a previous version, restricted to the perfectly elastic case, able to account for the high sensitivity to initial conditions and for redundancy without assuming any particular collision sequence (Barjau et al., Multibody Syst. Dyn. 31:497–517, 2014). Energy losses associated with compression and expansion in percussive analysis is a matter as complex as the physical phenomena involved, at the nanoscale level, for different materials. Simplified models can be developed for specific purposes, which can retain the most relevant trends of internal damping and at the same time be suitable for a particular analytical approach of impact mechanics. In the context of this article, energy dissipation due to material deformation is introduced through a linear-by-part elastoplastic model consisting on two elementary sets of springs and dry-friction dampers. The first set accounts for inelastic behavior (energy loss without permanent indentation), whereas the second one introduces plasticity (that is, permanent indentation). In inelastic and plastic collisions, instantaneous unilateral constraints may appear, thus reducing the number of degrees of freedom (DOF) of the system. The calculation of the corresponding normal contact force at the constrained points is then necessary in order to detect whether the constraint holds or disappears (either because a new compression or an expansion phase starts, or because contact is lost). Different simulated application examples are presented and thoroughly discussed.