Contact force multiscale calculation in the framework of the non-smooth dynamic approach

Abstract

Smooth contact models derived from the Hertz theory are widely used in structural dynamics analysis to calculate variable in time forces, stresses, and deformations. However, these models require very small time steps during the period in which bodies are in contact to integrate the equations of motion, yielding in a highly time-consuming numerical solution. Furthermore, penetration between bodies is unavoidable. On the other hand, nonsmooth techniques use an impact law to calculate the impulses. They arrive to a scheme with a constant time step resulting in very efficient calculations. However, these techniques do not provide a straightforward approach to calculate the variable in time contact forces that are needed to verify or design the structural components. In this work, a new methodology of calculation of impact forces that combines the impulse values obtained from non-smooth algorithms together with a local contact force law derived from continuous force models is presented. Thus, the computational time required to calculate the contact forces is reduced significantly. Several numerical examples are presented to show the robustness and performance of the proposed methodology.