A Floating Frame of Reference Approach to Study Fracture in Flexible Multibody Systems using Peridynamics

Abstract Multibody dynamic (MBD) analysis enables the study of mechanical systems with bodies undergoing large displacements and rotations, connected by joints and force elements. These bodies often interact with their environment and operate over long time frames. A previous study proposed integrating peridynamics (PD) into MBD to model structural deformations, including nonlinear behaviour like crack initiation and propagation. However, the high computational cost of that formulation limited its application to realistic materials and long simulations. This work introduces two new formulations to address the computational challenges arising from the contrasting time scales of rigid and flexible motions. Both approaches are based on a floating frame of reference (FFR), allowing the separation of rigid body motion from flexible deformation. When deformations are small, component mode synthesis (CMS) reduces the model order and limits high frequencies, enabling larger time steps while maintaining accuracy and stability. For nonlinear deformations or fracture, a full FFR without order reduction is used. Numerical examples of a slider-crank system compare the new approaches with the previous one, showing significant efficiency improvements. A landing gear model further demonstrates their potential in realistic applications. These developments lay the groundwork to explore fracture prediction in mechanical systems.