Flexible multibody dynamics formulation using Peridynamic theory

In the nonlocal theory of peridynamic the partial derivatives that appear in the classical (local) continuum mechanics are replaced with integral equations. This is an important feature of peridynamic theory allowing it to be easily applied to problems where partial derivatives of the displacement field may not exist (e.g. sharp corners, bifurcation) inside an elastic continuum medium. Crack edge is an example where displacement field is not continuous and hence partial derivatives are undefined. In the past decade peridynamic theory has attracted researchers in modeling crack initiation and propagation, specifically phenomena like crack branching and multiple micro-crack interactions where other classical (local) theories may experience challenges. Despite its remarkable results peridynamics is still a relatively new topic and it has room for development. One area of development is coupling the peridynamics theory with the traditional multibody dynamics. This will provide a useful simulation tool in damage prediction of rotating parts such as wind turbines or helicopter rotor blades. In this paper, a coupled formulation of peridynamics and flexible multibody dynamics is presented. A floating frame of references (FFR) approach is taken to capture the large rotation and translation of a body that itself is modeled by using peridynamic theory.