Isogeometric collocation for nonlinear dynamic analysis of Cosserat rods with frictional contact

We present a novel isogeometric collocation method for nonlinear dynamic analysis of three-dimensional, slender, elastic rods. The approach is based on the geometrically exact Cosserat model for rod dynamics. We formulate the governing nonlinear partial differential equations as a first-order problem in time and develop an isogeometric semi-discretization of position, orientation, velocity and angular velocity of the rod centerline as NURBS curves. Collocation then leads to a nonlinear system of first-order ordinary differential equations, which can be solved using standard time integration methods. Furthermore, our model includes viscoelastic damping and a frictional contact formulation. The computational method is validated and its practical applicability shown using several numerical applications of nonlinear rod dynamics.