Modeling and Simulation of Elasto-Plastic Multibody Systems with Damage

Flexible multibody systems are studied where plasticity is induced by inertial forces. Such a situation may occur when the stiffness of a structure is weakened by an operation under catastrophic environmental conditions. To analyze this phenomenon, plane motions of beam elements with large rigid body motion and moderately large deformation are considered. The equations of motions for the problem are derived by Hamilton’s principle extended to nonconservative systems. Stiffening terms are included via the second order theory of structures. The elastic part of the multibody system generates differential algebraic equations (DAEs). Implicit Runge Kutta schemes are used to transform the DAEs into a nonlinear system of equations which have to be solved for every timestep. The nonlinear part of strain is solved by a fixed-point iteration, where the nonlinear system of equations is solved in every step of the iteration. The high efficiency of this method is due to the fact that the fixed-point iteration of the nonlinear strain is computationally less demanding for the large number of unknowns than the Newton-based nonlinear solver used for the elastic part. The algorithm is optimized by time and space-wise adaptive discretization. As a result, during time-steps with pure elastic deformation a higher order time-integration rule can be used with much larger time-steps as compared to the steps with plastification. A damage law is build into the algorithm in order to treat a wider variety of problems, such as low-cycle fatigue of a machine element. A slider crank mechanism is investigated where low-cycle fatigue of a machine element occurs due to high velocities of the mechanism. Characteristic solution variables are shown as well as the functioning of the adaptive algorithm.