Numerical Simulation of Large Plastic Deformations and Free Flight of a Beam After Impact with a Rigid Stop

A numerical method for analyzing fast-flowing dynamic behavior of a system of bodies during their contact interaction is investigated. The research method is based on the analysis of solution convergence when the finite element grid is condensed and the time step is reduced. The algorithm and the corresponding computer program were developed by the authors. The problem is considered in a geometrically and physically nonlinear formulation, large elastic and plastic deformations are considered. The finite element method is used. The simplest triangular finite element with a linear displacement field is used. The initial grid of finite elements is assumed to be uniform; in the process of plate deformation, it is greatly modified, since large displacements are simulated. Plane strain is considered. The criterion for the onset of plastic shear is shear stress achieving a certain limit set in the conditions of the problem. The relationship between strain and stress implemented in the program implies taking into account the strain history of the material at a given point, and not just the current value of strain. The model also allows to consider unloading, if such is the case. The calculation model is focused on the correct consideration of geometry with large displacements and rotation angles, allows consideration of free flight of the components of the model, their contact interaction. In terms of integrating the equations of motion, the program relies on an explicit calculation scheme with Adams extrapolation. The application of the described algorithm is based on the example problem of a flying short beam (plate) hitting a rigid stop. The example considers impact interaction, rebound from the stop, and free flight of the vibrating beam. The elastic and inelastic behavior of the material is compared. The wave nature of the solution is demonstrated. The example is comprehensively analyzed, in particular, convergence is investigated when the grid is doubled and the time step is reduced. The maximum number of finite elements is 204800. The numerical algorithm has a number of features: constant stress acquisition and storage for planes oriented along the fixed global axes, and the possibility of shear deformation at any of the critical planes. It is concluded that it is impossible to achieve convergence for accelerations when the grid is condensed, and it is concluded that this impossibility is not fatal for the method. As an alternative, it is proposed to determine the acceleration of the center of mass of the beam or any fragment of the model.