A novel non-linearly explicit second-order accurate L-stable methodology for finite deformation: Hypoelastic/hypoelasto-plastic structural dynamics problems

A novel non-linearly explicit second-order accurate L-stable computational methodology for integrating the non-linear equations of motion without non-linear iterations during each time step, and the underlying implementation procedure is described. Emphasis is placed on illustrative non-linear structural dynamics problems employing both total/updated Lagrangian formulations to handle finite deformation hypoelasticity/hypoelasto-plasticity models in conjunction with a new explicit exact integration procedure for a particular rate form constitutive equation. Illustrative numerical examples are shown to demonstrate the robustness of the overall developments for non-linear structural dynamics applications.