A hybrid explicit solution technique for quasi-static transients

In certain instances, such as in the modelling of manufacturing process, undesirable dynamic effects may accompany the use of an explicit transient solution, while the use of full dynamic relaxation is inefficient for this class of problem due to critical damping. In this paper, an approach that merges the salient features of dynamic relaxation with those of the fully explicit solution, is presented. The key objective of the method is the removal of unwanted dynamic (e.g. inertial) effects, while providing for a transient kinematic loading history. This work focusses on the development of an adaptive mass algorithm consistent with specified damping and time step for use within the framework of explicit time integration. The paper describes the hybrid solution formulation and the implementation of the proposed algorithm. Applications include an experimental punch test used for material characterization and a rolled joint expansion manufacturing process, both involving three-dimensional finite deformation.