Modeling of impact problems using an H-adaptive, explicit Lagrangian finite element method in three dimensions.

摘要

An h-adaptive algorithm was developed to enhance the modeling of 3D impact problems and implemented within an explicit, Lagrangian finite element code. Contact plays a pivotal role for this class of problems. As such, accurate resolution of the contact surface and surrounding region is critical to the success of any predictive approach. With a suitable choice of error indicator, the adaptive algorithm can dynamically modify the mesh so as to improve resolution in the contact region. An indicator based upon the root mean square error of the Green-Lagrange strain proved effective for this purpose. This indicator can be considered an extension of the recovery-based a posteriori estimator originated by Zienkiewicz and Zhu. An alternative indicator based upon the rate of deformation was also investigated. The merits of both indicators were quantified through a series of numerical tests using a novel benchmark problem involving a Taylor test with a square rod. These numerical tests assessed the convergence characteristics of the indicator as well as its performance within the time-based, forward-moving adaptive scheme. Implementation procedures for element refinement were also investigated. Of particular interest were the implications of 3D analysis on adaptivity. Specific issues of interest concerned data structure and implementation, coupling effects between adaptivity and element deletion, and potential interaction with traditional approaches for treatment of contact. The effectiveness of the algorithm was demonstrated for a number of 3D problems, involving both penetrating and non-penetrating impacts.