Time integration errors and energy conservation properties of the Stormer Verlet method applied to MPM

Abstract

The success of the Material Point Method (MPM) in solving many challenging problems nevertheless raises some open questions regarding the fundamental properties of the methodsuchastheenergyconservationsincebeingaddressedbyBardenhagenandbyLoveand Sulsky. Similarly while low order symplectic time integration techniques are used with MPM, higher order methods have not been used. For this reason the Stormer Verlet method, a popular and widely-used symplectic method is applied to MPM. Both the time integration error and the energy conservation properties of this method applied to MPM are considered. The method is showntohavelocallythirdorderaccuracyofenergyconservationintime. Thisisincontrastto the locally second order accuracy in energy conservation of the methods that are used in many MPM calculations. This third accuracy accuracy is demonstrated both locally and globally on a standard MPM test example.