Optimal Transportation Meshfree (OTM) method for simulating extremely large deformation and ballistic limit impact problems. The method combines concepts from Optimal Transportation theory with material-point sampling and local max-ent meshfree approximation. The proposed OTM method generalizes the Benamou-Brenier differential formulation of optimal mass transportation problems to problems including arbitrary geometries, essential boundary conditions, constitutive behavior, and multibody contacts. An energy- based material-point erosion algorithm is also proposed for simulating discontinuous material failure phenomena. Three dimensional OTM simulations with material-point erosion algorithm of impact of metallic plates by spherical particles over a range of impact velocity and thicknesses of plates have been performed to study the performance and efficiency of the OTM method. In-house experiments with the same configurations have been conducted to validate the OTM method.

We have presented an Optimal Transportation Meshfree (OTM) method which enables the prediction of terminal ballistics. The theoretical basis of the OTM method guarantees the exact conservation of mass, linear and angular momentum. The proposed material point erosion algorithm greatly extends the applicability of the OTM method. The performance and accuracy of the proposed method has been tested by three dimensional ballistic limit impact simulations and in-house experiments. The agreement between numerical and experimental results is excellent.