Discrete Element Method for Modeling Penetration

The Discrete Element Method (DEM) discretizes a material using rigid elements of simple shape. Each element interacts with neighboring elements through appropriate interaction laws. The number of elements is typically large and is limited by computer speed. The method has seen widespread applications to modeling particulate media and more recently to modeling solids such as concrete, ceramic, and metal. For problems with severe damage, DEM offers a number of attractive features over continuum based numerical methods, with the primary feature being a seamless transition from solid phase to particulate phase. This study illustrates the potential of DEM for modeling penetration and briefly points out its numerous advantages. A weakness of DEM is that its convergence properties are not understood. The crucial question is whether convergence is obtained as DEM element size vanishes in the limit of model refinement. The major focus of our investigation will be a careful study of convergence for modeling the degradation of a solid into fragments. Our results show that indeed convergence is obtained in several specific test problems. Moreover, elastic interelement stiffness and damping properties were proven to be particle size-independent. However, convergence in material failure due to crack growth is obtained only if the interparticle potentials are properly constructed as functions of DEM element size and bulk material properties such as elastic modulus and fracture toughness.