This is an abstract for
NWU2013: Advances in Computational Mechanics with Emphasis on Fracture and Multiscale Phenomena. Workshop honoring Professor Ted Belytschko’s 70th Birthday. April 18, 2013 – April 20, 2013, Evanston, IL, USA
The organizers allocated only 10 minutes for each person’s talk (including big wigs like Tom Hughes), so we might just present this topic in the form of a puppet show with enough information to tickle the audience to chat with us about it in the hallway!
Rebecca Brannon*, Alireza Sadeghirad, James Guilkey
Department of Mechanical Engineering
University of Utah
Salt Lake City, UT, 84112
The material point method (MPM) saves field data at particles that move relative to a temporary background grid. Particle domains are polygons (polyhedra in 3D) that tessellate the body. Until recently, only conventional FEM basis functions (e.g., tent functions in 1-D) have been used on the grid to solve the weak form of the momentum equation in an updated Lagrange formulation. A new method, called convected particle domain interpolation (CPDI) replaces each FEM basis function with the interpolation of that same function to particle corners . This new CPDI basis inherits linear completeness from the source FEM basis while having the advantage of stretching with particles to avoid numerical fracture while also providing more accurate evaluation of the grid’s nodal force and mass integrals (see  for an animation). The generalized interpolation material point (GIMP) framework  identifies variants of MPM to differ only by their (often implicit) adoption of different “particle characteristic functions” in weighted averages appearing the nodal integrals, but the de facto use of approximate weight functions is herein validated. By optimizing the integrand to both particle and mesh topology and also by accommodating more accurate descriptions of angled boundaries (essential for mesoscale simulations), CPDI noticeably improves rate of convergence and achieves stable results in problems that otherwise exhibit spurious numerical fracture caused by fractional particles per cell. These improvements are illustrated through rigorous verification testing via the method of manufactured solutions.
 A. Sadeghirad, R. M. Brannon, and J. Burghardt, “A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations”, International Journal for Numerical Methods in Engineering, 86(12): 1435-1456, 2011.
 Bardenhagen S, Kober E. The generalized interpolation material point method. CMES – Computer Modeling in Engineering and Sciences 2004; 5:477–495.