Dr. Mike Hillman
Karagozian and Case, Inc.

Nodally-Integrated RKPM for Deposition-Based Three-Dimensional Printing

ABSTRACT: A stable and efficient nodally-integrated reproducing kernel particle method (RKPM) is introduced in this work for effective modeling of three-dimensional printing. Deposition types of printing involve topological changes, which can be handled well by meshfree methods, and a fully coupled thermo-mechanical response depending on the material at hand. Thermo-viscous and visco-plastic flow must often also be considered to handle the rheological material response. First, a thermo-mechanical formulation is developed, where it is shown that nodal integration of the coupled equations results in severe spurious oscillations in the solution, worse than pure mechanical problems. A naturally stabilized and variationally consistent nodal integration is then proposed for the coupled equations to stabilize the solution and provide nth order convergence in the two-field problem. Generalized thermo-mechanical theories of the hyperbolic type are also leveraged for a uniform explicit critical time step, with numerical results essentially the same as the classical theory. Benchmark problems are solved to demonstrate the effectiveness of the proposed method in obtaining stable and accurate RKPM solutions for simulations of three-dimensional printing, including fused deposition modeling and printing of fresh concrete.

BIOGRAPHY: Dr. Hillman is a Principal Scientist at Karagozian and Case (K&C) working to advance their multi-physics modeling and simulation techniques and their explicit dynamic meshfree code KC-FEMFRE. Dr. Hillman is an expert in meshfree methods and has over 30 publications in this area and more than 1,000 total citations. In addition to delivering invited talks and keynotes on the subject, he is also the coauthor of a new book “Meshfree and Particle Methods” with J.S. Chen and the late Ted Belystchko, to be available in 2023. Dr. Hillman holds a BS in Civil Engineering from the California State University, Fullerton, and an MS and PhD in Civil Engineering from the University of California, Los Angeles.

Before joining K&C, Dr. Hillman was an Associate Professor and endowed Kimball Early Career Professor of Civil Engineering at Pennsylvania State University. Dr. Hillman’s research focus is computational mechanics, with an emphasis on fundamental development of meshfree methods for the effective application to structural and material failure. He has over 13 years’ experience developing explicit dynamic finite element and meshfree solvers, where his research has been implemented into codes used by the DOD and DOE, the commercial software LS-DYNA, and codes used by private industry. Dr. Hillman is the originator of the concept of variationally consistent integration, which allows unprecedented accuracy in challenging applications such as penetration/fragment-impact, blast-loaded structures, landslides, explosive welding, earth moving, and 3D printing. He has extensively developed advanced nodal integration schemes and shock treatments for accelerated and robust meshfree computations in these problems, including “NSNI”. In 2020, Hillman received the NSF CAREER Award based on a new hybrid meshfree method that allowed convergent solutions in non-local particle methods for the first time.