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I received my Ph.D. in civil engineering in 2013 from UCLA, and worked as a postdoctoral scholar in the Department of Structural Engineering and the Center for Extreme Events Research (CEER) at UC San Diego. I joined Penn State in 2016 as the L. Robert and Mary L. Kimball Professor and was promoted to Associate Professor in Civil Engineering with tenure. My research program was funded by NSF, the DOD, and private industry, and I received the NSF Career Award for my research in meshfree methods. I joined Karagozian and Case, Inc. as a Principal Scientist in 2022 to develop their RKPM code KC-FEMFRE.
My research interests are nonlinear computational solid mechanics for computationally challenging applications such as penetration/fragment-impact, blast-loaded structures, landslides, explosive welding, earth moving, and 3D printing. My aim is to develop industrial strength Galerkin meshfree methods (like RKPM) that provide robust solutions in these applications in the form of unconditional numerical spatial stability without tunable parameters, convergence, and superior run-times compared with other approaches. |
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To this end I've introduced the concept of variational consistency, which dictates the requirements for attaining arbitrary-order accuracy in the Galerkin solution to partial differential equations. I also developed a method to satisfy these conditions ("VCI") in an efficient and flexible manner applicable to fragmentation problems. Practically, this guarantees that not only the solution will exactly reproduce constant or higher order stresses and strains, but converge with refinement; in the end we find that we can use far fewer degrees of freedom for predictive analysis than say, SPH. Later the variational consistency conditions were subsequently leveraged for developing methods, the most well known being Dongdong Wang group's reproducing kernel gradient smoothing.
My other relatively well-known contributions are naturally stabilized nodal integration ("NSNI") and reproducing kernel peridynamics ("RKPD"). NSNI provides stable solutions in meshfree methods without tunable parameters (like artificial viscosity) with low-cost amenable to large-scale analysis. It has been extended to FEM, IGA, and Peridynamics by Yuri Bazilevs' group at Brown, and served as the basis for other research including the material point method. RKPD has also been extended and developed further by other groups after it's inception.
Core contributions like VCI and NSNI have been implemented into codes used by the DoD (US Army Corps of Engineers' NMAP, NMAP-Micro, and MECA), DoE (Sandia National Laboratories' SIERRA), the commercial code LS-DYNA, as well as codes used in private industry (MEGA - Case New Holland Industrial America LLC, and FEMFREE - Karagozian & Case Inc.).
| hillman_cv_feb2026.pdf |