A Thermo-mechanical Meshfree Formulation with Application to Simulation of Additive Manufacturing

ABSTRACT: Coupled thermo-mechanical physics are present in several applications such as the popular three-dimensional printing technique of fused deposition modeling (FDM), which is the focus of the present work. For FDM, the problem includes large-strain thermomechanical analysis with thermo-viscous fluid flow, as well as topological changes in the domain. The latter issue presents a serious challenge for traditional mesh-based numerical methods which require remeshing. To overcome this, a meshfree numerical approach for solving the associated fully coupled governing equations is developed. First, a stabilized nodal integration is proposed for the thermo-mechanical problem to provide stable and efficient analysis. A variationally consistent integration method to correct the error in nodal integration is then introduced. Several benchmark problems solved to demonstrate the effectiveness of the proposed method for fully coupled classical and generalized thermoelasticicity, finite-strain thermoplasticity, and thermoviscous fluid flow. FDM simulations are also presented, with the results verified with solutions from other numerical methods.

BIOGRAPHY: Dr. Michael Hillman is an Assistant Professor of Civil Engineering at Penn State and is the holder of the Kimball Professorship. His research is focused on the development of robust numerical methods for simulating coupled problems, problems with extreme deformations, and methods for simulating fracture in composite microstructures. His research has been implemented into production codes used by the DOD and DOE, the commercial code LS-DYNA, as well as codes for private industry. Dr. Hillman received his PhD in civil engineering in 2013 from UCLA, and worked as a postdoctoral scholar at UC San Diego until he joined Penn State in 2016. He is an elected member of several technical committees, serves on several editorial boards, and has helped to organize twenty minisymposia. His research is currently being funded by the National Science Foundation, the Army Corps of Engineers, and Karagozian and Case, Inc. In 2020, Hillman received the CAREER Award from NSF.