Speaker Bio and Abstract


Michael Hillman, Ph.D.
L. Robert and Mary L. Kimball Assistant Professor of Civil Engineering
The Pennsylvania State University

Seminar Title

“Meshfree Computational Frameworks for Extreme Event Simulation"


Extreme events such as natural and man-made disasters contribute to a significant loss of life and property. Effective numerical methods facilitate the advancement of protection against extreme conditions by enabling threat estimation and evaluation of damage mitigation strategies. Meshfree methods can overcome the shortcomings of traditional finite element methods for simulating extreme conditions, however careful attention must be paid to the accuracy and stability of the numerical solution due to the difficulty in performing domain integration. Nodal integration is efficient, and is particularly attractive for these simulations since it maintains meshfree characteristics. However, non-convergent solutions are obtained due to the low integration accuracy, and severe underestimation of the energy associated with small-wavelength modes results in instability of the numerical solution.

A general framework to achieve the optimal order of convergence consistent with the order of approximation space without high-order quadrature is proposed to address the shortcoming of low solution accuracy due to nodal integration. First, the variational consistency conditions for achieving arbitrary order Galerkin exactness in a boundary value problem are derived, and a variationally consistent integration (VCI) method is then formulated to satisfy these conditions. It is demonstrated that under the VCI framework, optimal convergence can be achieved while using low-order quadrature rules. The instability in nodal integration is addressed by introducing a Taylor series expansion of the nodal strains with implicit gradients for computational efficiency and stability. The proposed method is validated under a wide range of extreme conditions, and examples are provided to demonstrate the effectiveness of the method for modeling extreme events such as bullet penetration, blast-loaded structures, and landslides.

Speaker Bio

Dr. Michael Hillman is currently an Assistant Professor of Civil Engineering at Penn State and holds the endowed L. Robert and Mary L. Kimball Career Development Professorship. His research focus is the development of robust numerical methods for structures under extreme loadings that facilitate damage assessment and the advancement of protective technologies. His research has been implemented into several simulation codes, such as Sandia National Laboratory’s SIERRA code, and codes used by the U.S. Army Engineer Research and Development Center. Dr. Hillman received his 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 until he joined Penn State in 2016.

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