University of Notre Dame College of Engineering
C-SWARM | Center for Shock Wave-processing of Advanced Reactive Materials

C-SWARM

Center for Shock Wave-processing of Advanced Reactive Materials

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An Embedded Mesh Method for Coupling Lagrangian and ALE Finite Element Models

Mike Puso, P.h.D.

Methods for coupling overlapping foreground and background discretizations (e.g. embedded mesh, overset and immersed boundary methods) can make tractable complex models (Fig. 1). Here, an embedded mesh approach is developed to couple foreground Lagrangian finite element meshes (or SPH discretizations) to a background ALE mesh [1,2]. A Lagrange multiplier approach is used to enforce velocity constraints at the interface. Modifications are made to the advection scheme to account for the background fluid flow around the foreground body. The schemes for computing the Lagrange multipliers and time integrating the explicit equations of motion were designed to be provably stable. Details of the stability analysis will be presented. It is also shown that the method has no deleterious affect on the stable Courant time steps i.e. there is no modification of the time step to account for the embedded mesh. Consequently, the proposed approach exhibits excellent robustness in a variety of rigorous analyses. Mesh studies are presented demonstrating convergence. Example problems including contact, penetration, blast, SPH foreground and failure with evolving fragmentation are also presented.

Fig. 1 Foreground Lagrange plate mesh (grey) and pipe meshes (orange and yellow) overlap a
background grid composed of air (blue) and high explosive (red).Fig. 1 Foreground Lagrange plate mesh (grey) and pipe meshes (orange and yellow) overlap a background grid composed of air (blue) and high explosive (red). The blast causes the plate to crush the pipes and compress air trapped in pipes. The background ALE mesh is “pulled” into areas to follow shocks and capture details.

[1] M. Puso, J. Sanders, R. Settgast, and B. Liu “An Embedded Mesh Method in a Multiple Material ALE”, Computer Methods in Applied Mechanics and Engineering (15) 245-246, pp.273-289, (2012).
[2] M. Puso, E. Kokko, R. Settgast, J. Sanders, B. Liu “An Embedded Mesh Method: Mathematical and Numerical Aspects” International Journal for Numerical Methods in Engineering 104 697-720, (2015).

Work performed under the HPC Software Application Institute on Blast Protection for Platforms and Personnel under funding from the DoD HPC Modernization Program

Featured People

Mike Puso, P.h.D.Mike Puso, P.h.D.

Lawrence Livermore
National Laboratory

 

Dr. Puso graduated from UC Davis with a PhD in structural mechanics in 1995. Upon graduating, he got a position at Lawrence Livermore National Laboratory as a research engineer and code developer and has been employed there since. In addition to being one of the lead developers on a number of the lab codes (DYNA3D, ALE3D etc.) he has published a number of papers in the area of contact mechanics, finite element technology, particle methods, rigid body dynamics, polymer material models and fluid structure interaction. During his tenure, he also was PI on a number of industrial technology transfer projects including a superplastic forming project with Boeing and a spring back predictability project with GM, Ford and Chrysler. In addition, he has taught graduate finite element classes at UC Berkeley. He is currently the project lead on a combined DOD and LLNL project to produce better simulation techniques to aid in the design of blast protection for military personnel vehicles.