An understanding of vectors, matrix algebra, differential equations, basic numerical methods and basic engineering mechanics/physics is assumed. Participants should also be familiar with using some hydrocode whether Lagrangian, Eulerian or ALE based, as well as a desire to better understand the underlying physics, numeric and computational aspects that make up these Hydrocodes.

• Continuum Mechanics Basics
• Lagrangian, Eulerian and ALE Reference States
• Deformation and Motion
• Time Derivatives, Deformation Gradient, Rotation Matrix
• Strain, Velocity Gradient, Rate of Deformation
• Pressure and Deviatoric Stress
• Constitutive Behavior Intro
• Shock Waves
• Conservation Laws - Mass, Momentum and Energy
• Internal Energy
• Explicit Finite Element Method (FEM)
• What is explicit? What is implicit?
• 1D and 2D FEM Interpolation, 2D parametric Coordinates
• Derivatives w.r.t. x and y
• Total Lagrangian and Updated Lagrangian Formuations
• B Matrix and the Internal Force vector f
• Central Difference Time Operator
• Critical Time Step
• Full and Reduced Integration and Hourglassing
• Structural Elements - Beams, Plates and Shells
• Fracture and Failure
• Waves and the Equation of Sate (EOS)
• Elastic Waves
• Pressure and the EOS
• Wave Speeds
• Free Surfaces and Fixed Boundaries
• Shock Waves
• Conservation of Mass, Momentum and Energy
• Us - Up Relationship
• Mie-Gruneisen EOS
• Impact Against a Rigid Wall
• Detonation Basics
• CTH EOS Options

The objective of this three day short course is to present and discuss in detail the basic aspects of Lagrangian/Structural Hydrocodes. Participants will learn pertinent aspects of: continuum mechanics, the Explicit Finite Element Method (FEM), wave propagation and shock physics including the Equation of State (EOS), and time stepping and instability. An important goal is a better understanding of the computational physics/mechanics underlying these hydrocodes - i.e., what makes them "tick".

Participants will learn how to apply their knowledge of hydrocodes and modeling techniques to problems of interest. The dynamic behavior of modern structures and materials subjected to very transient loadings can be quite complex, especially when some sort of failure is precipitated. Modeling tools used for the simulation of such highly transient and nonlinear problems fall under the general heading of hydrocodes. Important problem applications for such software includes: impact of objects, design and analysis of structures, as well as military applications such as the design and simulation of weapon systems and their effects on targets. Commercial Finite Element Method (FEM) programs such as LS-DYNA and ABAQUS-EXPLICIT are widely used for structural analysis and design throughout the world. The Department of Defense (DoD) as well as the Department of Energy (DOE) apply many hydrocodes such as the widely used DOE codes CTH, ALE3D, and Presto. This is not a short course on how to use a specific code, nor is it just a bunch of theory and equations. Rather it is a computational orientated short course designed to help the attendee gain a better basic understanding of these complex analysis tools and how to apply them. Helping the attendees to better "think like the experts think" is a key concern and goal.

Dr. Carl T. Dyka received his Ph.D. in Engineering Mechanics in 1978 from the University of Connecticut. He received his MS in Structural Engineering in 1974 and BS in Civil Engineering in 1973 both from the University of Massachusetts. He has been an analyst for the Naval Surface Warfare Center (NSWC) since 2000.

Currently he is a senior analyst in the Lethality and Effectiveness Branch at NSWC-Dahlgren, in Dahlgren, VA. During most of the 1990's, he was a researcher in computational mechanics at the Naval Research Laboratory in Washington, DC.

In the 1980's, Dr. Dyka was an analyst and finite element developer/researcher for the Electric Boat Division of General Dynamics in Groton, CT. During the 1980's and into the early 1990's he was also an adjunct professor at the University of Connecticut and taught several different graduate courses.

Dr. Dyka has wide experience in computational mechanics that includes: R&D in finite element and constitutive relations, boundary element, particle methods, structural acoustics, fluid-structure interaction; extensive analysis experience using several widely know analysis codes; teaching at the graduate course level as well as at the short course level; and a significant amount of commuter programming and code development.

He is recognized by the both the DoD and DOE as a national level expert in Computational Structural Mechanics.

Currently Dr. Dyka serves in an advisor capacity to High Performance Computing (HPC) as the Computational Technology Area (CTA) in Computational Structural Mechanics. HPC has a total of ten CTA's covering the computational and applications spectrum of interest for the DoD. The CTA's function as an advisory board to top level HPC management.

1. Nonlinear Finite Elements for Continua and Structures, T. Belyschko, W. K. Liu and B. Moran, Wiley 2000.
2. Dynamic Behavior of Materials, M. A. Meyers, Wiley 1994.

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