Deformation Wave Codes

In this section, we discuss the role of numerical simulations in studying the response of materials and structures to large deformation or shock loading. The methods we consider here are based on solving discrete approximations to the continuum equations of mass, momentum, and energy balance. Such computational techniques have found widespread use for research and engineering applications in government, industry, and academia. 

Numerical simulations offer several potential advantages over experimental methods for studying dynamic material behavior. For example, simulations allow nonintrusive investigation of material response at interior points of the sample. No gauges, wires, or other instrumentation are required to extract the information on the state of the material. The response at any of the discrete points in a numerical simulation can be monitored throughout the calculation simply by recording the material state at each time step of the calculation. Arbitrarily fine resolution in space and time is possible, limited only by the availability of computer memory and time. 

Furthermore, in many cases, calculational studies can be done in less time and at lower cost than experimental studies. In general, small changes in problem parameters, such as material thicknesses, impact conditions, or 

Numerical simulations are designed to solve, for the material body in question, the system of equations expressing the fundamental laws of physics to which the dynamic response of the body must conform. The detail provided by such first-principles solutions can often be used to develop simplified methods for predicting the outcome of physical processes. These simplified analytic techniques have the virtue of calculational efficiency and are, therefore, preferable to numerical simulations for parameter sensitivity studies. Typically, rather restrictive assumptions are made on the bounds of material response in order to simplify the problem and make it tractable to analytic methods of solution. Thus, analytic methods lack the generality of numerical simulations and care must be taken to apply them only to problems where the assumptions on which they are based will be valid. 

These codes have stressed the current supercomputer, whether it was the CDC 6600 in the 1970s, the Grays in the 1980s, or the massively parallel computers of the 1990s. Multimillion cell calculations are routinely performed at Sandia National Laboratories with the CTH [1], [2] code, yet 

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This chapter is a brief diseussion of large deformation wave codes for multiple material problems and their applications. There are numerous other reviews that should be studied [7], [8]. There are reviews on transient dynamics codes for modeling gas flow over an airfoil, incompressible flow, electromagnetism, shock modeling in a single fluid, and other types of transient problems not addressed in this chapter. 

Large Deformation Wave Codes quantity advected... 

The finite difference numerical simulation was carried out by solving the Euler equations by the Lagrangian approach. The DANE code was used for computation. The air bubble radius was 1.0 mm and the shock overpressure was 1 kbar. Computational grids were, in the axlsymmetric Cartesian coordinates, 150 x 300 and one grid size was 0.025 mm. Figure 5 shows the sequential isobars. It is clearly seen that the peak pressure appear on the side where the shock first impinged the bubble, and the bubble deformation starts which indicates the microjet initiation. However, the rebound shock is so weak that, if compared with the incident shock, the wave front could not be resolved in this numerical scheme. 

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