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A specialized computer program has been assembled that can calculate the effects of a deformable axisymmetric projectile impacting a visco-elastic medium. An earlier Eulerian code, EVE, was designed to calculate the impact of a rigid projectile with a visco-elastic medium. Another existing code, the Lagrangian CRAM, capable of calculating the deformation of a multi-material projectile due to pressure loading along the projectile surface, was adapted to the calculation of projectile deformation. The LYNX code was developed by modifying and linking these EVE and CRAM codes so that the EVE code provides a pressure loading along the projectile surface and the CRAM code calculates the resultant deformation and motion of the projectile. This process is rep-ated, using realistic time steps, for as long as the problem is of interest. A discussion of the program and the user-supplied input is given in Volume I of this report. A test calculation in which a lead cylinder impacts gelatin is described and discussed. The results of this calculation agree with measurements made at the Ballistic Research Laboratories. A listing of the version of the program which is operational on the S3 Univac 1108 facility is given in Volume 2., See also Volume 1 dated Nov 1974, ADA018740.

The response of thin targets to projectile impact is investigated under the assumption that membrane theory is sufficient to describe the interaction theoretically derived. Residual velocities of penetrating projectiles for a number of materials are compared with experimental data. The method allows data for a specific target thickness, projectile size and projectile velocity to be used in determining the ballistic properties under other impact conditions. This requires that a value for the ballistic figure of merit, W, be obtained for each material, which can then be used to rank a number of materials in a quantitative fashion, even though the tests performed were quite dissimilar.

A specialized computer program has been assembled that can calculate the effects of a deformable axisymmetric projectile impacting a visco-elastic medium. An earlier Eulerian code, EVE, was designed to calculate the impact of a rigid projectile with a visco-elastic medium. Another existing code, the Lagrangian CRAM, capable of calculating the deformation of a multi-material projectile due to pressure loading along the projectile surface, was adapted to the calculation of projectile deformation. The LYNX code was developed by modifying and linking these EVE and CRAM codes so that the EVE code provides a pressure loading along the projectile surface and the CRAM code calculates the resultant deformation and motion of the projectile. This process is repeated, using realistic time steps, for as long as the problem is of interest. A discussion of the program and the user-supplied input is given in Volume I of this report. A test calculation in which a lead cylinder impacts gelatin is described and discussed. The results of this calculation agree with measurements made at the Ballistic Research Laboratories. A listing of the version of the program which is operational on the S3 Univac 1108 facility is given in Volume II. (Author)

When a plane shock wave moving through one material meets an interface with a new material, the shock is transmitted at a different strength into the target material and a new wave is reflected back into the parent material. The strength of the transmitted wave is determined in this report for the case when both materials are solid and can be described by a Mie-Gruneisen equation of state.

In the past four years several authors have reported Eulerian hydrodynamic codes for the computation of compressible fluid flows in which the independent variables are two space dimensions and time. The present paper describes the generalization of such a code to include also the forces due to strength which arise within the material to resist shear deformation. In choosing the precise model for such a generalization, it is useful to recall that Eulerian codes have proven to be especially suited to the description of flows in which material elements undergo extreme distortion. It is in precisely this area of treating extreme distortions that Lagrangian codes, despite their success in treating other aspects of strength-dependent deformation, encounter serious difficulties. In order, then, to fill the apparent need for a strength code which is capable of the simple and efficient computation of flows involving large deformations, the present code development was initiated in 1965. The code has subsequently been the subject of continuing development during the course of a number of applications., Sponsored in part by DARPA. See also Part 3, AD678567.

Equations for the motion of a continuous medium capable of supporting shear stresses are reported by a number of authors, but the complete set does not appear to have been published in a form suitable for solution by Eulerian hydrodynamic codes. Specifically, the Eulerian equations of motion for a compressible medium acted upon by a general stress tensor are required. In this volume the equations of motion are discussed starting from the principles of mass, momentum and energy conservation for finite masses. From these the differential equations of motion are derived. The constitutive equations relating stress and strain are required to complete the mathematical description. It is also shown that the difference equations for hydrodynamic codes can be conveniently obtained from the integral form of the conservation laws. The nature of a medium is specified by its equation of state, which is used to calculate the pressure from the density and specific internal energy, and a tensor constitutive equation relating deviator stresses, deviator strains and their rates. Constitutive equations for the shear stresses are discussed and the appropriate forms for elastic, elastic-plastic and rigid-plastic solids as well as for viscous fluids are presented., See also Part 2, AD678566.

The computer program is listed in detail and the general information necessary to set up and run problems is provided. A dictionary of terms used in the program is also included, as well as a number of tables and charts describing the program in outline form. Forms for setting up a sample problem are also given. This information provides the user with a capability to run his own problems and, in addition, the intent is to describe the code in enough detail that any changes the user may require can be readily made., See also Addendum, AD678568.

The work reported consists of three task areas: (a) development of constitutive models and computer methods for calculating stress wave effects in geologic media in the vicinity of a buried energy source, (b) verification of the computer models and their application to examine the sensitivity of ground motion predictions to the material parameters assumed in the constitutive models, and (c) development of methods for calculating the perturbation of residual tectonic stress-strain distributions induced by changing the pore water pressure.

This addendum describes a number of improvements to the version of OIL-RPM documented in GAMD-8497. In EDIT and MAP the changes represent primarily a streamlining of the program. The small change to CDT ensures stability in a more rational manner. The requirements for enlarging the grid are also described, and a flow chart of the equation of state subroutine (ES) is included., See also Part 1, AD678565.

Sponsored in part by the DARPA.

The three principal areas of activity, (1) Numerical solutions of problems in impact, (2) Code development for solving impact problems, and (3) Analytical work on the theory of the impact process, are reviewed, utilizing wherever possible cited papers which have been published during this past year as part of the project work. The investigations covered in these papers are described only briefly in the present status report, familiarity with or availability of the original documents being assumed. The major part of the present discussion is devoted to a status report of unfinished work on the problem of computing strength-dependent and viscous impact flows. A computer program is described for generalizing Eulerian hydrodynamic codes to include these effects and sample calculations are given., See also AD0608870.

This study is devoted primarily to solid-solid impact at velocities in the meteoric range. A continuous Eulerian hydrodynamic code is used to numerically integrate the flow equations for several series of impact problems. The impact velocity, the projectile shape, the density of the projectile, and the equation of state of the interacting materials are varied. Impact crater dimensions are found to increase as the 0.58 power of the impact velocity. Projectiles of the same mass but different densities have the same overall impact effects on the target, for velocities above about 10 to the 6th power cm/sec. Onedimensional and axisymmetric impacts are also computed for materials with an ideal-gas equation of state. These calculations provide some important comparisons with analytical work on the problem of hypervelocity impact. (Author)