Material Model Testing in the DYNA3D Code: Material Models 1 through 5

Abstract

This report is the first volume in an effort to study the material model implementations in DYNA3D, using the latest developmental version of the code. Input files were derived from a template supplied by Jerry Lin to perform an equation-of-state study. Most of the simulations use 10 cubes, each 1 cm on a side with a density of 8.03 (steel). Each of the cubes tests a different aspect of the material model. The first three cubes are testing normal stresses and normal strains (uniaxial stresses and strains) placed on the cube parallel to the x-axis, y-axis and z-axis, respectively. The x (or y or z) = 1 face of the cube is moved along the x-axis (or y-axis or z-axis) to test the model, while the opposite side remains in the x (or y or z) = 0 plane. For some of the tests, the nodes are free to move perpendicular to the applied strain to allow the cross-sectional area of the cube to change in response to being placed under pressure or tension (to test Poisson’s Ratio), while in others the nodes are frozen to eliminate dynamic effects resulting from the code. The cube is placed in tension along the axis being tested and then released, followed by a cycle of compression and release. This tension/compression cycle is repeated 3 more times. The additional cycles allow for the model to be tested under different loads. For these calculations, the amount by which the cube is stretched and compressed is varied from cycle to cycle to allow testing of model features. Cubes number 4 and 5 are intended to test xy shear stresses/strains. This is done by sliding one face of the cube in its plane parallel to the axis of interest. For example, for cube 4, the upper face of the cube is slid in the y=1 plane in a direction parallel to the x-axis (so there are no changes in the y and z coordinates of the points in the plane) and then returned to its starting position. This preserves the volume of the cube, so there is no change in density or pressure. The cycle is repeated 8 times. For cube 5, the plane of the cube satisfying x=1 is slid in this plane in a direction parallel to the y-axis and then returned to its starting position. This preserves the volume of the cube, so there is no change in density or pressure. The cycle is repeated 8 times. Cubes number 6 through 9 repeat these tests for yz shear stresses/strains (Cubes 6 and 7) and zx shear stresses and strains (Cubes 8 and 9). For reasons discussed in the next paragraph, it is unclear if these tests represent a state of pure shear stress and shear strain in the code. Application of shear stresses and strains should not, in general, result in the appearance of normal stresses and strains in Cubes 4 - 9. In the infinitesimal limit, this result might be obtained. However, DYNA3D is a finite deformation code and in the real deformations used in the code, this result is not achieved and the individual components of the normal stresses and strains are non-zero during the cycling. However, the sums of the normal strains are zero in these tests and, except in the case of thermally dependent models, so are the sums of the normal stresses. Cube 10 tests the response of the material model to a hydrostatic loading of the cube. The load curve used for the first three tests is used again and applied to each of the 8 nodes in a manner causing the cube to be either compressed or expanded. This compression/tension cycle is repeated 4 times. The additional cycles allow for the model to be tested under different loads. The amount by which the cube is stretched and compressed is varied from cycle to cycle to allow testing of model features. This document will discuss the testing of Material Models 1 through 5. Relevant results from the test cubes will be discussed. A discussion of the results from all 10 test cubes will be presented only if necessary.