Gordon R. Johnson

SPH for high velocity impact computations

Abstract SPH (Smooth Particle Hydrodynamics) techniques provide the capability to perform high distortion impact computations in a Lagrangian framework. It is also possible to link SPH nodes with standard finite elements such that solutions can be obtained for problems involving both highly distorted flow and structural response. This paper presents the basic computational algorithm which includes a recently developed Normalized Smoothing Function. It discusses issues associated with smoothing functions, smoothing distances, free boundaries, material interfaces and artificial viscosity. It also presents techniques to allow SPH nodes to interact with standard finite element grids through sliding, attachment and automatic generation of SPH nodes from distorted finite elements. Examples are provided to illustrate the capabilities, algorithms and issues.

NORMALIZED SMOOTHING FUNCTIONS FOR SPH IMPACT COMPUTATIONS

This paper presents a normalized smoothing function (NSF) algorithm that can improve the accuracy of smooth particle hydrodynamics (SPH) impact computations. It is presented specifically for axisymmetric geometry, but the principles also apply to plane strain and three-dimensional geometry. The approach consists of adjusting the standard smoothing functions for every node (and every cycle) such that the normal strain rates are computed exactly for conditions of constant strain rates (linear velocity distributions). This, in turn, generally improves accuracy for non-uniform strain rates. This can significantly improve the accuracy for free boundaries, for non-uniform arrangements of SPH nodes, and for small smoothing distances. A new smoothing function is also introduced. The NSF algorithm is shown to provide improved accuracy for a series of cylinder impact examples that includes two different smoothing functions and two different smoothing distances.

Response of boron carbide subjected to large strains, high strain rates, and high pressures

This article presents an analysis of the response of boron carbide (B4C) to severe loading conditions that produce large strains, high strain rates, and high pressures. Experimental data from the literature are used to determine and/or estimate constants for the JH-2 constitutive model for brittle materials. Because B4C is a very strong material, it is not always possible to determine the constants explicitly. Instead they must sometimes be inferred from the limited experimental data that are available. The process of determining constants provides insight into the constitutive behavior for some loading conditions, but it also raises questions regarding the response under other loading conditions. Several Lagrangian finite element and Eulerian finite difference computations are provided to illustrate responses for a variety of impact and penetration problems.

Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations

Abstract This paper describes and demonstrates how a Smooth Particle Hydrodynamics (SPH) algorithm can be incorporated into a standard Lagrangian code such as EPIC. The SPH technique is also Lagrangian, but it has variable nodal connectivity and can handle severe distortions in a manner comparable with Eulerian codes. Included is the SPH algorithm for axisymmetric geometry, example problems using only the SPH option, and example problems where the SPH grid is coupled to the standard EPIC grid. The coupling techniques allow for attachment, sliding, and automatic generation of SPH nodes.

Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations

Abstract Lagrangian particle methods, such as smooth particle hydrodynamics, have been developed recently to include the effect of strength, and these techniques have been successfully applied to high velocity impact problems. These methods allow for variable nodal connectivity and can handle severe distortions in a manner comparable with Eulerian codes. The particle methods generally require more computer time than do standard finite element techniques, and are not accurate under some conditions. As a result, there are some advantages associated with linking the particle methods to standard finite elements. If the particle portion of the grid is restricted to those regions that are severely distorted, then the required computer time is reduced and the accuracy may be increased in the standard finite element grid. This paper describes and demonstrates techniques that include attachment, sliding and automatic generation of particles, which are linked to a standard finite element grid. Computed results show good agreement with test data.

An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation

This paper presents an explicit 2D Lagrangian algorithm to automatically convert distorted elements into meshless particles during dynamic deformation. It also provides the contact and sliding algorithms to link the particles to the finite elements. For this approach the initial grid is composed entirely of finite elements and the response is computed with finite elements until portions of the grid become highly strained. When finite elements on the boundaries reach a user-specified plastic strain they are converted to particles and linked to the adjacent finite element grid. This approach allows for the use of accurate and efficient finite elements in the lower distortion regions, and for the use of meshless particles in the higher distortion regions. Example computations are presented to demonstrate the accuracy and utility of this approach.

Artificial viscosity effects for SPH impact computations

This paper considers the effects of artificial viscosity for Smooth Particle Hydrodynamics (SPH) computations. Results are presented for five different problems that each uses six different varieties of artificial viscosity. The results for some of the problems are significantly affected by the artificial viscosity.

Lagrangian EPIC code computations for oblique, yawed-rod impacts onto thin-plate and spaced-plate targets at various velocities

Abstract This paper presents Lagrangian EPIC code computations for oblique, yawed-rod impacts onto thin-plate and spaced-plate targets at various velocities. The baseline set of computations considers a nominal obliquity of 65 degrees and a nominal impact velocity of 1300 m/s, onto thin-plate targets at nominal yaw angles of 0, 10, and +10 degrees. The yaw angles are achieved by inducing velocities into the plates. These results are compared to test data and MESA code results published previously. Additional sets of computations are presented to show the effect of increased impact velocities at nominal values of 2600 m/s and 5200 m/s. Some spaced-plate computations are also included.

Symmetric contact and sliding interface algorithms for intense impulsive loading computations

This paper presents symmetric contact and sliding interface algorithms for intense impulsive loading computations due to high velocity impact and explosive detonation. These algorithms are presented for both 2D and 3D geometry, and they include the effect of friction. These algorithms can be used in a fully automatic mode, where the user is not required to input the sliding interfaces, or they can be used with user specified interfaces. Also included are the interface determination algorithms and the searching algorithms. These algorithms are an extension of an earlier 2D algorithm that is dependent on the order that the interface nodes are processed. The new symmetric algorithms are not order-dependent. In addition to providing more accurate computations, the new symmetric algorithms are better suited for parallel processing.

A three-dimensional abrasion algorithm for projectile mass loss during penetration

A three-dimensional finite-element algorithm is presented for the computation of projectile mass loss due to abrasion at a projectile/target interface. The algorithm is an extension of the algorithm previously presented by the authors for axisymmetric computations. A description of the algorithm emphasizes the additional complexities introduced by three dimensions. The most significant complexity is the adjustment of the Lagrangian projectile mesh to avoid the convergence of nodes at the tip of the projectile nose as mass is removed from the nose. This adjustment is achieved in three dimensions by combining periodic calls to a rezoning algorithm (that redistributes the interior nodes of the mesh without changing connectivities) with an incremental adjustment of the surface nodes (that is applied tangent to the surface each timestep.) Numerical examples include comparisons to test data and demonstrations of the effects of non-axisymmetric impact.