Stephen R. Beissel

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 aluminum nitride (including a phase change) to large strains, high strain rates, and high pressures

This article contains a description of a computational constitutive model for brittle materials subjected to large strains, high strain rates, and high pressures. The focus of this model is to determine the response of aluminum nitride under high velocity impact conditions that produce large strains, high strain rates, and high pressures. The strength is expressed as a function of the pressure, strain rate, and accumulated damage; and it allows for strength of both intact and failed material. The pressure is primarily expressed as a function of the volumetric strain, but it also includes the effect of bulking for the failed material. For materials without a phase change this model is an extension of the previous Johnson–Holmquist models for brittle materials. The primary new feature of this model is the capability to include a phase change, and this is required for aluminum nitride. Computations are performed to illustrate the capabilities of the model, to compare computed results to experimental results,...

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.

An abrasion algorithm for projectile mass loss during penetration

A finite-element algorithm is presented for the computation of projectile mass loss due to abrasion at a projectile/target interface. The algorithm includes an abrasion-rate model applied to the surface nodes of the projectile, an adjustment of nodal masses, an adjustment of element volumes, and fully automatic rezoning of the projectile as required. Calibration of the abrasion-rate model is followed by a comparison of computed results to experimental observations. Both depth of penetration and total projectile mass loss as a function of impact velocity are compared.

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.

Large-deformation triangular and tetrahedral element formulations for unstructured meshes

Abstract The increasing use of automatic mesh generators and remeshers has spurred the need for accurate and efficient triangular and tetrahedral elements in unstructured meshes. In large-deformation analysis of solids, accuracy and efficiency require the treatment of volumetric locking and element distortions, respectively. In this paper, a mixed formulations is proposed to treat these issues, and applied to triangular and tetrahedral elements. The formulations enforces, in the weak sense, the expression for the volumetric strain in terms of the deformation gradient. The mixed formulation is combined with an irreducible formulation to provide a balance between the treatment of volumetric locking and the maintenance of an adequate critical timestep. Three techniques are proposed to determine such a balance at the local (element) level. Example computations in two and three dimensions of an iron cylinder impacting a rigid surface are used to demonstrate the formulations, and to compare them to the irreducible displacement-based formulation.

Conversion of Finite Elements into Meshless Particles for Penetration Computations Involving Ceramic Targets

This paper presents a new computational algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. It also presents computed results for projectiles impacting ceramic targets. The new computational algorithm, together with an appropriate ceramic model, provides computed results that are in good agreement with test data. Included are problems involving dwell and penetration. This computational approach is especially well‐suited for brittle materials such as ceramics, because the conversion from elements into particles generally occurs after the material has failed. The result is that the particles represent only failed material, which does not produce any tensile stresses. For some particle algorithms it is possible to introduce tensile instabilities, but this is not a concern if the particles represent only failed material.