Publications

Abstract not provided.

This report provides an updated set of users` instructions for PRONTO3D. PRONTO3D is a three-dimensional, transient, solid dynamics code for analyzing large deformations of highly nonlinear materials subjected to extremely high strain rates. This Lagrangian finite element program uses an explicit time integration operator to integrate the equations of motion. Eight-node, uniform strain, hexahedral elements and four-node, quadrilateral, uniform strain shells are used in the finite element formulation. An adaptive time step control algorithm is used to improve stability and performance in plasticity problems. Hourglass distortions can be eliminated without disturbing the finite element solution using either the Flanagan-Belytschko hourglass control scheme or an assumed strain hourglass control scheme. All constitutive models in PRONTO3D are cast in an unrotated configuration defined using the rotation determined from the polar decomposition of the deformation gradient. A robust contact algorithm allows for the impact and interaction of deforming contact surfaces of quite general geometry. The Smooth Particle Hydrodynamics method has been embedded into PRONTO3D using the contact algorithm to couple it with the finite element method.

SPH (Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. In the present study, the SPH algorithm has been subjected to detailed testing and analysis to determine the feasibility of using PRONTO/SPH for the analysis of various types of underwater explosion problems involving fluid-structure and shock-structure interactions. Of particular interest are effects of bubble formation and collapse and the permanent deformation of thin walled structures due to these loadings. These are exceptionally difficult problems to model. Past attempts with various types of codes have not been satisfactory. Coupling SPH into the finite element code PRONTO represents a new approach to the problem. Results show that the method is well-suited for transmission of loads from underwater explosions to nearby structures, but the calculation of late time effects due to acceleration of gravity and bubble buoyancy will require additional development, and possibly coupling with implicit or incompressible methods. © 1995 Springer-Verlag.

There is an instability in certain S.P.H. (Smoothed Particle Hydrodynamics method) material dynamics computations. Evidence from analyses and experiments suggests that the instabilities in S.P.H. are not removable with artificial viscosities. However, the analysis shows that a type of conservative smoothing does remove the instability. Also, numerical experiments, on certain test problems, show that SPHCS, and S.P.H. code with conservative smoothing, compares well in accuracy with computations based on the von Neumann-Richtmyer method.

SPH (Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. In the present study, the SPH algorithm has been subjected to detailed testing and analysis to determine its applicability in the field of solid dynamics. An important result of the work is a rigorous von Neumann stability analysis which provides a simple criterion for the stability or instability of the method in terms of the stress state and the second derivative of the kernel function. Instability, which typically occurs only for solids in tension, results not from the numerical time integration algorithm, but because the SPH algorithm creates an effective stress with a negative modulus. The analysis provides insight into possible methods for removing the instability. Also, SPH has been coupled into the transient dynamics finite element code PRONTO, and a weighted residual derivation of the SPH equations has been obtained.

The strain rate in steady shock waves is proportional to the fourth power of shock amplitude for a wide variety of materials over a broad range of strain rates. A model based on this observation gives good agreement not only with steady-wave profiles but also with data on non-steady waves in aluminum. In apparent contrast, data on vanadium and uranium at low strain rates indicates a departure from the fourth power law if the wave profiles are assumed to be steady. However, when predicted profiles are produced by allowing the waves to propagate and evolve over the actual experimental sample thickness, the fourth power model gives excellent agreement with the wave profile data even though the wave profiles in the calculations have not yet reached steady state. The implication is that the experimental data do not represent steady waves, and the model is predicting the correct evolution of non-steady waves in vanadium and uranium. 7 refs., 2 figs.