Martin W. Heinstein

Coupling of smooth particle hydrodynamics with the finite element method

Abstract A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code pronto . In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within pronto will be outlined. Example SPH pronto calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or “bow tie” elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within pronto allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm.

Contact—impact modeling in explicit transient dynamics☆

Abstract In this article we discuss the treatment of contact—impact modeling in a large deformation explicit dynamic setting. Such problems are posed mathematically by demanding the usual satisfaction momentum balance equations and boundary conditions for each body separately, while imposing an additional set of constraints that govern the interaction of these bodies with each other. In applying such methods to contact problems we emphasize two requirements: first, that the treatment of contact should follow from the development of the local (weak) and global (strong) forms of the contact equations in the continuum setting. Algorithms developed from this framework are seen to readily handle the three-dimensional multi-body friction case. Second, and equally important especially in large applications is the practical aspect of computing the closest point projection for contact nodes, an essential component of defining the contact constraints. This calculation is global in nature, accounting for the fact that contact—impact involves multiple bodies interacting in unforeseeable ways. These requirements have guided the development of algorithms capable of treating contact—impact in PRONTO3D (M.W. Heinstein, S.W. Attaway, J.W. Swegle, F.J. Mello, A general purpose contact detection algorithm for nonlinear structural analysis sodes, SAND92-2141, Sandia National Laboratories, Albuquerque, N-87185, 1992) are discussed in this paper.

AN ALGORITHM FOR THE MATRIX-FREE SOLUTION OF QUASISTATIC FRICTIONAL CONTACT PROBLEMS

A contact enforcement algorithm has been developed for matrix-free quasistatic finite element techniques. Matrix-free (iterative) solution algorithms such as non-linear conjugate gradients (CG) and dynamic relaxation (DR) are desirable for large solid mechanics applications where direct linear equation solving is prohibitively expensive, but in contrast to more traditional Newton–Raphson and quasi-Newton iteration strategies, the number of iterations required for convergence is typically of the same order as the number of degrees of freedom of the model. It is therefore crucial that each of these iterations be inexpensive to per-form, which is of course the essence of a matrix free method. In applying such methods to contact problems we emphasize here two requirements: first, that the treatment of the contact should not make an average equilibrium iteration considerably more expensive; and second, that the contact constraints should be imposed in such a way that they do not introduce spurious energy that acts against the iterative solver. These practical concerns are utilized to develop an iterative technique for accurate constraint enforcement that is suitable for non-linear conjugate gradient and dynamic relaxation iterative schemes. Copyright

ACME: Algorithms for Contact in a Multiphysics Environment API Version 1.3

An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.

Bending Effects in the Frictional Energy Dissipation in Lap Joints

Frictional energy dissipation in joints is an issue of long-standing interest in the effort to predict damping of built up structures. Even obtaining a qualitative understanding of how energy dissipation depends on applied loads has not yet been accomplished. Goodman postulated that in harmonic loading, the energy dissipation per cycle would go as the cube of the amplitude of loading. Though experiment does support a power-law relationship, the exponent tends to be lower than Goodman predicted. Recent calculations discussed here suggest that the cause of that deviation has to do with reshaping of the contact patch over each loading period.

New Approximations for Elastic Spheres Under an Oscillating Torsional Couple

The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Pade rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.

Simulation of orthogonal cutting with smooth particle hydrodynamics

There is an active literature on the simulation of cutting processes through finite element methods. Such efforts are motivated by the enormous economic importance of machining processes and the desire to adjust processes so as to optimize product and throughput, but suffer from some difficulties inherent to the finite element method. An alternative approach, which appears to overcome most of those difficulties, is that of Smooth Particle Hydrodynamics (SPH).Though some finite element work is reviewed here, the focus of this paper is on the demonstration of the SPH technique of to simulate orthogonal cutting.

Adagio 4.20 User’s Guide

Adagio is a Lagrangian, three-dimensional, implicit code for the analysis of solids and structures. It uses a multi-level iterative solver, which enables it to solve problems with large deformations, nonlinear material behavior, and contact. It also has a versatile library of continuum and structural elements, and an extensive library of material models. Adagio is written for parallel computing environments, and its solvers allow for scalable solutions of very large problems. Adagio uses the SIERRA Framework, which allows for coupling with other SIERRA mechanics codes. This document describes the functionality and input structure for Adagio.

Summary compilation of shell element performance versus formulation.

This document compares the finite element shell formulations in the Sierra Solid Mechanics code. These are finite elements either currently in the Sierra simulation codes Presto and Adagio, or expected to be added to them in time. The list of elements are divided into traditional two-dimensional, plane stress shell finite elements, and three-dimensional solid finite elements that contain either modifications or additional terms designed to represent the bending stiffness expected to be found in shell formulations. These particular finite elements are formulated for finite deformation and inelastic material response, and, as such, are not based on some of the elegant formulations that can be found in an elastic, infinitesimal finite element setting. Each shell element is subjected to a series of 12 verification and validation test problems. The underlying purpose of the tests here is to identify the quality of both the spatially discrete finite element gradient operator and the spatially discrete finite element divergence operator. If the derivation of the finite element is proper, the discrete divergence operator is the transpose of the discrete gradient operator. An overall summary is provided from which one can rank, at least in an average sense, how well the individual formulations can be expected to perform in applications encountered year in and year out. A letter grade has been assigned albeit sometimes subjectively for each shell element and each test problem result. The number of As, Bs, Cs, et cetera assigned have been totaled, and a grade point average (GPA) has been computed, based on a 4.0-system. These grades, combined with a comparison between the test problems and the application problem, can be used to guide an analyst to select the element with the best shell formulation.

Solution Verification of Frictional Contact Problems in Explicit Transient Dynamics

Contact is a commonly used capability i n explicit transient dynamics codes. Yet the quality of the solution to these problems is often unknown. Typically, users are left to determine if they “look acceptable.” In this talk we present the solution verification efforts underway for frictional con tact problems in PRESTO, a massively parallel large deformation transient dynamics code developed at Sandia National Laboratories. It is common practice in explicit transient dynamics to seek a balance between computational efficiency and accuracy (especia lly on massively parallel computers). In this presentation, the constrained set of fully discretized equations of motion is examined and various approaches for verifying solution accuracy of them are discussed. A set of frictional contact verification prob lems will be presented that give results of our investigations, including solution and mesh converge studies. I. Introduction HIS paper describes ongoing efforts in the verification and validation of frictional contact in large deformation solid mechanics problems with dynamic effects. Such explicit codes are now commonly used for a variety of applications, especially those involving contact/impact, contact with sliding, and contact with frictional sliding using some interface response (typically Coulomb f riction). Central difference time integration is the time integrator of choice for most of thee problems because of its simplicity and efficiency. Over the many years that explicit transient dynamics codes have been used, their efficiency has been the domi nant focus. It is common practice to seek a balance between computational efficiency and accuracy, especially on massively parallel computers. Here, we wish to explore the quality of explicit solutions, particularly those involving frictional contact. Spe cifically, in this paper we present the solution verification efforts underway (and challenges) for frictional contact problems in Presto, a massively parallel large deformation transient dynamics code developed at Sandia National Laboratories. We begin with an examination of the fully discretized equations of motion and then look at various approaches for verifying solution accuracy of them. Finally, we conclude with a set of frictional contact verification problems used to present the results of our ong oing investigation, including solution and mesh convergence studies.