Publications

Niederhaus, John H.; Voth, Thomas E.; Mosso, Stewart J.

Abstract not provided.

Voth, Thomas E.; Mosso, Stewart J.; Niederhaus, John H.

Abstract not provided.

Niederhaus, John H.; Voth, Thomas E.; Mosso, Stewart J.

Abstract not provided.

International Journal of Theoretical and Applied Multiscale Mechanics

Robbins, Joshua R.; Voth, Thomas E.

Abstract not provided.

Robbins, Joshua R.; Voth, Thomas E.

Abstract not provided.

Voth, Thomas E.

Abstract not provided.

Rider, William J.; Love, Edward L.; Voth, Thomas E.; Mosso, Stewart J.; Niederhaus, John H.; Strack, Otto E.; Robinson, Allen C.

Abstract not provided.

Voth, Thomas E.; Strickland, James H.

Abstract not provided.

AIP Conference Proceedings

Robbins, Joshua R.; Voth, Thomas E.

The extended Finite Element Method (X-FEM) is a finite-element based discretization technique developed originally to model dynamic crack propagation [1]. Since that time the method has been used for modeling physics ranging from static meso-scale material failure to dendrite growth. Here we adapt the recent advances of Vitali and Benson [2] and Song et. al. [3] to model dynamic loading of a polycry stalline material. We use demonstration problems to examine the method's efficacy for modeling the dynamic response of polycrystalline materials at the meso-scale. Specifically, we use the X-FEM to model grain boundaries. This approach allows us to i) eliminate ad-hoc mixture rules for multi-material elements and ii) avoid explicitly meshing grain boundaries. © 2007 American Institute of Physics.

Gill, David D.; Atwood, Clinton J.; Robbins, Joshua R.; Voth, Thomas E.

Aerospace designers seek lightweight, high-strength structures to lower launch weight while creating structures that are capable of withstanding launch loadings. Most 'light-weighting' is done through an expensive, time-consuming, iterative method requiring experience and a repeated design/test/redesign sequence until an adequate solution is obtained. Little successful work has been done in the application of generalized 3D optimization due to the difficulty of analytical solutions, the large computational requirements of computerized solutions, and the inability to manufacture many optimized structures with conventional machining processes. The Titanium Cholla LDRD team set out to create generalized 3D optimization routines, a set of analytically optimized 3D structures for testing the solutions, and a method of manufacturing these complex optimized structures. The team developed two new computer optimization solutions: Advanced Topological Optimization (ATO) and FlexFEM, an optimization package utilizing the eXtended Finite Element Method (XFEM) software for stress analysis. The team also developed several new analytically defined classes of optimized structures. Finally, the team developed a 3D capability for the Laser Engineered Net Shaping{trademark} (LENS{reg_sign}) additive manufacturing process including process planning for 3D optimized structures. This report gives individual examples as well as one generalized example showing the optimized solutions and an optimized metal part.

Computer Methods in Applied Mechanics and Engineering

Voth, Thomas E.; Mosso, Stewart J.; Robbins, Joshua R.

Here, we examine the coupling of the patterned-interface-reconstruction (PIR) algorithm with the extended finite element method (X-FEM) for general multi-material problems over structured and unstructured meshes. The coupled method offers the advantages of allowing for local, element-based reconstructions of the interface, and facilitates the imposition of discrete conservation laws. Of particular note is the use of an interface representation that is volume-of-fluid based, giving rise to a segmented interface representation that is not continuous across element boundaries. In conjunction with such a representation, we employ enrichment with the ridge function for treating material interfaces and an analog to Heaviside enrichment for treating free surfaces. We examine a series of benchmark problems that quantify the convergence aspects of the coupled method and examine the sensitivity to noise in the interface reconstruction. Finally, the fidelity of a remapping strategy is also examined for a moving interface problem.

American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

Bishop, Joseph E.; Voth, Thomas E.; Brown, Kevin H.

The physics of ballistic penetration mechanics is of great interest in penetrator and counter-measure design. The phenomenology associated with these events can be quite complex and a significant number of studies have been conducted ranging from purely experimental to 'engineering' models based on empirical and/or analytical descriptions to fully-coupled penetrator/target, thermo-mechanical numerical simulations. Until recently, however, there appears to be a paucity of numerical studies considering 'non-ideal' impacts [1]. The goal of this work is to demonstrate the SHISM algorithm implemented in the ALEGRA Multi-Material ALE (Arbitrary Lagrangian Eulerian) code [13]. The SHISM algorithm models the three-dimensional continuum solid mechanics response of the target and penetrator in a fully coupled manner. This capability allows for the study of 'non-ideal' impacts (e.g. pitch, yaw and/or obliquity of the target/penetrator pair). In this work predictions using the SHISM algorithm are compared to previously published experimental results for selected ideal and non-ideal impacts of metal penetrator-target pairs. These results show good agreement between predicted and measured maximum depth-of-penetration, DOP, for ogive-nose penetrators with striking velocities in the 0.5 to 1.5 km/s range. Ideal impact simulations demonstrate convergence in predicted DOP for the velocity range considered. A theory is advanced to explain disagreement between predicted and measured DOP at higher striking velocities. This theory postulates uncertainties in angle-of-attack for the observed discrepancies. It is noted that material models and associated parameters used here, were unmodified from those in the literature. Hence, no tuning of models was performed to match experimental data. Copyright © 2005 by ASME.

Bishop, Joseph E.; Voth, Thomas E.; Brown, Kevin H.

Abstract not provided.

Bishop, Joseph E.; Hensinger, David M.; Voth, Thomas E.; Wong, Michael K.; Robinson, Allen C.

Abstract not provided.

Bishop, Joseph E.; Hensinger, David M.; Voth, Thomas E.; Wong, Michael K.; Robinson, Allen C.

The success of Lagrangian contact modeling leads one to believe that important aspects of this capability may be used for multi-material modeling when only a portion of the simulation can be represented in a Lagrangian frame. We review current experience with two dual mesh technologies where one of these meshes is a Lagrangian mesh and the other is an Arbitrary Lagrangian/Eulerian (ALE) mesh. These methods are cast in the framework of an operator-split ALE algorithm where a Lagrangian step is followed by a remesh/remap step. An interface-coupled methodology is considered first. This technique is applicable to problems involving contact between materials of dissimilar compliance. The technique models the more compliant (soft) material as ALE while the less compliant (hard) material and associated interface are modeled in a Lagrangian fashion. Loads are transferred between the hard and soft materials via explicit transient dynamics contact algorithms. The use of these contact algorithms remove the requirement of node-tonode matching at the soft-hard interface. In the context of the operator-split ALE algorithm, a single Lagrangian step is performed using a mesh to mesh contact algorithm. At the end of the Lagrangian step the meshes will be slightly offset at the interface but non-interpenetrating. The ALE mesh nodes at the interface are then remeshed to their initial location relative to the Lagrangian body faces and the ALE mesh is smoothed, translated and rotated to follow Lagrangian body. Robust remeshing in the ALE region is required for success of this algorithm, and we describe current work in this area. The second method is an overlapping grid methodology that requires mapping of information between a Lagrangian mesh and an ALE mesh. The Lagrangian mesh describes a relatively hard body that interacts with softer material contained in the ALE mesh. A predicted solution for the velocity field is performed independently on both meshes. Element-centered velocity and momentum are transferred between the meshes using the volume transfer capability implemented in contact algorithms. Data from the ALE mesh is mapped to a phantom mesh that surrounds the Lagrangian mesh, providing for the reaction to the predicted motion of the Lagrangian material. Data from the Lagrangian mesh is mapped directly to the ALE mesh. A momentum balance is performed on both meshes to adjust the velocity field to account for the interaction of the material from the other mesh. Subsequent, remeshing and remapping of the ALE mesh is performed to allow large deformation of the softer material. We overview current progress using this approach and discuss avenues for future research and development.

Wong, Michael K.; Brunner, Thomas A.; Garasi, Christopher J.; Haill, Thomas A.; Mehlhorn, Thomas A.; Drake, Richard R.; Hensinger, David M.; Robbins, Joshua R.; Robinson, Allen C.; Summers, Randall M.; Voth, Thomas E.

ALEGRA is an arbitrary Lagrangian-Eulerian multi-material finite element code used for modeling solid dynamics problems involving large distortion and shock propagation. This document describes the basic user input language and instructions for using the software.

International Journal for Numerical Methods in Fluids

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy, it is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework.

International Journal for Numerical Methods in Fluids

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework.

Voth, Thomas E.

Abstract not provided.

Brown, Kevin H.; Brown, Kevin H.; Voth, Thomas E.; Glass, Micheal W.; Gullerud, Arne S.; Heinstein, Martin W.; Jones, Reese E.

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.

Christon, Mark A.; Voth, Thomas E.; Martinez, Mario J.

This report presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speeds, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis (aka von Neumann analysis) provides an automatic process for separating the spectral behavior of the discrete advective operator into its symmetric dissipative and skew-symmetric advective components. Further it is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, streamline upwind control-volume, produce both an artificial diffusivity and an artificial phase speed in addition to the usual semi-discrete artifacts observed in the discrete phase speed, group speed and diffusivity. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behavior in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behavior. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework.

Boucheron, Edward A.; Haill, Thomas A.; Peery, James S.; Petney, Sharon P.; Robbins, Joshua R.; Robinson, Allen C.; Summers, Randall M.; Voth, Thomas E.; Wong, Michael K.; Brown, Kevin H.; Budge, Kent G.; Burns, Shawn P.; Carroll, Daniel E.; Carroll, Susan K.; Christon, Mark A.; Drake, Richard R.; Garasi, Christopher J.

ALEGRA is an arbitrary Lagrangian-Eulerian finite element code that emphasizes large distortion and shock propagation. This document describes the user input language for the code.

Schmidt, Rodney C.; DesJardin, Paul E.; Voth, Thomas E.; Christon, Mark A.; Kerstein, Alan R.; Wunsch, Scott E.

This report describes research and development of the large eddy simulation (LES) turbulence modeling approach conducted as part of Sandia's laboratory directed research and development (LDRD) program. The emphasis of the work described here has been toward developing the capability to perform accurate and computationally affordable LES calculations of engineering problems using unstructured-grid codes, in wall-bounded geometries and for problems with coupled physics. Specific contributions documented here include (1) the implementation and testing of LES models in Sandia codes, including tests of a new conserved scalar--laminar flamelet SGS combustion model that does not assume statistical independence between the mixture fraction and the scalar dissipation rate, (2) the development and testing of statistical analysis and visualization utility software developed for Exodus II unstructured grid LES, and (3) the development and testing of a novel new LES near-wall subgrid model based on the one-dimensional Turbulence (ODT) model.

Blackwell, Bennie F.; Gill, Walt; Dowding, Kevin J.; Voth, Thomas E.

Abstract not provided.

Voth, Thomas E.; Christon, Mark A.

The Reproducing Kernel Particle Method (RKPM) is a discretization technique for partial differential equations that uses the method of weighted residuals, classical reproducing kernel theory and modified kernels to produce either ``mesh-free'' or ``mesh-full'' methods. Although RKPM has many appealing attributes, the method is new, and its numerical performance is just beginning to be quantified. In order to address the numerical performance of RKPM, von Neumann analysis is performed for semi-discretizations of three model one-dimensional PDEs. The von Neumann analyses results are used to examine the global and asymptotic behavior of the semi-discretizations. The model PDEs considered for this analysis include the parabolic and hyperbolic (first and second-order wave) equations. Numerical diffusivity for the former and phase speed for the later are presented over the range of discrete wavenumbers and in an asymptotic sense as the particle spacing tends to zero. Group speed is also presented for the hyperbolic problems. Excellent diffusive and dispersive characteristics are observed when a consistent mass matrix formulation is used with the proper choice of refinement parameter. In contrast, the row-sum lumped mass matrix formulation severely degraded performance. The asymptotic analysis indicates that very good rates of convergence are possible when the consistent mass matrix formulation is used with an appropriate choice of refinement parameter.