Publications

Brannon, Rebecca M.; Jensen, Richard P.; Strack, Otto E.

Abstract not provided.

Brannon, Rebecca M.; Jensen, Richard P.; Strack, Otto E.

Abstract not provided.

Proposed for publication in Acta Geotechnica.

Fossum, Arlo F.; Brannon, Rebecca M.

This paper summarizes the results of a theoretical and experimental program at Sandia National Laboratories aimed at identifying and modeling key physical features of rocks and rock-like materials at the laboratory scale over a broad range of strain rates. The mathematical development of a constitutive model is discussed and model predictions versus experimental data are given for a suite of laboratory tests. Concurrent pore collapse and cracking at the microscale are seen as competitive micromechanisms that give rise to the well-known macroscale phenomenon of a transition from volumetric compaction to dilatation under quasistatic triaxial compression. For high-rate loading, this competition between pore collapse and microcracking also seems to account for recently identified differences in strain-rate sensitivity between uniaxial-strain 'plate slap' data compared to uniaxial-stress Kolsky bar data. A description is given of how this work supports ongoing efforts to develop a predictive capability in simulating deformation and failure of natural geological materials, including those that contain structural features such as joints and other spatial heterogeneities.

Brannon, Rebecca M.; Strack, Otto E.; Fossum, Arlo F.

Abstract not provided.

Brannon, Rebecca M.; Strack, Otto E.

Abstract not provided.

Wilson, Andrew T.; Brannon, Rebecca M.

In this article we describe stress nets, a technique for exploring 2D tensor fields. Our method allows a user to examine simultaneously the tensors eigenvectors (both major and minor) as well as scalar-valued tensor invariants. By avoiding noise-advection techniques, we are able to display both principal directions of the tensor field as well as the derived scalars without cluttering the display. We present a CPU-only implementation of stress nets as well as a hybrid CPU/GPU approach and discuss the relative strengths and weaknesses of each. Stress nets have been used as part of an investigation into crack propagation. They were used to display the directions of maximum shear in a slab of material under tension as well as the magnitude of the shear forces acting on each point. Our methods allowed users to find new features in the data that were not visible on standard plots of tensor invariants. These features disagree with commonly accepted analytical crack propagation solutions and have sparked renewed investigation. Though developed for a materials mechanics problem, our method applies equally well to any 2D tensor field having unique characteristic directions.

Brannon, Rebecca M.

Abstract not provided.

Brannon, Rebecca M.; Bronowski, David R.

To establish mechanical properties and failure criteria of silicon carbide (SiC-N) ceramics, a series of quasi-static compression tests has been completed using a high-pressure vessel and a unique sample alignment jig. This report summarizes the test methods, set-up, relevant observations, and results from the constitutive experimental efforts. Results from the uniaxial and triaxial compression tests established the failure threshold for the SiC-N ceramics in terms of stress invariants (I{sub 1} and J{sub 2}) over the range 1246 < I{sub 1} < 2405. In this range, results are fitted to the following limit function (Fossum and Brannon, 2004) {radical}J{sub 2}(MPa) = a{sub 1} - a{sub 3}e -a{sub 2}(I{sub 1}/3) + a{sub 4} I{sub 1}/3, where a{sub 1} = 10181 MPa, a{sub 2} = 4.2 x 10{sup -4}, a{sub 3} = 11372 MPa, and a{sub 4} = 1.046. Combining these quasistatic triaxial compression strength measurements with existing data at higher pressures naturally results in different values for the least-squares fit to this function, appropriate over a broader pressure range. These triaxial compression tests are significant because they constitute the first successful measurements of SiC-N compressive strength under quasistatic conditions. Having an unconfined compressive strength of {approx}3800 MPa, SiC-N has been heretofore tested only under dynamic conditions to achieve a sufficiently large load to induce failure. Obtaining reliable quasi-static strength measurements has required design of a special alignment jig and load-spreader assembly, as well as redundant gages to ensure alignment. When considered in combination with existing dynamic strength measurements, these data significantly advance the characterization of pressure-dependence of strength, which is important for penetration simulations where failed regions are often at lower pressures than intact regions.

Fossum, Arlo F.; Brannon, Rebecca M.

Abstract not provided.

Rogers, David R.; Brannon, Rebecca M.

An important challenge encountered during post-processing of finite element analyses is the visualizing of three-dimensional fields of real-valued second-order tensors. Namely, as finite element meshes become more complex and detailed, evaluation and presentation of the principal stresses becomes correspondingly problematic. In this paper, we describe techniques used to visualize simulations of perturbed in-situ stress fields associated with hypothetical salt bodies in the Gulf of Mexico. We present an adaptation of the Mohr diagram, a graphical paper and pencil method used by the material mechanics community for estimating coordinate transformations for stress tensors, as a new tensor glyph for dynamically exploring tensor variables within three-dimensional finite element models. This interactive glyph can be used as either a probe or a filter through brushing and linking.

Fossum, Arlo F.; Brannon, Rebecca M.

The mathematical and physical foundations and domain of applicability of Sandia's GeoModel are presented along with descriptions of the source code and user instructions. The model is designed to be used in conventional finite element architectures, and (to date) it has been installed in five host codes without requiring customizing the model subroutines for any of these different installations. Although developed for application to geological materials, the GeoModel actually applies to a much broader class of materials, including rock-like engineered materials (such as concretes and ceramics) and even to metals when simplified parameters are used. Nonlinear elasticity is supported through an empirically fitted function that has been found to be well-suited to a wide variety of materials. Fundamentally, the GeoModel is a generalized plasticity model. As such, it includes a yield surface, but the term 'yield' is generalized to include any form of inelastic material response including microcrack growth and pore collapse. The geomodel supports deformation-induced anisotropy in a limited capacity through kinematic hardening (in which the initially isotropic yield surface is permitted to translate in deviatoric stress space to model Bauschinger effects). Aside from kinematic hardening, however, the governing equations are otherwise isotropic. The GeoModel is a genuine unification and generalization of simpler models. The GeoModel can employ up to 40 material input and control parameters in the rare case when all features are used. Simpler idealizations (such as linear elasticity, or Von Mises yield, or Mohr-Coulomb failure) can be replicated by simply using fewer parameters. For high-strain-rate applications, the GeoModel supports rate dependence through an overstress model.

Proposed for publication in Coordinated & Multiple Views in Exploratory Visualization, Special Issue of Information Visualization Journal, Vol 2 No. 4, Palgrave/Macmillan.

Crossno, Patricia J.; Crossno, Patricia J.; Rogers, David R.; Brannon, Rebecca M.; Coblentz, David D.

Abstract not provided.

Crossno, Patricia J.; Crossno, Patricia J.; Rogers, David R.; Brannon, Rebecca M.

Abstract not provided.

Brannon, Rebecca M.; Brannon, Rebecca M.

The theory, numerical algorithm, and user documentation are provided for a new ''Centroidal Voronoi Tessellation (CVT)'' method of filling a region of space (2D or 3D) with particles at any desired particle density. ''Clumping'' is entirely avoided and the boundary is optimally resolved. This particle placement capability is needed for any so-called ''mesh-free'' method in which physical fields are discretized via arbitrary-connectivity discrete points. CVT exploits efficient statistical methods to avoid expensive generation of Voronoi diagrams. Nevertheless, if a CVT particle's Voronoi cell were to be explicitly computed, then it would have a centroid that coincides with the particle itself and a minimized rotational moment. The CVT code provides each particle's volume and centroid, and also the rotational moment matrix needed to approximate a particle by an ellipsoid (instead of a simple sphere). DIATOM region specification is supported.

Brannon, Rebecca M.; Brannon, Rebecca M.

The theory and algorithm for the Material Point Method (MPM) are documented, with a detailed discussion on the treatments of boundary conditions and shock wave problems. A step-by-step solution scheme is written based on direct inspection of the two-dimensional MPM code currently used at the University of Missouri-Columbia (which is, in turn, a legacy of the University of New Mexico code). To test the completeness of the solution scheme and to demonstrate certain features of the MPM, a one-dimensional MPM code is programmed to solve one-dimensional wave and impact problems, with both linear elasticity and elastoplasticity models. The advantages and disadvantages of the MPM are investigated as compared with competing mesh-free methods. Based on the current work, future research directions are discussed to better simulate complex physical problems such as impact/contact, localization, crack propagation, penetration, perforation, fragmentation, and interactions among different material phases. In particular, the potential use of a boundary layer to enforce the traction boundary conditions is discussed within the framework of the MPM.

Brannon, Rebecca M.

A theory is developed for the response of moderately porous solids (no more than {approximately}20% void space) to high-strain-rate deformations. The model is consistent because each feature is incorporated in a manner that is mathematically compatible with the other features. Unlike simple p-{alpha} models, the onset of pore collapse depends on the amount of shear present. The user-specifiable yield function depends on pressure, effective shear stress, and porosity. The elastic part of the strain rate is linearly related to the stress rate, with nonlinear corrections from changes in the elastic moduli due to pore collapse. Plastically incompressible flow of the matrix material allows pore collapse and an associated macroscopic plastic volume change. The plastic strain rate due to pore collapse/growth is taken normal to the yield surface. If phase transformation and/or pore nucleation are simultaneously occurring, the inelastic strain rate will be non-normal to the yield surface. To permit hardening, the yield stress of matrix material is treated as an internal state variable. Changes in porosity and matrix yield stress naturally cause the yield surface to evolve. The stress, porosity, and all other state variables vary in a consistent manner so that the stress remains on the yield surface throughout any quasistatic interval of plastic deformation. Dynamic loading allows the stress to exceed the yield surface via an overstress ordinary differential equation that is solved in closed form for better numerical accuracy. The part of the stress rate that causes no plastic work (i.e-, the part that has a zero inner product with the stress deviator and the identity tensor) is given by the projection of the elastic stressrate orthogonal to the span of the stress deviator and the identity tensor.The model, which has been numerically implemented in MIG format, has been exercised under a wide array of extremal loading and unloading paths. As will be discussed in a companion sequel report, the CKP model is capable of closely matching plate impact measurements for porous materials.

Brannon, Rebecca M.

Several concepts (and assumptions) from the literature for porous metals and ceramics have been synthesized into a consistent model that predicts an admissibility limit on a material's porous yield surface. To ensure positive plastic work, the rate at which a yield surface can collapse as pores grow in tension must be constrained.