Publications

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.

This report summarizes numerical analyses conducted to assess the relative importance on penetration depth calculations of rock constitutive model physics features representing the presence of microscale flaws such as porosity and networks of microcracks and rock mass structural features. Three-dimensional, nonlinear, transient dynamic finite element penetration simulations are made with a realistic geomaterial constitutive model to determine which features have the most influence on penetration depth calculations. A baseline penetration calculation is made with a representative set of material parameters evaluated from measurements made from laboratory experiments conducted on a familiar sedimentary rock. Then, a sequence of perturbations of various material parameters allows an assessment to be made of the main penetration effects. A cumulative probability distribution function is calculated with the use of an advanced reliability method that makes use of this sensitivity database, probability density functions, and coefficients of variation of the key controlling parameters for penetration depth predictions. Thus the variability of the calculated penetration depth is known as a function of the variability of the input parameters. This simulation modeling capability should impact significantly the tools that are needed to design enhanced penetrator systems, support weapons effects studies, and directly address proposed HDBT defeat scenarios.

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Software has been developed and extended to allow finite element (FE) modeling of ceramic powder compaction using a cap-plasticity constitutive model. The underlying, general-purpose FE software can be used to model even the most complex three-dimensional (3D) geometries envisioned. Additionally, specialized software has been developed within this framework to address a general subclass of axisymmetric compacts that are common in industry. The expertise required to build the input deck, run the FE code, and post-process the results for this subclass of compacts is embedded within the specialized software. The user simply responds to a series of prompts, evaluates the quality of the FE mesh that is generated, and analyzes the graphical results that are produced. The specialized software allows users with little or no FE expertise to benefit from the tremendous power and insight that FE analysis can bring to the design cycle. The more general underlying software provides complete flexibility to model more complicated geometries and processes of interest to ceramic component manufacturers but requires significantly more user interaction and expertise.

This report documents the development of constitutive material models for the overburden formations, reservoir formations, and underlying strata at the Lost Hills oil field located about 45 miles northwest of Bakersfield in Kern County, California. Triaxial rock mechanics tests were performed on specimens prepared from cores recovered from the Lost Hills field, and included measurements of axial and radial stresses and strains under different load paths. The tested intervals comprise diatomaceous sands of the Etchegoin Formation and several diatomite types of the Belridge Diatomite Member of the Monterey Formation, including cycles both above and below the diagenetic phase boundary between opal-A and opal-CT. The laboratory data are used to drive constitutive parameters for the Extended Sandler-Rubin (ESR) cap model that is implemented in Sandia's structural mechanics finite element code JAS3D. Available data in the literature are also used to derive ESR shear failure parameters for overburden formations. The material models are being used in large-scale three-dimensional geomechanical simulations of the reservoir behavior during primary and secondary recovery.

At low mean stresses, porous geomaterials fail by shear localization, and at higher mean stresses, they undergo strain-hardening behavior. Cap plasticity models attempt to model this behavior using a pressure-dependent shear yield and/or shear limit-state envelope with a hardening or hardening/softening elliptical end cap to define pore collapse. While these traditional models describe compactive yield and ultimate shear failure, difficulties arise when the behavior involves a transition from compactive to dilatant deformation that occurs before the shear failure or limit-state shear stress is reached. In this work, a continuous surface cap plasticity model is used to predict compactive and dilatant pre-failure deformation. During loading the stress point can pass freely through the critical state point separating compactive from dilatant deformation. The predicted volumetric strain goes from compactive to dilatant without the use of a non-associated flow rule. The new model is stable in that Drucker's stability postulates are satisfied. The study has applications to several geosystems of current engineering interest (oil and gas reservoirs, nuclear waste repositories, buried targets, and depleted reservoirs for possible use for subsurface sequestration of greenhouse gases).

The iterative advanced mean value algorithm (AMV+), introduced nearly ten years ago, is now widely used as a cost-effective probabilistic structural analysis tool when the use of sampling methods is cost prohibitive (Wu et al., 1990). The need to establish confidence bounds on calculated probabilities arises because of the presence of uncertainties in measured means and variances of input random variables. In this paper an algorithm is proposed that makes use of the AMV+ procedure and analytically derived probability sensitivities to determine confidence bounds on calculated probabilities.

Parameter estimation for modern viscoplastic constitutive models often requires data from many tests. Sensitivity coefficients can be used to design an efficient test matrix and reduce testing requirements. The present study derives sensitivity coefficients for each model parameter in the Munson-Dawson constitutive model and evaluates them for several load histories.

All valid constitutive equations must satisfy two general invariance principles as well several other principles. In this paper the MDCF (Multimechanism Deformation Coupled Fracture) model for rock salt is shown to be thermodynamically consistent, coordinate invariant, frame indifferent, and physically admissible. Additionally, the stress rates used in the formulation are shown to be kinematically consistent with the Cauchy stress rates.