The representation of material heterogeneity (also referred to as "spatial variation") plays a key role in the material failure simulation method used in ALEGRA. ALEGRA is an arbitrary Lagrangian-Eulerian shock and multiphysics code developed at Sandia National Laboratories and contains several methods for incorporating spatial variation into simulations. A desirable property of a spatial variation method is that it should produce consistent stochastic behavior regardless of the mesh used (a property referred to as "mesh independence"). However, mesh dependence has been reported using the Weibull distribution with ALEGRA's spatial variation method. This report describes efforts towards providing additional insight into both the theory and numerical experiments investigating such mesh dependence. In particular, we have implemented a discrete minimum order statistic model with properties that are theoretically mesh independent.
A complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration energy contributions. Inelasticity is introduced through the nonlinear equations of finite strain plasticity which utilize the temperature dependent Johnson–Cook yield model. Material failure is incorporated into the model by a coupling of the damage history variable to the energy potentials. The numerical evaluation of the IEOS requires a nonlinear solution of stress, temperature and history variables associated with elastic trial states for stress and temperature. The model is implemented into the ALEGRA shock and multi-physics code and the applications presented include single element deformation paths, the Taylor anvil problem and an energetically driven thermo-mechanical problem.
This report introduces the concepts of Bayesian model selection, which provides a systematic means of calibrating and selecting an optimal model to represent a phenomenon. This has many potential applications, including for comparing constitutive models. The ideas described herein are applied to a model selection problem between different yield models for hardened steel under extreme loading conditions.
A finite strain formulation of the Johnson Cook plasticity and damage model and it's numerical implementation into the ALEGRA code is presented. The goal of this work is to improve the predictive material failure capability of the Johnson Cook model. The new implementation consists of a coupling of damage and the stored elastic energy as well as the minimum failure strain criteria for spall included in the original model development. This effort establishes the necessary foundation for a thermodynamically consistent and complete continuum solid material model, for which all intensive properties derive from a common energy. The motivation for developing such a model is to improve upon ALEGRA's present combined model framework. Several applications of the new Johnson Cook implementation are presented. Deformation driven loading paths demonstrate the basic features of the new model formulation. Use of the model produces good comparisons with experimental Taylor impact data. Localized deformation leading to fragmentation is produced for expanding ring and exploding cylinder applications.
A method for providing non-diffuse transport of material quantities in arbitrary Lagrangian- Eulerian (ALE) dynamic solid mechanics computations is presented. ALE computations are highly desirable for simulating dynamic problems that incorporate multiple materials and large deformations. Despite the advantages of using ALE for such problems, the method is associ- ated with diffusion of material quantities due to the advection transport step of the computa- tional cycle. This drawback poses great difficulty for applications of material failure for which discrete features are important, but are smeared out as a result of the diffusive advection op- eration. The focus of this work is an ALE method that incorporates transport of variables on discrete, massless points that move with the velocity field, referred to as Lagrangian material tracers (LMT), and consequently prevents diffusion of certain material quantities of interest. A detailed description of the algorithm is provided along with discussion of its computational aspects. Simulation results include a simple proof of concept, verification using a manufac- tured solution, and fragmentation of a uniformly loaded thin ring that clearly demonstrates the improvement offered by the ALE LMT method.
The physical foundations and domain of applicability of the Kayenta constitutive model are presented along with descriptions of the source code and user instructions. Kayenta, which is an outgrowth of the Sandia GeoModel, includes features and fitting functions appropriate to a broad class of materials including rocks, rock-like engineered materials (such as concretes and ceramics), and metals. Fundamentally, Kayenta is a computational framework for generalized plasticity models. As such, it includes a yield surface, but the term (3z(Byield(3y (Bis generalized to include any form of inelastic material response (including microcrack growth and pore collapse) that can result in non-recovered strain upon removal of loads on a material element. Kayenta supports optional anisotropic elasticity associated with joint sets, as well as optional deformation-induced anisotropy through kinematic hardening (in which the initially isotropic yield surface is permitted to translate in deviatoric stress space to model Bauschinger effects). The governing equations are otherwise isotropic. Because Kayenta is a unification and generalization of simpler models, it can be run using as few as 2 parameters (for linear elasticity) to as many as 40 material and control parameters in the exceptionally rare case when all features are used. For high-strain-rate applications, Kayenta supports rate dependence through an overstress model. Isotropic damage is modeled through loss of stiffness and strength.
Titanium and the titanium alloy Ti64 (6% aluminum, 4% vanadium and the balance ti- tanium) are materials used in many technologically important applications. To be able to computationally investigate and design these applications, accurate Equations of State (EOS) are needed and in many cases also additional constitutive relations. This report describes what data is available for constructing EOS for these two materials, and also describes some references giving data for stress-strain constitutive models. We also give some suggestions for projects to achieve improved EOS and constitutive models. In an appendix, we present a study of the 'cloud formation' issue observed in the ALEGRA code. This issue was one of the motivating factors for this literature search of available data for constructing improved EOS for Ti and Ti64. However, the study shows that the cloud formation issue is only marginally connected to the quality of the EOS, and, in fact, is a physical behavior of the system in question. We give some suggestions for settings in, and improvements of, the ALEGRA code to address this computational di culty.