Swan, S. and R. Brannon (2009)
Illustration of stair-stepping typical of finite sampling from a Weibull distribution
Current simulations of material deformation are a balance between computational effort and accuracy of the simulation. To increase the accuracy of the simulated material response, the simulation becomes more computationally intensive with finer meshes and shorter timesteps, increasing the time and resource requirements needed to perform the simulation. One method for improving predictions of brittle failure while minimizing computational overhead is to implement statistical variability for the material properties being simulated. This method has low computational overhead and requires a relatively small increase in resource requirements while significantly increasing the precision of simulation results. Currently, most simulation frameworks inaccurately describe brittle and heterogeneous materials as uniform bodies of equal strength and consistency. This over-simplification underscores the need to implement statistical variability to help better predict material response and failure modes for materials that contain intermittent abnormalities such as changes in hardness, strength, and grain size throughout the specimen. Uintah, the computational framework developed by the University of Utah’s C-SAFE program, has a simplistic native Gaussian distribution function that was hard-coded into select material models. The goal of this research is to create an easily duplicable method for enabling dynamic global variability according to a Weibull distribution in constitutive models in Uintah and to implement said ability into the constitutive model Kayenta. The main application of Kayenta is to simulate geological response to penetration and perforation. For the purpose of simulating failure in brittle geological samples, the Weibull distribution produces realistic statistical scatter in constituent properties that correlates well to flaws and irregularities observed in laboratory tests.
T.J. Fuller, R.M. Brannon, O.E. Strack, J.E. Bishop
Displacement profile for Thermo-Kayenta at the end of the simulation. the red dots represent the experimental profiles
A persistent challenge in simulating damage of natural geological materials, as well as rock-like engineered materials, is the development of efficient and accurate constitutive models.The common feature for these brittle and quasi-brittle materials are the presence of flaws such as porosity and network of microcracks. The desired models need to be able to predict the material responses over a wide range of porosities and strain rate. Kayenta  (formerly called the Sandia GeoModel) is a unifi ed general-purpose constitutive model that strikes a balance between rst-principles micromechanics and phenomenological or semi-empirical modeling strategies. However, despite its sophistication and ability to reduce to several classical plasticity theories, Kayenta is incapable of modeling deformation of ductile materials in which deformation is dominated by dislocation generation and movement which can lead to signi cant heating. This stems from Kayenta’s roots as a geological model, where heating due to inelastic deformation is often neglected or presumed to be incorporated implicitly through the elastic moduli.The sophistication of Kayenta and its large set of extensive features, however, make Kayenta an attractive candidate model to which thermal eff ects can be added. This report outlines the initial work in doing just that, extending the capabilities of Kayenta to include deformation of ductile materials, for which thermal e ffects cannot be neglected. Thermal e ffects are included based on an assumption of adiabatic loading by computing the bulk and thermal responses of the material with the Kerley Mie-Gruneisen equation of state and adjusting the yield surface according to the updated thermal state. This new version of Kayenta, referred to as Thermo-Kayenta throughout this report, is capable of reducing to classical Johnson-Cook plasticity in special case single element simulations and has been used to obtain reasonable results in more complicated Taylor impact simulations in LS-Dyna. Despite these successes, however, Thermo-Kayenta requires additional re nement for it to be consistent in the thermodynamic sense and for it to be considered superior to other, more mature thermoplastic models. The initial thermal development, results, and required refinements are all detailed in the following report.
Summary of the basic equations of mechanics, along with abbreviated derivations.
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