Publication: Validating Theories for Brittle Damage

R.M. Brannon, J.M. Wells, and O.E. Strack

Realistic-looking, uneven damage zones in Brazilian simulations compare favorably with laboratory data for observable damage

Validating simulated predictions of internal damage within armor ceramics is preferable to simply assessing a models ability to predict penetration depth, especially if one hopes to perform subsequent ‘‘second strike’’ analyses. We present the results of a study in which crack networks are seeded by using a statistically perturbed strength, the median of which is inherited from a deterministic ‘‘smeared damage’’ model, with adjustments to reflect experimentally established size effects. This minor alteration of an otherwise conventional damage model noticeably mitigates mesh dependencies and, at virtually no computational cost, produces far more realistic cracking patterns that are well suited for validation against X-ray computed tomography (XCT) images of internal damage patterns. For Brazilian, spall, and indentation tests, simulations share qualitative features with externally visible damage. However, the need for more stringent quantitative validation, software quality testing, and subsurface XCT validation, is emphasized.

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Research: Weibull fragmentation in the Uintah MPM code

Tough disk impacting brittle disk

Below are links to two simulations of disks colliding. The first is elastic and the second uses a fracture model with spatially variable strength based on a scale-dependent Weibull realization. Both take advantage of the automatic contact property of the MPM.

WeibConstMovie:  disks colliding without fracture

WeibPerturbedGood: disks colliding with heterogeneous fracture

This basic capability to support statistically variable strength in a damage model has been extended to the Kayenta plasticity model in Uintah.

Publication: Initial inclusion of thermodynamic considerations in Kayenta

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 [1] (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.

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Publication: Survey of Four Damage Models for Concrete

R.M. Brannon and S. Leelavanichkul

RHT Model: Contour plots of damage: side, front, and back view of the target (top to bottom).

Four conventional damage plasticity models for concrete, the Karagozian and Case model (K&C),the Riedel-Hiermaier-Thoma model (RHT), the Brannon-Fossum model (BF1), and the Continuous Surface Cap Model (CSCM) are compared. The K&C and RHT models have been used in commercial finite element programs many years, whereas the BF1 and CSCM models are relatively new. All four models are essentially isotropic plasticity models for which plasticity is regarded as any form of inelasticity. All of the models support nonlinear elasticity, but with different formulations.All four models employ three shear strength surfaces. The yield surface bounds an evolving set of elastically obtainable stress states. The limit surface bounds stress states that can be reached by any means (elastic or plastic). To model softening, it is recognized that some stress states might be reached once, but, because of irreversible damage, might not be achievable again. In other words, softening is the process of collapse of the limit surface, ultimately down to a final residual surface for fully failed material. The four models being compared differ in their softening evolution equations, as well as in their equations used to degrade the elastic stiffness. For all four models, the strength surfaces are cast in stress space. For all four models, it is recognized that scale effects are important for softening, but the models differ significantly in their approaches. The K&C documentation, for example, mentions that a particular material parameter affecting the damage evolution rate must be set by the user according to the mesh size to preserve energy to failure. Similarly, the BF1 model presumes that all material parameters are set to values appropriate to the scale of the element, and automated assignment of scale-appropriate values is available only through an enhanced implementation of BF1 (called BFS) that regards scale effects to be coupled to statistical variability of material properties. The RHT model appears to similarly support optional uncertainty and automated settings for scale-dependent material parameters. The K&C, RHT, and CSCM models support rate dependence by allowing the strength to be a function of strain rate, whereas the BF1 model uses Duvaut-Lion viscoplasticity theory to give a smoother prediction of transient effects. During softening, all four models require a certain amount of strain to develop before allowing significant damage accumulation. For the K&C, RHT, and CSCM models, the strain-to-failure is tied to fracture energy release, whereas a similar effect is achieved indirectly in the BF1 model by a time-based criterion that is tied to crack propagation speed.

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Publication: A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media

R. M. Brannon and S. Leelavanichkul

Octahedral isosurfaces for a) the unacceptable, b) the admissible, and c) the admissible

Classical plasticity and damage models for porous quasi-brittle media usually suffer from mathematical defects such as non-convergence and nonuniqueness.Yield or damage functions for porous quasi-brittle media often have yield functions with contours so distorted that following those contours to the yield surface in a return algorithm can take the solution to a false elastic domain. A steepest-descent return algorithm must include iterative corrections; otherwise,the solution is non-unique because contours of any yield function are non-unique. A multi-stage algorithm has been developed to address both spurious convergence and non-uniqueness, as well as to improve efficiency. The region of pathological isosurfaces is masked by first returning the stress state to the Drucker–Prager surface circumscribing the actual yield surface. From there, steepest-descent is used to locate a point on the yield surface. This first-stage solution,which is extremely efficient because it is applied in a 2D subspace, is generally not the correct solution,but it is used to estimate the correct return direction.The first-stage solution is projected onto the estimated correct return direction in 6D stress space. Third invariant dependence and anisotropy are accommodated in this second-stage correction. The projection operation introduces errors associated with yield surface curvature,so the two-stage iteration is applied repeatedly to converge. Regions of extremely high curvature are detected and handled separately using an approximation to vertex theory. The multi-stage return is applied holding internal variables constant to produce a non-hardening solution. To account for hardening from pore collapse (or softening from damage), geometrical arguments are used to clearly illustrate the appropriate scaling of the non-hardening solution needed to obtain the hardening (or softening) solution.

For errata (transcription errors in two of the verification solutions), please see:

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Merits and shortcomings of conventional smeared damage models

Initial teardrop yield and third-invariant limit surfaces in the Kayenta model

Four classical damage models for concrete (three of which are available in commercial codes) have been compared and critiqued, showing that they all share the notions of a “teardrop” yield surface that can harden and (for some models) translate until reaching a three-invariant fracture limit surface that then collapses to account for softening (i.e., permanent loss of strength).   Practical engineering models for rock and ceramics are similar.  The common drawbacks of these models (primarily severe mesh dependence) can be mitigated, though not eliminated, by seeding their material properties in the simulation with spatial variability (aleatory uncertainty) and by using appropriate scale effects for the strength and failure progression properties. Continue reading