PUBLICATION: An efficient binning scheme with application to statistical crack mechanics

This paper has an algorithm that alleviates the computational burden of evaluating summations involving thousands or millions of terms, each of which is statistically variable.  It is a simple binning strategy that replaces the large (thousand or million-member) population of terms with a much smaller representative (~10 member) weighted population. This binning method typically gives ~500x computational efficiency boost.

10realizations

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Publication (Abstract and Erratum): Second-order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces

Abstract:

Convected particle domain interpolation (CPDI) is a recently developed extension of the material point method, in which the shape functions on the overlay grid are replaced with alternative shape functions, which (by coupling with the underlying particle topology) facilitate efficient and algorithmically straightforward evaluation of grid node integrals in the weak formulation of the governing equations. In the original CPDI algorithm, herein called CPDI1, particle domains are tracked as parallelograms in 2-D (or parallelepipeds in 3-D). In this paper, the CPDI method is enhanced to more accurately track particle domains as quadrilaterals in 2-D (hexahedra in 3-D). This enhancement will be referred to as CPDI2. Not only does this minor revision remove overlaps or gaps between particle domains, it also provides flexibility in choosing particle domain shape in the initial configuration and sets a convenient conceptual framework for enrichment of the fields to accurately solve weak discontinuities in the displacement field across a material interface that passes through the interior of a grid cell. The new CPDI2 method is demonstrated, with and without enrichment, using one-dimensional and two-dimensional examples.

Bib data:

Sadeghirad, A., R. M. Brannon, J.E. Guilkey (2013) Second-order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces, Int. J. Num. Meth. Engr., vol. 95, 928-952

URL: http://dx.doi.org/10.1002/nme.4526

Bibtex entry:

@ARTICLE{Sadeghirad2013,
author = {A. Sadeghirad and R.M. Brannon and J.E. Guilkey},
title = {Second-order convected particle domain interpolation ({CPDI2}) with
enrichment for weak discontinuities at material interfaces},
journal = {Intl. J. Num. Meth. Engng.},
year = {2013},
volume = {95},
pages = {928–952}
}

Erratum:  Eq. 33 should be

Corrected Eq. 33

Publication: Aleatory quantile surfaces in damage mechanics

ABSTRACT: In statistical damage mechanics, a deterministic failure limit surface is replaced with a scale-dependent family of quantile surfaces. An idealized homogeneous isotropic matrix material containing cracks of random size and orientation is used to elucidate expected mathematical character
of aleatory uncertainty and scale effects for initiation of damage in a brittle material. Scope is limited to statistics and scale dependence for the ONSET (not subsequent progression) of shear-driven failure. Exact analytical solutions for probability of such failure (with an interesting pole-point visualization) are derived for axisymmetric extension or compression of a single-crack sample. A semi-analytical bound on the failure CDF is found for a multi-crack specimen by integrating the single-crack probability over an exponential crack size distribution for which the majority of flaws are small enough to be safe from failure at any orientation. Resulting tails of the predicted failure distribution differ from Weibull theory,
especially in the third invariant.

Selected cool pictures (see the article for more images):

2014AleatoryQuantileSurfacesPic1

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Uintah Simulations of Perforation Experiments

Perforation

ABSTRACT: A simulation of a simple penetration experiment is performed using Material Point Method (MPM) through the Uintah Computational Framework (UCF) and interpreted using the post-processing visualization program VisIt. MPM formatting sets a background mesh with explicit boundaries and monitors the interaction of particles within that mesh to predict the varying movements and orientations of a material in response to loads. The modeled experiment compares the effects of an aluminum sphere impacting an aluminum sheet at varying velocities. In this work, the experiment called launch T-1428 (by Piekutowski and Poorman) is simulated using UCF and VisIt. The two materials in the experiment are both simulated using a hypoelastic-plastic model. Varying grid resolutions were used to verify the convergent behavior of the simulations to the experimental results. The validity of the simulation is quantified by comparing perforation hole diameter. A full 3-D simulation followed and was also compared to experimental results. Results and issues in both 2-D and 3-D simulation efforts are discussed. Both the axisymmetric and 3-D simulation results provided very good data with clear convergent behavior.

See the link below for the full report.

Experiment in Uintah

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Abstract: Deformation and Fracture of Heterogeneous Media using Boundary-Conforming Convected Particle Characteristic Functions in the Material Point Method

This is an abstract for

NWU2013: Advances in Computational Mechanics with Emphasis on Fracture and Multiscale Phenomena. Workshop honoring Professor Ted Belytschko’s 70th Birthday.  April 18, 2013 – April 20, 2013, Evanston, IL, USA

The organizers allocated only 10 minutes for each person’s talk (including big wigs like Tom Hughes), so we might just present this topic in the form of a puppet show with enough information to tickle the audience to chat with us about it in the hallway!

Authors:

Rebecca Brannon*, Alireza Sadeghirad,  James Guilkey

Department of Mechanical Engineering

University of Utah

Salt Lake City, UT, 84112

*Email: Rebecca.Brannon@utah.edu

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Conference Poster: Scaled surrogate Hertzian bearing pairs for contact and wear testing

Contact pressures

Sanders, A. P., and R. M. Brannon. (2012). “ Scaled surrogate Hertzian bearing pairs for contact and wear testing.” Transactions of the Orthopaedic Research Society 2012 Annual Meeting, San Francisco, CA, Feb. 4-7, Poster 2070. 2012 ORS poster 01 small

Abstract

New implant bearing materials require extensive laboratory testing before clinical use, but the currently practiced contact and wear test methods impose limitations. Screening wear tests of prototype materials are typically done using simple bearing shapes (such as a ball-on-flat pair) and low loads. These tests are relatively simple and inexpensive, but they lack representative bearing shapes and contact stresses. Simulator wear tests on full-scale components overcome this shortcoming by implementing higher loads and complex, physiologic motion patterns. However, these tests are lengthy and expensive; so, they are reserved for final design testing. Surrogate test specimens that would mimic the contact mechanics of full-scale bearing pairs could improve the relevance of early screening tests. This research examines the hypothesis that a reduced-scale surrogate Hertzian contact pair can elicit a smaller scale, equal stress version of the contact response of a larger original contact pair. A chosen original contact pair mimics a knee implant femoral-tibial condylar interface, and a full-scale surrogate pair is found using recently published formulas. New formulas were derived to find a smaller version of the surrogate pair. The contact pairs were tested in quasi-static normal loading, and their contact patches were measured to evaluate the hypothesis.

 

Conference Poster: Modeling, Testing, and Analysis of Impulse Response of Femoral Head Reduction in Ceramic Hip Prostheses

Kakarla, D., A. P. Sanders, S. Siskey, K. Ong, N. Ames, J. O. Ochoa, and R. M. Brannon. (2012). “Modeling, Testing, and Analysis of Impulse Response of Femoral Head Reduction in Ceramic Hip Prostheses.” Transactions of the Orthopaedic Research Society 2012 Annual Meeting, San Francisco, CA, Feb. 4-7, Poster 2076.

Abstract

Hip simulator wear tests including micro-separation conditions have revealed that abnormal loading events can outweigh normal loading conditions in causing wear of hard-on-hard bearings. Yet, there is a paucity of data to describe the mechanics of abnormal events such as edge loading by femoral neck impingement or femoral head subluxation. Though the magnitude of head subluxation has been measured in-vivo for a variety of human activities, there are apparently no corresponding reports of the concurrent head-liner contact forces; accurate measurements of the same may be rendered difficult by the transient, impulsive nature of edge loading. This report provides initial laboratory results of an in-vitro and in-silico study of impulsive femoral head reduction whose ultimate aim is to quantify dynamic edge-loading contact forces and stresses. The study implements an engineering model of proximal-lateral head subluxation and edge loading as could occur in a lax hip during the swing phase of gait. Rapid reduction is caused by applying a sudden cranio-caudal motion to the acetabular liner. In the laboratory, the femur’s response to this input is measured with strain gages and a laser vibrometer.