Simulation of sand/soil/clay thrown explosively into obstacles

Here are a couple of cool movies created by CSM researcher, Biswajit Banerjee, in preparation for our project review this week:

  1. Clods of soil impact a plate:  A major advantage of the Material Point Method (developed as part of this research effort) is that it automatically allows material interaction without needing a contact algorithm.
  2. Extrapolated buried explosive ejecta. The sample is in a centrifuge to get higher artificial gravity, so the particles move to the side because of the Coriolis effect!

PUBLICATION: Continuum effective-stress approach for high-rate plastic deformation of fluid-saturated geomaterials with application to shaped-charge jet penetration


AUTHORS: Michael A. Homel · James E. Guilkey · Rebecca M. Brannon

ABSTRACT: A practical engineering approach for modeling the constitutive response of fluid-saturated porous geomaterials is developed and applied to shaped-charge jet penetration in wellbore completion. An analytical model of a saturated thick spherical shell provides valuable insight into the qualitative character of the elastic– plastic response with an evolving pore fluid pressure. However, intrinsic limitations of such a simplistic theory are discussed to motivate the more realistic semi-empirical model used in this work. The constitutive model is implemented into a material point method code that can accommodate extremely large deformations.Consistent with experimental observations, the simulations of wellbore perforation exhibit appropriate dependencies of depth of penetration on pore pressure and confining stress.


@article{  year={2015},  issn={0001-5970},  journal={Acta Mechanica},  doi={10.1007/s00707-015-1407-2},  title={Continuum effective-stress approach for high-rate plastic deformation of fluid-saturated geomaterials with application to shaped-charge jet penetration},  url={},  publisher={Springer Vienna},  author={Homel, Michael A. and Guilkey, James E. and Brannon, Rebecca M.},  pages={1-32},  language={English}  }

Linear algebra applied to sundials

CSM alumnus, Scot Swan, offers Sundials_and_Linear_Algebra,  which is a short (informal) writeup on the equations that are used for making standard horizontal dials.   Challenge: see if Scot’s write up is consistent with the calculator at

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Undergraduate researcher applies binning to study aleatory uncertainty in nonlinear buckling foundation models


Sophomore undergraduate, Katharin Jensen, has developed an easily understood illustration of the effect of aleatory uncertainty, which means natural point-to-point variability in systems. She has put statistical variability on the lengths of buckling elements in the following system:


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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.


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Errata for two verification publications


This posting provides errata for an analytical solution that appeared in the following two publications:

Brannon, R. M. and S. Leelavanichkul (2010) A multi-stage return algorithm for solving the classical damage component of constitutive models for rocks, ceramics, and other rock-like media. Int. J. Fracture v. 163(1), pp. 133-149.

K.C. Kamojjala, R. Brannon, A. Sadeghirad, and J. Guilkey (2013) Verification tests in solid mechanics, Engineering with Computers, 1-21.

As pointed out by Dr. Andy Tonge, they both contain a the same transcription error that was not in the original unpublished working document where the details of the solution are archived.  The following excerpt from the original unpublished working document contains correct formulas:  PlasticityVerification2excerpt.   See the red comment boxes in this file for details.

Pyrrhonism (AKA fallibilism) is not contentious

Fallibilism goes beyond the simple recognition that everyone is fallible. It demands that any ethical and equitable quest for truth (or beauty) must be founded on a commitment (not just willingness) to SEEK OUT (not just be open to) alternative viewpoints, which might contradict those of other people (friend or foe) and might even run counter to one’s own cherished beliefs (including a belief in fallibilism itself)!


Graham’s hierarchy of disagreement

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Tips for writing literature reviews

This posting aims to help graduate students write a good literature review for their qualifying exam, proposal, or thesis.

In the Department of Mechanical Engineering at the University of Utah, the qualifier examination is not a proposal, so there is no expectation that your Qual paper should propose new research.  Your literature review should, however, critically assess existing research in the subject area by pointing out specific limitations of (and, if applicable, errors in) existing published work.   The qualifier paper is meant to show that you can string together a coherent scholarly discussion.   The qualifier paper can have a fairly broad literature review as long as it still limits attention to mechanical engineering topics. The proposal document, on the other hand, should include a literature review that is more tightly related to your proposed research, as your aim is to convince the committee that your proposed work is (1) important to the field of Mechanical Engineering and (2) has not been done. The thesis document should include an updated literature review that suggests no one else has accomplished the same thing during the time you were working on it (or prior to your efforts, but inadvertently overlooked in your original literature review). The final thesis literature review should also thoroughly compare/contrast your own accomplishments with alternative approaches in contemporary literature.

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Streamlines, Streaklines, Pathlines, and Gridlines


The above animation aims to be a slight improvement over one on Wikipedia, which (incidentally) does not correctly describe the velocity field that it is depicting. The Wikipedia image doesn’t show a checkerboard of moving material, nor does it have a nice depiction of streamlines.

Before describing this animation, it might be helpful to look at a simpler motion (a rolling body) in order to review the difference between streamlines, streaklines, and pathlines. Consider a simple rigid body consisting of a disk of small radius (shown in gray below) along which it rolls along a tabletop, along with a larger-radius extension of the body (shown in color below) which can dip down below the table surface (as if there is a slot cut into the table so that part of the body rolls under it).

STREAMLINES: These are tangent to the instantaneous velocity field.  For a rolling rigid body, the motion is always circular about the instantaneous center of rotation at the bottom of the wheel. Accordingly, this image shows the streamlines at various points in time as the disk rolls along:


This image of streamlines is drawn not just on the body itself but also on its “virtual extension” in order to emphasize that (for rigid rolling) the instantaneous velocity is circular around the instantaneous center of rotation (bottom of the wheel). A particular set of streamlines is drawn in red. These are the ones that pass through a set of points that are evenly distributed on a spoke of the wheel (shown in black).

STREAKLINES: These are the lines you would see if a magic gremlin were to sit at a given location in space and “spraypaint” the material as it passes by.  Suppose that an assembly line of gremlins (located where you see the dots in the first image) are pointing their spray paint cans at the body while it rolls past. Then they would form the black streaklines shown here at various times:


Important: The streaklines are made by gremlins who are sitting still and spraying material as it passes by.

PATHLINES: Are made by gremlins who “ride” with the material, spraying a record of where they have been (as if we were watching the rolling body from behind a window, and those whacky gremlins would spray paint onto the window as they pass by). Accordingly, here are the pathlines for group of gremlins who were initially coincident with the gremlins in the above streakline plot:


GRIDLINES are any set of lines that are painted on the body like tattoos. Such lines move with the body (like a tattoo).


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