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isotropic part of a fourth-order tensor, as well as a scalar measure of anisotropy ranging from 0 to 1.https://csmbrannon.net/wp-content/uploads/2015/08/voigtandmandelbases.pngVoigtAndMandelBaseshttps://csmbrannon.net/wp-content/uploads/2015/08/mandelnotation.pngMandelNotationhttps://csmbrannon.net/wp-content/uploads/2015/08/voigtnotation.pngVoigtNotation2018-09-02T02:59:33+00:00monthlyhttps://csmbrannon.net/2018/07/27/truss-myths-and-analysis/https://csmbrannon.net/wp-content/uploads/2018/07/trianglesnotnecorsuffortrussstability.pngTrianglesNotNecOrSufForTrussStabilityThis structure would be a stable truss even though it's not made entirely of triangles.2018-07-27T21:04:36+00:00monthlyhttps://csmbrannon.net/2018/05/17/visualization-of-rotation/https://csmbrannon.net/wp-content/uploads/2013/11/spheremappingweb.gifsphereMappingWebLambert area-preserving mapping of a sphere to a 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continuum concept. Homogenization and identification of an RVE is based on the value of x for which perturbations fall below numerical round-off error for a given application.2016-05-03T07:32:51+00:00monthlyhttps://csmbrannon.net/2011/03/07/conjugate-stress-and-strain-caveats-w-distortion-and-deformation-distinction/2016-05-02T18:27:43+00:00monthlyhttps://csmbrannon.net/2011/06/22/nonuniquenessandinstabilityofnonassplas/2016-04-29T19:35:20+00:00monthlyhttps://csmbrannon.net/2013/09/29/particle-basis-function-in-the-cpdi-method/https://csmbrannon.net/wp-content/uploads/2013/09/stretch_ppc0-5_opt2.gifStretch_ppc0.5_opt2https://csmbrannon.net/wp-content/uploads/2013/09/translate_ppc0-5_opt2.gifTranslate_ppc0.5_opt2https://csmbrannon.net/wp-content/uploads/2013/09/stretch_ppc1_opt2.gifStretch_ppc1_opt2https://csmbrannon.net/wp-content/uploads/2013/09/translate_ppc1_opt2.gifTranslate_ppc1_opt2https://csmbrannon.net/wp-content/uploads/2013/09/translate_ppc2_opt2.gifTranslate_ppc2_opt2https://csmbrannon.net/wp-content/uploads/2013/09/stretch_ppc4_opt2.gifStretch_ppc4_opt2https://csmbrannon.net/wp-content/uploads/2013/09/translate_ppc4_opt2.gifTranslate_ppc4_opt2https://csmbrannon.net/wp-content/uploads/2013/09/stretch_ppc1_opt1.gifStretch_ppc1_opt1https://csmbrannon.net/wp-content/uploads/2013/09/translate_ppc1_opt1.gifTranslate_ppc1_opt1https://csmbrannon.net/wp-content/uploads/2013/09/stretch_ppc2_opt1.gifStretch_ppc2_opt12016-01-14T00:17:54+00:00monthlyhttps://csmbrannon.net/2015/03/02/streamlines-streaklines-pathlines-and-gridlines/https://csmbrannon.net/wp-content/uploads/2015/03/particlepathlinerolling.pngparticlePathLineRollinghttps://csmbrannon.net/wp-content/uploads/2015/03/streaklinesonbefore.pngstreaklinesOnBeforehttps://csmbrannon.net/wp-content/uploads/2015/03/particlestreamlinerolling.pngparticleStreamLineRollinghttps://csmbrannon.net/wp-content/uploads/2015/03/gridstreamstreakpath.gifGridStreamStreakPath2016-01-12T05:26:28+00:00monthlyhttps://csmbrannon.net/2015/05/15/tips-for-writing-literature-reviews/https://csmbrannon.net/wp-content/uploads/2015/05/5423b-seven_steps_rainbow.png5423b-seven_steps_rainbow2016-01-02T20:20:38+00:00monthlyhttps://csmbrannon.net/2015/07/20/undergraduate-researcher-applies-binning-to-study-large-groups-of-statistically-variable-buckling-columns/https://csmbrannon.net/wp-content/uploads/2015/07/20150721_katharinjensenavatar.jpg20150721_KatharinJensenAvatarhttps://csmbrannon.net/wp-content/uploads/2015/07/2015_2element_bucklinksystem_3ddrawing.jpg2015_2element_bucklinksystem_3Ddrawinghttps://csmbrannon.net/wp-content/uploads/2015/07/variability.pngVariabilityhttps://csmbrannon.net/wp-content/uploads/2015/07/bistablesystem.gifbistableSystem2015-10-01T06:07:58+00:00monthlyhttps://csmbrannon.net/2015/09/30/i-love-my-mom/https://csmbrannon.net/wp-content/uploads/2015/09/lovemom.pngLoveMom2015-12-30T01:43:24+00:00monthlyhttps://csmbrannon.net/2015/09/07/simulation-of-sandsoilclay-thrown-explosively-into-obstacles/https://csmbrannon.net/wp-content/uploads/2015/09/centrifugerigidparticlesnowall.gifCentrifugeRigidParticlesNoWallhttps://csmbrannon.net/wp-content/uploads/2015/09/fragmentshittingplateareniscadrained.gifFragmentsHittingPlateAreniscaDrained2015-09-08T04:35:09+00:00monthlyhttps://csmbrannon.net/2014/04/15/gibrichards/2015-09-03T02:03:35+00:00monthlyhttps://csmbrannon.net/2011/06/19/brannon-letterofreference/2015-08-21T00:18:32+00:00monthlyhttps://csmbrannon.net/2015/08/12/publicationcontinuumeffectivestress/https://csmbrannon.net/wp-content/uploads/2015/08/stressspacevisualization.pngStressSpaceVisualization2015-08-12T18:17:07+00:00monthlyhttps://csmbrannon.net/2014/03/09/holey-particle-basis-functions-for-2d-cpdi/https://csmbrannon.net/wp-content/uploads/2014/03/tbarpass.gifTBarPasshttps://csmbrannon.net/wp-content/uploads/2014/03/tbarhit.gifTBarHithttps://csmbrannon.net/wp-content/uploads/2014/03/pshape7.gifPshape7https://csmbrannon.net/wp-content/uploads/2014/03/pshape6.gifPshape6https://csmbrannon.net/wp-content/uploads/2014/03/pshape5.gifPshape5https://csmbrannon.net/wp-content/uploads/2014/03/pshape4.gifPshape4https://csmbrannon.net/wp-content/uploads/2014/03/pshape3.gifPshape3https://csmbrannon.net/wp-content/uploads/2014/03/pshape2.gifPshape2https://csmbrannon.net/wp-content/uploads/2014/03/pshape1.gifPshape1https://csmbrannon.net/wp-content/uploads/2014/03/allpictab.gifallpictab2015-08-10T22:25:18+00:00monthlyhttps://csmbrannon.net/2011/09/01/annulus-twist/2015-07-27T21:05:09+00:00monthlyhttps://csmbrannon.net/2012/03/13/aldridge-spherical-source-verification-test-for-dynamic-continuum-codes/2015-07-23T23:27:50+00:00monthlyhttps://csmbrannon.net/people/2015-07-23T06:57:13+00:00weekly0.6https://csmbrannon.net/2015/07/22/linear-algebra-applied-to-sundials/2015-07-23T04:19:10+00:00monthlyhttps://csmbrannon.net/2015/07/20/publication-binning/https://csmbrannon.net/wp-content/uploads/2015/07/4000realizations.gif4000realizationshttps://csmbrannon.net/wp-content/uploads/2015/07/10realizations.gif10realizations2015-07-21T05:33:40+00:00monthlyhttps://csmbrannon.net/2011/03/06/thermostatics-derivative-simplification-tables/2015-0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Eq. 332015-07-16T00:55:47+00:00monthlyhttps://csmbrannon.net/2015/06/20/pyrrhonism-aka-fallibilism-is-not-contentious/https://csmbrannon.net/wp-content/uploads/2015/06/graham_hierarchy_of_disagreement.pngGraham_Hierarchy_of_Disagreement2015-07-16T00:49:35+00:00monthlyhttps://csmbrannon.net/2011/06/13/publication-a-multi-stage-return-algorithm-for-solving-the-classical-damage-component-of-constitutive-models-for-rocks-ceramics-and-other-rock-like-media/2015-07-15T17:51:15+00:00monthlyhttps://csmbrannon.net/2015/07/12/errata-for-two-verification-publications/https://csmbrannon.net/wp-content/uploads/2015/07/computer-doh.jpgcomputer-doh2015-07-13T05:10:38+00:00monthlyhttps://csmbrannon.net/research/publications/2015-06-21T07:52:14+00:00weekly0.6https://csmbrannon.net/2011/08/13/perfect-triples-nice-unit-vectors-and-nice-orthogonal-matrices/2015-05-05T20:58:54+00:00monthlyhttps://csmbrannon.net/2015/02/12/von-mises-cylinder-circle-or-ellipse/https://csmbrannon.net/wp-content/uploads/2015/02/misescylinderandmisesellipse1.gifMisesCylinderAndMisesEllipsehttps://csmbrannon.net/wp-content/uploads/2015/02/misescylinderandmisesellipse.gifMisesCylinderAndMisesEllipse2016-01-01T07:40:47+00:00monthlyhttps://csmbrannon.net/2011/03/01/eperimental-assessment-of-unvalidated-assumptions-in-classical-plasticity-theory/2014-12-30T07:42:54+00:00monthlyhttps://csmbrannon.net/2011/03/03/rotation-a-review-of-useful-theorems-involving-proper-orthogonal-matrices-referenced-to-threedimensional-physical-space/2014-12-30T07:41:52+00:00monthlyhttps://csmbrannon.net/2011/03/06/the-thermoelastic-square/2014-12-30T07:40:37+00:00monthlyhttps://csmbrannon.net/2011/06/01/introduction-to-mohrs-circle/2014-12-30T07:39:56+00:00monthlyhttps://csmbrannon.net/2011/06/01/instability-of-any-nonassociative-plasticity-model/2014-12-30T07:39:20+00:00monthlyhttps://csmbrannon.net/2011/06/13/publication-survey-of-four-damage-models-for-concrete/2014-12-30T07:38:46+00:00monthlyhttps://csmbrannon.net/2011/06/22/publication-on-the-thermodynamic-requirement-of-elastic-stiffness-anisotropy-in-isotropic-materials/2014-12-30T07:38:09+00:00monthlyhttps://csmbrannon.net/2011/08/09/tutorial-multi-linear-regression/2014-12-30T07:37:30+00:00monthlyhttps://csmbrannon.net/2011/09/04/streamline-visualization/2014-12-30T07:36:19+00:00monthlyhttps://csmbrannon.net/2011/09/12/plasticity-insight-algorithms/2014-12-30T07:35:46+00:00monthlyhttps://csmbrannon.net/2011/11/21/slides-rock-and-brittle-media/2014-12-30T07:35:07+00:00monthlyhttps://csmbrannon.net/2012/01/30/meyersbrannon2012/2014-12-30T07:33:59+00:00monthlyhttps://csmbrannon.net/2012/08/02/publication-influence-of-nonclassical-plasticity-features-on-shock-wave-existence-and-spectral-solutions/2014-12-30T07:29:31+00:00monthlyhttps://csmbrannon.net/2012/08/07/stretch-rotation-and-intuition-about-strain-rate-approximations/2014-12-30T07:28:10+00:00monthlyhttps://csmbrannon.net/2011/08/24/tutorial-visualizing-deformation/2014-12-30T07:25:20+00:00monthlyhttps://csmbrannon.net/2013/11/02/f-tables-for-prescribed-deformation/https://csmbrannon.net/wp-content/uploads/2013/11/ftablea1.pngFtableAhttps://csmbrannon.net/wp-content/uploads/2013/11/ftable_vgrid.pngFtable_vGridhttps://csmbrannon.net/wp-content/uploads/2013/11/ftable_ugrid.pngFtable_uGridhttps://csmbrannon.net/wp-content/uploads/2013/11/ftable_xgrid.pngFtable_xGridhttps://csmbrannon.net/wp-content/uploads/2013/11/ftable_stillgrid.pngFtable_stillGridhttps://csmbrannon.net/wp-content/uploads/2013/11/ftable_motionstar.gifFtable_motionstarSame deformation with superimposed rotationhttps://csmbrannon.net/wp-content/uploads/2013/11/ftable_motion.gifFtable_motionMotion without superimposed rotationhttps://csmbrannon.net/wp-content/uploads/2013/11/ftablea.pngFtableA2014-12-30T07:24:50+00:00monthlyhttps://csmbrannon.net/2014/05/22/publication-aleatory-quantile-surfaces-in-damage-mechanics/https://csmbrannon.net/wp-content/uploads/2014/05/2014aleatoryquantilesurfacespic3.png2014AleatoryQuantileSurfacesPic3https://csmbrannon.net/wp-content/uploads/2014/05/2014aleatoryquantilesurfacespic2.png2014AleatoryQuantileSurfacesPic2https://csmbrannon.net/wp-content/uploads/2014/05/2014aleatoryquantilesurfacespic1.png2014AleatoryQuantileSurfacesPic12014-12-30T07:22:58+00:00monthlyhttps://csmbrannon.net/7th-mpm-workshop/gallery/2014-11-29T02:26:21+00:00weekly0.6https://csmbrannon.net/7th-mpm-workshop/about-mpm-workshop/2014-11-29T02:25:00+00:00weekly0.6https://csmbrannon.net/2014/11/15/the-fourteenth-los-alamos-dynamics-summer-school/2014-11-15T20:08:48+00:00monthlyhttps://csmbrannon.net/2014/08/07/welcome-new-computational-mechanics-professor-ashley-spear/https://csmbrannon.net/wp-content/uploads/2014/08/spearmaterialscharacterization.pngSpearMaterialsCharacterizationDr. Spear's work (in collaboration with Carnegie Mellon and Lawrence Livermore Lab) using the Advanced Photon Source to obtain synchrotron-based measurments of 3D crack evolution in polycrystalline 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