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Material failure theoryFlexural modulusStrain energy density functionStrain-rate tensorStrength of materialsStiffness matrixNeo-hookean solidStructural mechanicsMoody chartHyperelastic materialDynamic structure factorFlexural strengthPhysics of failureLinear elasticityShear and moment diagramFour-point flexural testStress intensity factorBlack's equationTsai-hill failure criterionBiharmonic equationStandard linear solid modelDarcy friction factor formulaeTopology optimizationEquation of stateStructural integrity and failureSolid mechanicsPhase diagramConstitutive equationMaxwell stress tensorCompressive strengthRainflow-counting algorithmSimons' formulaIsing modelSpectral graph theoryOgden hyperelastic modelEffective medium approximationsTensile testingGeometric mean theoremFinite strain theoryRheometrySteinmetz's equationStructure factorPoisson's ratioPoisson summation formulaLaplacian matrixJ-integralStrain hardening exponentFatigueMolecular orbital diagramGeometric flowAlternative stress measuresForming limit diagramDynamical systems theoryLiouville field theoryAlgebraic analysisEyring equationDynamic amplification factorClass field theoryGibbs isothermInfluence lineScherrer equationElastic modulusRoot locusDensity functional theoryGurney equationsPoroelasticityBateman equationFreundlich equationGauge theoryRadial distribution functionExperimental uncertainty analysisDiagramCrack growth equationCartan decompositionFracture in polymersMaterial derivativeSection modulusMaterials informaticsRicci flowCatastrophe theoryFraunhofer diffraction equationCharpy impact testThermomechanical analysisStress triaxialityFractal derivativePartial differential equationElectromagnetic tensorFunctional analysisStructural dynamicsBendingCorrelation functionTriple product ruleBet theoryResonating valence bond theoryShear strengthMean-field theoryFredholm integral equationDarboux's theoremDynamical mean-field theoryTheorem of three moments