# Advanced Solid Mechanics: Simplified Theory:Simplified Theory

MatterLocation as a factor affecting material propertiesHeterogeneous MaterialHomogeneous MaterialOrientation as a factor affecting material propertiesAnisotropic MaterialOrthotropic MaterialIsotropic MaterialStressForce and stressComponents of stressStress equilibrium equationStress transformationsPrincipal stress and maximum shear stressDeviatoric stressOctahedral stressPlane stressStrainDeformation and StrainLagrangian descriptionStrain Compatibility EquationStrain TransformationPrincipal Strain and Maximum Shear StrainDeviatoric StrainOctahedral StrainPlane StrainStress-Strain RelationshipsTypes of relationshipsGeneralised stress-strain relationshipMaterial with symmetrical properties about z axisOrthotropic materialOrthotropic material with same properties along y and z axesHomogeneous materialIsotropic materialPlane stress and plane strain for an isotropic materialSolutions for ElasticityStress-displacement relationshipNavier equationsBeltami-Michell stress compatibility equationsAiry stress functionSolutions for PlasticityYields criteriaTresca Yields CriterionVon Mises Yields CriterionPlastic workAssociated flow ruleHardening effect