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1、Nottingham Centrefor GeomechanicsGEOTECHNICAL ANALYSIS Deformations and StrainsNottingham Centrefor GeomechanicsDeformations and Strainsshear strainNormal strain (extension strain):xuxu+uInitial stateDeformed stateNottingham Centrefor GeomechanicsShear StrainNottingham Centrefor GeomechanicsTransfor
2、mation of Strains yxtsLike stresses, strains depends on coordinates system usedNottingham Centrefor GeomechanicsMohr-Circle for Strainsyyyxxyxx y0 xAtsttssststANottingham Centrefor GeomechanicsCompatibility of StrainsFor two displacement components (u,v), we have three strain components. Therefore,
3、these three strain components are not completely independent. Eliminate (u,v) from the above three equations, we get:Nottingham Centrefor GeomechanicsStress-Strain RelationshipzzyyxxzzyyxxWhere E = Youngs modulus = Poissons ratioNottingham Centrefor GeomechanicsShear ModulusShear modulus links shear
4、 stress to shear strain in the following way:G = Shear modulusTwo elastic constants (E,) or (G, ) fully define stress-strain relationshipNottingham Centrefor GeomechanicsStress-Strain Relationship for two dimensional problems ( zz= 0)yyyxxyxx y0 xyyyxxyxx y0 xPlane stressNottingham Centrefor GeomechanicsStress-Strain Relationship for 2D plane strain problemsComplete relationship:Nottingham Centrefor GeomechanicsExe.(1)Prove the Compatibility of Strains (2) For a triaxial stress state of a soil specimen, determine strain under elastic state.
