弹性模型外文翻译

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1、附录1外文翻译原文3.2Elasticmodels3.2.1AnisotropyAnisotropicmaterialhasthesamepropertiesinalldirections—wecannotdis-tinguishanyonedirectionfromanyother.Samplestakenoutofthegroundwithanyorientationwouldbehaveidentically.However,weknowthatsoilshavebeendepositedinsomeway—forexample,sedimentarysoilswill

2、knowabouttheverticaldirectionofgravitationaldeposition.Theremayinadditionbeseasonalvariationsintherateofdepositionsothatthesoilcontainsmoreorlessmarkedlayersofslightlydifferentgrainsizeand/orplasticity.Thescaleoflayeringmaybesuffcientlysmallthatwedonotwishtotrytodistinguishseparatematerials

3、,butthelayeringtogetherwiththedirectionaldepositionmayneverthelessbesuffcienttomodifytheproperiesofthesoilindifferentdirections—inotherwordstocauseittobeanisotropic.Wecanwritethestiffnessrelationshipbetweenelasticstrainincrementandstressincrementcompactlyaswhereisthestiffnessmatrixandhencei

4、sthecompliancematrix.Foracompletelygeneralanisotropicelasticmaterialwhereeachlettera,b,...is,inprinciple,anindependentelasticpropertyandthenecessarysymmetryofthesti?nessmatrixfortheelasticmaterialhasreducedthemaximumnumberofindependentpropertiesto21.Assoonastherearematerialsymmetriesthenthe

5、numberofindependentelasticpropertiesfalls(Crampin,1981).Forexample,formonoclinicsymmetry(zsymmetryplane)thecompliancematrixhastheform:andhasthirteenelasticconstants.Orthorhombicsymmetry(distinctx,yandzsymmetryplanes)givesnineconstants:whereascubicsymmetry(identicalx,yandzsymmetryplanes,toge

6、therwithplanesjoiningoppositesidesofacube)givesonlythreeconstants:Figure3.9:Independentmodesofshearingforcross-anisotropicmaterialIfweaddthefurtherrequirementthatandsetand，thenwerecovertheisotropicelasticcompliancematrixof(3.1).Thoughitisobviouslyconvenientifgeotechnicalmaterialshavecertain

7、fabricsymmetrieswhichconferareductioninthenumberofindependentelasticproperties,ithastobeexpectedthatingeneralmaterialswhichhavebeenpushedaroundbytectonicforces,byice,orbymanwillnotpossessanyofthesesymmetriesand,insofarastheyhaveadomainofelasticresponse,w