theory of finite deformations of porous solids .pdf

《theory of finite deformations of porous solids .pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、TheoryofFiniteDeformationsofPorousSolidsM.A.BIOTCommunicatedbyG.TEMPLE1.Introduction.Thelinearmechanicsoffluid-saturatedporousmediaasdevelopedbytheauthorwasreviewedanddiscussedindetailintwoearlierpapers[l],[2].Initsfinalformitisbasedonthelinearthermody

2、namicsofirreversibleprocesses.Itisapplicabletothemostgeneralcaseofanisotropyandincludesnotonlythebasicprinciplesofclassicalthermodynamicsbutalsotheeffectsofcoupledflowsofirreversibleprocesses.Thermoelasticdissipationisalsoimplicitsincetheheatfluxisnoth

3、ingbutoneoftheinternalthermo-dynamiccoordinatesofthesystem.Thesolidmatrixitselfmaybeviscoelastic.Actuallythetheoryisevenmoregeneralsinceittakesintoaccountthevisco-elasticinteractionofthefluidwiththesolid.duetothemicromechanicsoffluidpenetrationincracks

4、whicharemuchsmallerthanthepores.Animportantconceptderivedfromtheexistenceofadissipationfunctionforthefluidisthatof“Viscodynamicoperator”[2].Thisisanoperationalsymmetrictensorwhichdescribesthefrequency-dependentbehaviorofthefluid.Thesymmetricchar-actero

5、fthistensorleadstoimportantconclusionsinthetheoryofacousticpropagation.Regardingtheextensiontonon-linearproblemsafirststepisconstitutedbyatheorywhichintroducesthenon-linearsuperpositionofastateofinitialstressandincrementaldeformations[3].Thisalsoleadst

6、oananalysisoffinitedeformationsbasedonstress-rates.Inthiscasethedeformationisconsideredasacontinuoussequenceofincrementaldeformations141.Theconceptsandmethodsintroducedinthisincrementaltheoryleadquitenaturallytothenextdevelopmentwhichconsidersadescript

7、ionoffinitedeformationusingmaterialcoordinates.Inparticulartheconceptofpressurefunctionforaporousmediumwhichwasintroducedinthetheoryofincrementaldeformations[3]providesoneoftheessentialmeansbywhichthisextensionofthetheorycanbeaccom-plished.Themechanics

8、ofporousmediaisthusbroughttothesamelevelofdevelopmentoftheclassicaltheoryoffinitedeformationsinelasticity.Inordertorestrictthelengthofthepaper,thetheoryispresentedinthecontextofquasi-staticandisothermaldeformations.597IndianaUniversityM