橡胶材料的基本实验及本构关系模型

3.13.21)1/(1)1(23−+=+=bcbccεεεσσbεbσcεcσ3.3zz)1()3,3(21−+−−=JgIIfU∑=−=NiiiJDg12)1(1∑∑=+=−+−−=NjiNiiijiijJDIICU11221)1(1)3()3(0µ0k10011002),(2DkCC=+=µ1=N21201110)1(1)3()3(−+−+−=JDICICU0=ijC0≠jiNiNiiiiJDICU21010)1(1)3(−+−=∑∑==3N=iiiiiiJDICU2313010)1(1)3(−+−=∑∑==)(1OC10=)01.0()1.0(20OOC−−30C)40.1()20.1(30−+−+EOEOC10C20C30C()211∑=−=nitestithiTTE3-8testiTthiTijCijCthiT,...1,)(1nkXCTNjikijijthi==∑=+λ3-9)(kijXλ1=N0=∂∂ijCE3-10)(3NN21M+=....1,)()()()(1112NmlTXCTXXnktestkklmijnkNjitestkklmkij=+=∑∑∑===+λλλ3-11ijC1λ2λ3λiNiiNiiiJDUiii2113212)1(1)3(2∑∑==−+−++=αααλλλαµ132131=→=−λλλλλiiJ1I2I1I2I2a21N21−===,,α0µ∑==Nii10µµmaii....1,=Nm2=2m=4m=[])()(111)()()()1(rkrjkmjnkijrjkrikririEPPPaa−==+∑∑+−=γδ3-14rnkEtestkthktestkkTTTE−=3-15ikPiaithktestkikikaTTaEP∂∂−=∂∂=13-16)0(iµ)0(iα)(211−−−=∂∂iiciithkTααλλαµ3-17λλλαµλλαµαααααln)(2)(21111−−−−−−−−=∂∂iiiiciiciiithkcT3-18⎪⎩⎪⎨⎧−−−=planarif,1biaxiaif,2uniaxialif,21c3-191-13OgdenN=31-14OgdenN=4Arruda-Boyce⎟⎟⎠⎞⎜⎜⎝⎛−−+−=∑=−JJDICUiiiimiln211)3(251122λµ673750519C705019C105011C201C21C54321=====,,,,51...CCµ0µmλD2K0=1-5Arruda-BoyceanderWaals[]⎟⎟⎠⎞⎜⎜⎝⎛−−+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎟⎟⎠⎞⎜⎜⎝⎛−−+−−−=JJDIUmln21123~32)1ln()3(2232αηηλµ21)1(~IIIββ+−=β1I2II~33~2−−=mIληVanderWaals1-6VanderWaals