橡胶计算中本构模型的选择

OgdenArruda-BoyceVanderWaalsN2NNNOgden2N)1()3,3(21−+−−=JgIIfU1-1∑=−=NiiiJDg12)1(1∑∑=+=−+−−=NjiNiiijiijJDIICU11221)1(1)3()3(1-2NDiDi0N0µ0kN=110011002),(2DkCC=+=µ1-31=NMooney-Rivlin21201110)1(1)3()3(−+−+−=JDICICU1-400=ijC0≠jiNiNiiiiJDICU21010)1(1)3(−+−=∑∑==1-53N=Yeoh[2]iiiiiiJDICU2313010)1(1)3(−+−=∑∑==1-6Ogden1λ2λ3λ[3]iNiiNiiiJDUiii2113212)1(1)3(2∑∑==−+−++=αααλλλαµ1-7132131=→=−λλλλλiiJOgden1I2IOgden0µ∑==Nii10µµ1-8⎟⎟⎠⎞⎜⎜⎝⎛−−+−=∑=−JJDICUiiiimiln211)3(251122λµ1-9673750519C705019C105011C201C21C54321=====,,,,51...CCµ0µmλD2K0=VanderWaals[4][]⎟⎟⎠⎞⎜⎜⎝⎛−−+⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎟⎟⎠⎞⎜⎜⎝⎛−−+−−−=JJDIUmln21123~32)1ln()3(2232αηηλµ1-1021)1(~IIIββ+−=β1I2II~33~2−−=mIλη[6]1)1/(1)1(23−+=+=bcbbcεεεσσbεbσcεcσ3OgdenOgden3Ogden11Neo-hookean3-13-23-33333Ogden1Ogden1Neo-hookean1Ogden0.00.20.40.60.81.01.21.4012345670.00.20.40.60.81.01.21.4012345670.00.10.20.30.40.50.60.00.51.01.52.02.53.03.54.04.53-45mm6.7mm3-63-10~6mm6mm3Ogden1.35%Neo-Hookean1OgdenNeo-Hookean11%Ogden35%0123456705101520255mmkN/mm%2.220OgdenN=32.19-1.35OgdenN=11.43-35.59Neo-Hookean1.98-10.81OgdenNeo-HookeanMarlowOgden[7]~