isotropic ideal solids △ △Z v: Poisson ratio v= △m/mo △l/l E E=2(1+v)=3B(1-2v) Incompressible solids v=0.5 E=3G
isotropic ideal solids EG B 2 1 3 12 Q Q Q: Poisson ratio 'm 'l 0 0 / / m m t l l H Q H ' ' Incompressible solids Q=0.5 E=3G 6
anisotropic ideal solids Oxx=axExxtary ExytaxEx t a =ao o ta+ σ」=[a[] LE,=la, 'lo, generalized hook,'s law广义虎克定律)
anisotropic ideal solids ... xx xx xx xy xy xz xz V HHH aaa ij ij ij ª º ª ºª º V H a ¬ ¼ ¬ ¼¬ ¼ Vxx Vyy Vzz generalized hook’s law (ᒯѹ㱾ݻᇊᖻ) 7 ' ij ij ij ª º ª ºª º H V a ¬ ¼ ¬ ¼¬ ¼ ' ' ' ... xx xx xx xy xy xz xz HVVV aaa
Nonlinear behaviors of Materials Property Elongation at break Elongation Initial modulus Strength f△ 08= f△/V odE=lfal/Vo=W/Vo Work(功) of Unit volume
Nonlinear Behaviors of Materials Property 8 VH 0 0 f l A l ' 0 'f lV/ 0 V Hd fdl V / ³ ³ Work(࣏ (of Unit Volume 0 W V/ Initial modulus Strength
7.2 Rubber (Elastomers) and rubber Elasticity General properties of elastomers The individual polymer chains of elastomers are held together by weak termolecular bonding forces which allow rapid chain slippage when a moderate pulling force is employed. Cross-links, which are introduced during vulcanization(硫化), permit rapid 经 elongation of the principal sections, to a point where the chains are stretched to Typical applied-force elongation behavior of rubber their elastic limit. Any additional elongation causes primary bond breakage. The cross-links which are the boundaries for the principal sections, permit the rubber to“ remember” its original shape, Sulphur bridges Hard domain with邮啦 that is, the original orientation of the linking cis-1, 4- Structure of thermo povIoDrene particular chains. plastic elastomers
7.2 Rubber (Elastomers) and Rubber Elasticity ¾ General properties of elastomers ¾ The individual polymer chains of elastomers are held together by weak intermolecular bonding forces, which allow rapid chain slippage when a moderate pulling force is employed. ¾ Cross-links, which are introduced during vulcanization (⺛ॆ), permit rapid elongation of the principal sections, to a point where the chains are stretched to their elastic limit. Any additional elongation causes primary bond breakage. The cross-links, which are the boundaries for the principal sections, permit the rubber to “remember” its original shape, that is, the original orientation of the particular chains. Typical applied-forceelongation behavior of rubber Sulphur bridges linking cis-1,4- polyisoprene Structure of thermoplastic elastomers 9
8 旦 Vulcanized rubber Unvulcanized rubber 200 400 Elongation, o
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