By I. M. Ward
Ward and Sweeney, either affiliated with the IRC in Polymer technological know-how and expertise on the college of Leeds, united kingdom, introduce the mechanical habit of strong polymers, including new fabric on mechanical relaxations and anisotopy, composites modeling, nonlinear viscoelasticity, and fracture of tricky polymers to this moment version. The available strategy of the ebook has been retained for this variation, with each one bankruptcy designed to be self-contained and the idea and purposes of the topic brought the place acceptable. bankruptcy difficulties and mathematical appendices are incorporated. The publication is for college kids of fabrics, chemistry, physics, and engineering.
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Extra info for An introduction to Mechanical Properties of Solid Polymers
33)) for uniaxial stretching becomes RECENT DEVELOPMENTS IN THE MOLECULAR THEORY OF RUBBER ELASTICITY 49 ! NkT 1=2 À1 ºchain º À 1=º2 n L f ¼ 3 ºchain n1=2 (3:37) Arruda and Boyce  showed that the eight-chain model performed much better than three- and four-chain models in predicting the behaviour of vulcanized rubber in uniaxial and biaxial tension and shear, and also performed excellently in modelling uniaxial and plane strain compression of gum and neoprene rubber. Wu and van der Giessen  produced a further generalization to an inﬁnitely large number of chains – the full network model.
Polymer, 22, 1010 (1981). 11. Edwards, S. F. , Polymer, 27, 483 (1986). 12. Arruda, E. M. and Boyce, M. , J. Mech. Phys. Solids, 41, 389 (1993). 13. Wu, P. D. , J. Mech. Phys. Solids, 41, 427 (1993). 14. , Comput. Theor. Polym. , 9, 27 (1999). 15. Stepto, R. F. T. and Taylor, D. J. , Macromol. , 93, 261 (1995). 16. Stepto, R. F. T. and Taylor, D. J. , J. Chem. Soc. , 91, 2639 (1995) 17. Flory, P. , Crescenzi, V. and Mark, J. , J. Am. Chem. , 67, 3202 (1971). 18. Taylor, D. J. , Stepto, R. F. , Jones, R.
E. 2 above. The entropy of the freely jointed chain s is proportional to the logarithm of the number of conﬁgurations Ù so that s ¼ k ln Ù where k is Boltzmann’s constant. If dx dy dz is constant, the number of conﬁgurations available to the chain is proportional to the probability per unit volume p(x, y, z). The entropy of the chain is thus given by s ¼ c À kb2 r 2 ¼ c À kb2 (x 2 þ y 2 þ z 2 ) (3:21) where c is an arbitrary constant. 4 The elasticity of a molecular network We wish to calculate the strain-energy function for a molecular network, assuming that this is given by the change in entropy of a network of chains as a function of strain.