An Introduction to the Mechanical Properties of Solid by I. M. Ward

By I. M. Ward

Presents a entire advent to the mechanical behaviour of good polymers. commonly revised and up-to-date all through, the second one version now comprises new fabric on mechanical relaxations and anisotropy, composites modelling, non-linear viscoelasticity, yield behaviour and fracture of difficult polymers.

The obtainable strategy of the publication has been retained with every one bankruptcy designed to be self contained and the idea and purposes of the topic conscientiously brought the place acceptable. the most recent advancements within the box are incorporated along labored examples, mathematical appendices and an in depth reference.

  • Fully revised and up to date all through to incorporate the entire most modern advancements within the field
  • Worked examples on the finish of the chapter
  • An necessary source for college students of fabrics technology, chemistry, physics or engineering learning polymer science

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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.

Love, A. E. , A Treatise on the Mathematical Theory of Elasticity (4th edn), Macmillan, New York, 1944. 3. Ward, I. , Mechanical Properties of Solid Polymers (2nd edn), Wiley, Chichester, 1983. Further reading Solecki, R. and Conant, R. , Advanced Mechanics of Materials, Oxford University Press, Oxford, 2003. 1 General features of rubber-like behaviour The most noticeable feature of natural rubber and other elastomers is the ability to undergo large and reversible elastic deformation. It is not unexpected that stress can cause polymeric molecules to adopt an extended configuration, but at first sight it may seem surprising that on removal of the stress the molecules retract, on average, to their initial coiled form.

This gives º1 ¼ º and º2 ¼ º3 ¼ ºÀ1=2 (2:4) where we have used the incompressibility assumption º1 º2 º3 ¼ 1. 1) we have   @U 1 ¼ 2C1 º À 2 f ¼ @º º (2:6) This familiar equation is more usually represented as a consequence of the molecular theories of a rubber network. Here we see that it follows from purely phenomenological considerations as a simple constitutive equation for the finite deformation of an isotropic, incompressible solid. Materials that obey this relationship are sometimes called neo-Hookean.

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