By I. M. Ward
Ward and Sweeney, either affiliated with the IRC in Polymer technological know-how and know-how on the college of Leeds, united kingdom, introduce the mechanical habit of sturdy polymers, including new fabric on mechanical relaxations and anisotopy, composites modeling, nonlinear viscoelasticity, and fracture of tricky polymers to this moment variation. The obtainable procedure of the publication has been retained for this version, with each one bankruptcy designed to be self-contained and the idea and functions of the topic brought the place applicable. 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
Consider a point P2 , very close to P1 , that in the undisplaced position had coordinates (x + dx, y + dy, z + dz) and let the displacement that it has undergone have components (u + du, v + dv, w + dw). The quantities required are then du, dv and dw, the relative displacements. e. inﬁnitesimal, then du ¼ @u @u @u dx þ dy þ dz @x @y @z dv ¼ @v @v @v dx þ dy þ dz @x @y @z dw ¼ @w @w @w dx þ dy þ dz @x @y @z Thus we need to deﬁne the nine quantities @u , @x @u , . , etc: @y For convenience these nine quantities are regrouped and denoted as follows: e xx ¼ @u @x e yy ¼ @v @y e zz ¼ @w @z eyz ¼ @w @v þ @ y @z ezx ¼ @u @w þ @z @x exy ¼ @v @u þ @x @ y 2ø x ¼ @w @v À @ y @z 2ø y ¼ @u @w À @z @x 2ø z ¼ @v @u À @x @ y The ﬁrst three quantities e xx , e yy and e zz correspond to the fractional expansions or contractions along the x, y and z axes of an inﬁnitesimal element at P1.
Materials that obey this relationship are sometimes called neo-Hookean. e. Hooke’s law. References 1. Timoshenko, S. and Goodier, J. , Theory of Elasticity, McGraw-Hill International Editions, New York, 1970. 2. 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.
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.