By I. M. Ward

Offers a complete advent to the mechanical behaviour of stable polymers. generally revised and up to date all through, the second one variation now contains new fabric on mechanical relaxations and anisotropy, composites modelling, non-linear viscoelasticity, yield behaviour and fracture of tricky polymers.

The obtainable process of the publication has been retained with each one bankruptcy designed to be self contained and the speculation and functions of the topic rigorously brought the place acceptable. the most recent advancements within the box are incorporated along labored examples, mathematical appendices and an intensive reference.

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

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**Example text**

2, we can restrict our discussion to the case of normal strain without loss of generality. We choose principal extension ratios º1 , º2 and º3 parallel to the three rectangular coordinate axes x, y and z. The afﬁne deformation assumption implies that the relative displacement of the chain ends is deﬁned by the macroscopic deformation. 7 we take a system of coordinates x, y and z in the undeformed body. In this coordinate system a representative chain PQ has one end P at the origin. We refer any point in the deformed body to this system of coordinates.

E. for a chain of 100 bonds between cross-links the maximum extensibility is 10. 3 The entropy of a single chain The expression just derived indicates the reason for the high extensibility of lightly cross-linked rubbers and serves to introduce the important concept of a mean square length, but yields no information on the probability of a chain having a particular end-to-end length. This latter problem was ﬁrst analysed mathematically by Kuhn [4] and by Guth and Mark [5]. 3). The probability distribution for the position of the end Q is derived using approximations that are valid provided that the distance between the chain ends P and Q is much less than the extended chain length nl.

A shear strain e xz is related to the corresponding shear stress óxz by the relationship e xz ¼ óxz /G, where G is the shear modulus. 25 FINITE STRAIN ELASTICITY Thus we obtain the stress–strain relationships that are the starting point in many elementary textbooks of elasticity ([1], pp. 7–9): e xx ¼ 1 í ó xx À (ó yy þ ó zz ) E E e yy ¼ 1 í ó yy À (ó xx þ ó zz ) E E e zz ¼ 1 í ó zz À (ó xx þ ó yy ) E E e xz ¼ 1 ó xz G eyz ¼ 1 ó yz G exy ¼ 1 ó xy G A bulk modulus K, related to the fractional change in volume, can also be deﬁned, but only two of the quantities E, í, G and K are independent.