By I. M. Ward
Presents a entire creation to the mechanical behaviour of sturdy polymers. broadly 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 difficult polymers.
The obtainable technique of the publication has been retained with every one bankruptcy designed to be self contained and the speculation and functions of the topic conscientiously brought the place applicable. the newest advancements within the box are integrated along labored examples, mathematical appendices and an intensive reference.
- Fully revised and up to date all through to incorporate the entire newest advancements within the field
- Worked examples on the finish of the chapter
- An precious source for college students of fabrics technological know-how, chemistry, physics or engineering learning polymer science
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Additional resources for An Introduction to the Mechanical Properties of Solid Polymers
20). 6). This difference is related to changes in entropy, and so to tensile force. 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.
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.
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.
An Introduction to the Mechanical Properties of Solid Polymers by I. M. Ward