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 stable polymers, including new fabric on mechanical relaxations and anisotopy, composites modeling, nonlinear viscoelasticity, and fracture of tricky polymers to this moment variation. The available 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 acceptable. bankruptcy difficulties and mathematical appendices are integrated. The ebook is for college kids of fabrics, chemistry, physics, and engineering.
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Additional resources for An introduction to Mechanical Properties of Solid Polymers
For ﬁnite strains this is no longer true, but for simplicity we will choose to deﬁne the components of stress with reference to the equilibrium of a cube in the deformed body. The components of stress can then be deﬁned in exactly the same manner as for small strain elasticity. 26 THE DEFORMATION OF AN ELASTIC SOLID In practice, the signiﬁcance of this decision is that we must be careful to distinguish between true stresses ó, which relate to the stress tensor, and the convenience of using nominal stresses f, which are deﬁned as the force per unit area of unstrained cross-section.
2 The state of strain In elementary elasticity, which is concerned with the elastic behaviour of isotropic materials, it is usual to consider two types of strain only. 2(a)), and this deﬁnition of strain is an essential ingredient of the very familiar Hooke’s law of elasticity. 2(b). The lateral displacement divided by the perpendicular distance between the planes deﬁnes the ‘engineering’ shear strain, which is the angle Ł in the ﬁgure. e. components of extensional and shear strain, analogous to the components of tensile and shear stress.
Calculate the average number of monomers between cross-links. 2. 5000 at small 52 RUBBER-LIKE ELASTICITY strains. 4900? 3. What would be the root mean square end-to-end distance of a parafﬁnic chain ˚ and the consisting of 1000 carbon atoms? e. without the restriction that valence angles should remain constant). 4. A non-Gaussian rubber has the strain-energy function 1:3 U ¼ C1 (º11:3 þ º1:3 2 þ º3 À 3) where º1 , º2 and º3 are the principal extension ratios and C1 ¼ 4 3 105 Pa. If a piece of such a rubber is initially 1 m long and has a cross-sectional area of 6 3 10À4 m2 , ﬁnd the mass required to give a ﬁnal extended length of 3 m.
An introduction to Mechanical Properties of Solid Polymers by I. M. Ward