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 reliable polymers, including new fabric on mechanical relaxations and anisotopy, composites modeling, nonlinear viscoelasticity, and fracture of tricky polymers to this moment version. The available procedure of the ebook has been retained for this version, with every one bankruptcy designed to be self-contained and the speculation and purposes of the topic brought the place applicable. bankruptcy difficulties and mathematical appendices are incorporated. The e-book is for college students of fabrics, chemistry, physics, and engineering.
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Additional info for An introduction to Mechanical Properties of Solid Polymers
Thus ó xx ¼ aexx þ beyy þ cezz þ dexz þ . . etc: and e xx ¼ a9ó xx þ b9ó yy þ c9ó zz þ d9ó xz þ . . etc: where a, b . , a9, b9, are constants. This expression is the generalized Hooke’s law for both isotropic and anisotropic solids. Most of this textbook is concerned with isotropic solids where there is no coupling between tensile stresses and shear stresses, or between shear stresses and extensional strains, so that these equations reduce to forms such as ó xx ¼ aexx þ beyy þ cezz ó xz ¼ fexz and e xx ¼ a9ó xx þ b9ó yy þ c9ó zz e xz ¼ f 9ó xz To develop the generalized Hooke’s law for isotropic materials it is convenient to construct equations for the strains e xx , e yy , etc.
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. The actual network is replaced by an ideal network in which each segment of a molecule between successive points of cross-linkage is considered to be a Gaussian chain.
For this reason it is possible to apply equilibrium thermodynamics to determine how the stress is related to changes in both internal energy and entropy. The general nature of thermodynamics implies that this type of approach can give no direct information on molecular rearrangements but, when augmented by molecular theories of a statistical nature, it is possible to derive an equation of state that relates the force causing extension to molecular parameters. 6) above, which was derived as the equivalent of Hooke’s law for ﬁnite deformations.
An introduction to Mechanical Properties of Solid Polymers by I. M. Ward