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Polymer elasticity discrete and continuum models

  • Robert G. C. Arridge
  • Peter J. Barham
Conference paper
Part of the Advances in Polymer Science book series (POLYMER, volume 46)

Abstract

There is at present available in the literature on polymers and on materials science a wealth of information regarding measurements of mechanical properties. These properties are dependent upon many relevant physical parameters and most measurements take this into account. There is also available a great deal of information regarding the relations between molecular structure and macroscopic physical properties and many calculations have been made. The bridge between these two extremes (the macro and the micro) is constructed primarily by the use of models of structure.

Composites theory, which has developed from classical elasticity, combined with modelling techniques may point the way forward to a complete theory of the behaviour of polymers. However, it is clear from the literature that many experimentalists do not appreciate the niceties of the mathematical theories of elasticity and of continuum mechanics, nor, in some cases, the inaccuracies inherent in their experimental methods, while nearly all theorists have no conception of the problems encountered by the experimentalist when dealing with real materials and samples of finite size. We have therefore attempted in this review to bring theory and experiment closer together by highlighting some of the problems both of the theoretician and of the experimentalist.

After an introductory chapter we review in Chap. 2 the classical definition of stress, strain and modulus and summarize the commonly used solutions of the equations of elasticity. In Chap. 3 we show how these classical solutions are applied to various test methods and comment on the problems imposed by specimen size, shape and alignment and also by the methods by which loads are applied. In Chap. 4 we discuss non-homogeneous materials and the theories relating to them, pressing the analogies with composites and the value of the concept of the representative volume element (RVE). Chapter 5 is devoted to a discussion of the RVE for crystalline and non-crystalline polymers and scale effects in testing. In Chap. 6 we discuss the methods so far available for calculating the elastic properties of polymers and the relevance of scale effects in this context.

Keywords

Elastic Constant Representative Volume Element Anisotropic Material Surface Strain Torsion Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Robert G. C. Arridge
    • 1
  • Peter J. Barham
    • 1
  1. 1.H. H. Wills Physics LaboratoryUniversity of BristolBristolEngland

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