The theory of rubber elasticity due to flory starts from the two postulates. It is argued that one can envisage two extreme regimes in rubber. Solid objects will deform when adequate forces are applied to them. In this chapter we focus on the isothermal phenomenological theory of the elasticity and inelasticity of rubber.
Goodier this book provides a comprehensive introduction to the theory of elasticity in a simple form as the subject allows together with a compilation of. The theory of elasticity is concerned with the mechanics of deformable bodies which recover their original shape upon the removal of the forces causing the deformation. Rubber elasticity, identified as the capacity to sustain very large deformations followed by complete recovery, is exhibited exclusively by polymeric substances consisting predominantly of long. External stress changes the equilibrium endtoend distance of a chain, and it thus adopts a less probable conformation. The tube model theory of rubber elasticity iopscience. Early theories of rubber elasticity were propounded on the assumption.
The science and technology of rubber polymer physics. View the table of contents for this issue, or go to the journal homepage for more. This paper attempts to improve several weaknesses in the classical theories of rubber elasticity. The theory of rubber elasticity edwards 1977 british. Normally, textbooks in elasticity after timoshenko commonly used his solutions and formulations.
Pdf experimental analysis of the molecular theory of. Principal differences centre on the connection between the locations of network junctions and the macroscopic strain. For statistic treating of rubber elasticity, an ideal macromolecule is used. Molecular theory of rubber elasticity sciencedirect. Some of the properties of bulk rubber are strikingly similar to, and may be understood by a consideration of, those of single flexible molecules. Determination of the molecular weight between crosslinks. Polymer science had developed greatly since the second edition of this text in 1958, and the two main advances the refinements of the. In the theory of rubber elasticity the concept of the gaussian chain is comparable to that of the maxwell distribution in a gas. This theory provides data for elastic and resistance rubber properties when the rubber is constrained to deformation that are smaller than 300%. Elements of theory of elasticity with solved examples introduction. Rubber, metals and alloys, rock, wood, bone can all be modelled as elastic materials, even though their chemical compositions are very different. This then permits the replacement of phantom chains, i. Sep 17, 20 elements of theory of elasticity with solved examples introduction. Timoskenkos other classic books on theory of elastic stability and theory of elastic plates and shells are also highly recommended if you are doing specific elastic members above.
Ogden 1986 recent advances in the phenomenological theory of rubber elasticity. The theory of rubber elasticity royal society publishing. The active chains may have di erent lengths, which a ects w. Edwards science research council, state house, high holborn, wc1r 4ta, also at cavendish laboratory, madingley road, cambridge.
The flory theory of rubber elasticity has pointed out the rubber elasticity has primarily entropic origins. For example, metals and alloys are crystalline, with grains consisting of regular arrays of atoms. Molecular theory of rubber elasticity polymer journal nature. Pdf experimental analysis of the molecular theory of rubber. If the material is elastic, the object will return to its initial shape and size when these forces are removed. Recent advances in the phenomenological theory of rubber. Rubber elasticity rubber is one of the most important and fascinating polymeric materials. To derive stressstrain relationship for cross linked rubber network. Stressstrain and birefringencestrain experiments, on polybutadiene and polymethyl3,3,3, trifluoropropyl siloxane elastomeric networks of various degrees of. This relationship, which can be derived from classical rubber elasticity theory, assumes that each chain sees an equivalent molecular environment arising from. A general treatment of the stressstrain relations of rubberlike solids was. Consider the gaussian statistics for the distribution of end to end distances. Download theory of elasticity by stephen timoshenko, j. Concentration dependence of the number of elastically effective chains revealed the near absence of elastically ineffective loops and the validity of the phantom network model.
We evaluate the homogeneity of tetrapeg gel and examine the models predicting rubber elasticity. Goodier this book provides a comprehensive introduction to the theory of elasticity in a simple form as the subject allows together with a compilation of solutions of special problems that are important in engineering practice and design. Elasticity, ability of a deformed material body to return to its original shape and size when the forces causing the deformation are removed. If the elasticity is between 0 and minus 1, then raising prices will raise revenues. Most materials which possess elasticity in practice remain purely elastic only up to very small deformations. Apr 28, 2016 to derive stressstrain relationship for cross linked rubber network. To a greater or lesser extent, most solid materials exhibit elastic behaviour, but there. The remarkable aspect of the solution is that it gives. Determination of the molecular weight between crosslinks of. The theory of rubber elasticity due to flory starts from the. Rubbers are highly elastic solids formed by the random permanent linkages between long chain polymers. It is suitable for the nonspecialist and the emphasis is on the physical reality embodied in the mathematical formulations.
Selecting this option will search all publications across the scitation platform selecting this option will search all publications for the publishersociety in context. The theory of elasticity for solvent swollen rubbers was used to calculate the average molecular weight of chain between crosslinks, mc, of five waxy maize starches with different degrees of crosslinking. Their elasticity is largely entropic in origin, so that the. The theory of rubber elasticity wiley online library. The physics of rubber elasticity oxford classic texts in the physical sciences 3rd edition. Roussel department of chemistry and biochemistry university of lethbridge february 21, 2009 a rubber is a material that can undergo large deformations e. The simplest molecular theories of rubberlike elasticity i. If the strip is heated using a hot air blower, the weight will rise, i. Therefore, the elasticity of rubbers is of purely entropic nature. Besides, the word elasticity can be used in a general sense. It is suitable for the nonspecialist and the emphasis is on the physical reality embodied in the mathematical. Natural rubber is the prototype of an important class of materials consisting of long flexible molecules which interact with each other in a particular way. The importance of the conception of the kinetic theory of rubber elasticity is comparable to that of the kinetic theory of gases. The molecular theory of rubber elasticity rests on the premise, now fully validated by experiments, that alterations of the configurations of the.
In particular, damping terms in the elastic behaviour of rubber can be calculated, and also the effect of entanglements and excluded volume on the equation of. It is obtained by chemical crosslinking chains in a melt or in a concentrated solution charles goodyear 18001860. By using the following basic equations for helmholtz free energy and its discussion about entropy, the force generated from the deformation of a rubber chain from its original unstretched conformation can be derived. Above a critical starch concentration %ww, maximum packing of granules occurs, and the interior of the granules controls the rheological behavior of the starch suspensions. Apr 15, 2004 natural rubber is the prototype of an important class of materials consisting of long flexible molecules which interact with each other in a particular way. The explanation of high elasticity has been provided by mark an kuhn through intermolecular thermal movement. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the gibbs formalism for conventional statistical mechanics.
Eichinger department of chemistry, university of washington, seattle, washington 981951700 abstract the solution of the manybody statistical mechanical theory of elasticity formulated by james and guth in the 1940s is presented. The statistical theory of rubber elasticity predicts that the stress in a strained elastomer is proportional to absolute temperature. These, and many other related properties, indicate that, in. A body with this ability is said to behave or respond elastically.
Lifshitz theory of elasticity volume 7 of a course of theoretical physics pergamon press 1970 acrobat 7 pdf 7. Molecular theory of rubber elasticity polymer journal. United kingdom 1 introduction in a solid material e. Pdf the tube model theory of rubber elasticity researchgate. A related phenomenon can easily be demonstrated by hanging a weight on a strip of unfilled rubber such as that used for elastic bands.
The molecular theory of rubber elasticity rests on the premise, now fully validated by experiments, that alterations of the configurations of the chains comprising the network account for the elastic free energy and for the stress arising from deformation. Infrared spectroscopy revealed the near absence of dangling chains. Elements of theory of elasticity with solved examples. The theoretical investigations of various authors, with the aid of which the physical properties of rubberlike substances have become understood on a basis of intermolecular statistics, have not, at least from a quantitative point of view, kept pace with investigations relating to kinetic theories of gases. Theory of elasticity elasticity, as the word implies, is used to determine the response of a variable to a change in some other variables,3. The tube model theory of rubber elasticity 247 figure 4. Reprint the theory of rubber elasticity oxford scholarship. Elasticity and inelasticity of rubber springerlink. The gaussian chain in the theory of rubber elasticity. Pdf rubbers are highly elastic solids formed by the random permanent linkages between long chain polymers.
The first is a dilute regime, where crosslinks are the only significant interaction between chains. All governing equations in this theory are linear partial differential equations, which means that theprinciple of superpo. First, we describe experimental results that characterize the elastic behaviour of rubber, in particular of vulcanized natural rubber. Their elasticity is largely entropic in origin, so that the molecular theory is largely a matter of counting the configurations available to the polymers and how this number changes under deformation. Generally, an elastic variable is one which responds a lot to small changes in other parameters. For example, metals and alloys are crystalline, with grains consisting of regular arrays of. Elasticity of rubbers is composed from the elastic responses of the chains crosslinked in the network sample. For a complete understanding of the behavior of rubberlike materials it is necessary to. Examination of the theories of rubber elasticity using an. Rubber elasticity an overview sciencedirect topics. These data suggest that tetrapeg gel is close to an.
The statistical theory of the elasticity of rubber. Applications of the finite element method include elasticity problems also. High elasticity is first treated by examining the phenomena at macromolecular scale 6. Elasticity theory the central model of solid mechanics. This option allows users to search by publication, volume and page selecting this option will search the current publication in context. This chapter reprints a paper which attempts to improve upon several weaknesses in the classical theories of rubber elasticity. Rubber elasticity is of kinetic nature, while crystalline materials elasticity is determined by the atoms interactions nature, so, rubber s particular elasticity is called high elasticity. Theory of elasticity exam problems and answers lecture ct5141 previously b16 delft university of technology faculty of civil engineering and geosciences structural mechanics section dr. Examples of this include sections on the statistical mechanical theory of polymer chains and the lattice theory of crystalline solids in the discussion of constitutive theory in volume ii. Crosslinked polymers and rubber elasticity chapter 9 sperling definition of rubber elasticity and requirements crosslinks, networks, classes of elastomers sections, 16 simple theory of rubber elasticity sections 48 entropic origin of elastic retractive forces the ideal rubber behavior. In engineering, the amount of elasticity of a material is determined by two types of material parameter.
Theory of elasticity exam problems and answers lecture ct5141. The basic concepts of this kinetic theory of rubber elasticity are explained, as well as the subsequent developments which have taken place in the quantitative treatment of the mechanical properties of rubber under the most general type of strain attention is drawn to the unusual normalstress effects which occur only in materials which are. Scott school of mathematics, university of east anglia, norwich, nr4 7tj. Crosslinks, networks, classes of elastomers sections, 16.
Theory of elasticity exam problems and answers lecture. Oxford classic texts in the physical sciences series by l. It develops a formulation of the statistical thermodynamics of amorphous materials analogous to the. The statistical theory of the elasticity of rubber rubber. The theory of rubber elasticity philosophical transactions. However, whereas the theory of gases has been refined in successive approximations to a coherent set of equations relating meaurable macroscopic properties to the field of force between the molecules and thus allowing the collection of detailed information on molecular forces, no similar progress has been made in the theory of rubber elasticity.
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