A constitutive model for compressible elastomeric solids

A non-linear thermo-elastic constitutive model for the large deformations of isotropic materials is formulated. This model is specialized to account for the physics and thermodynamics of the elastic deformation of rubber-like materials, and based on these molecular considerations a constitutive model for compressible elastomeric solids is proposed. The new constitutive model generalizes the incompressible and isothermal model of Arruda and Boyce (1993) to include the compressibility and thermal expansion of these materials. The model is fit to existing experimental data on vulcanized natural rubbers to determine the material parameters for the rubbers examined. The fit between the simple model and the data is found to be very good for large stretches and moderate volume changes.

[1]  L. Treloar,et al.  The properties of rubber in pure homogeneous strain , 1975 .

[2]  L. Treloar,et al.  Stress-strain data for vulcanised rubber under various types of deformation , 1944 .

[3]  M. Gurtin,et al.  An introduction to continuum mechanics , 1981 .

[4]  J. Ericksen,et al.  Introduction to the thermodynamics of solids , 1991 .

[5]  P. Flory,et al.  Thermodynamic relations for high elastic materials , 1961 .

[6]  D. J. Montgomery,et al.  The physics of rubber elasticity , 1949 .

[7]  K. Meyer,et al.  Sur l'élasticité du caoutchouc , 1935 .

[8]  Hubert M. James,et al.  Theory of the Elastic Properties of Rubber , 1943 .

[9]  Lawrence A. Wood,et al.  Compressibility of Natural Rubber at Pressures Below 500 kg/cm2 , 1964, Journal of research of the National Bureau of Standards. Section A, Physics and chemistry.

[10]  W. Kuhn,et al.  Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe , 1942 .

[11]  M. Boyce,et al.  A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials , 1993 .

[12]  R. Ogden Non-Linear Elastic Deformations , 1984 .

[13]  R. Penn Volume Changes Accompanying the Extension of Rubber , 1970 .

[14]  R. Landel,et al.  Stored energy function and compressibility of compressible rubberlike materials under large strain , 1975 .

[15]  C. Truesdell,et al.  The Non-Linear Field Theories of Mechanics , 1965 .

[16]  R. E. Gibson,et al.  The Compressibility of Rubber , 1930 .

[17]  J. H. Weiner,et al.  Statistical Mechanics of Elasticity , 1983 .