Application of the network alteration theory for modeling the time-dependent constitutive behaviour of rubbers. Part I. General theory

Abstract The long-term time dependent irreversible deformation behaviour of rubber-like materials is characterized by large (irreversible) deformation, stress-relaxation, creep, permanent set and aging induced flexibility changes. These types of material behaviour are being described by combining the general (rubber) hyperelastic theory and Tobolsky's (network) alteration theory. To generalize Tobolsky's idea, the long-term time-dependent irreversible deformation behaviour is postulated as being caused by alterations of the original microstructure into new microstructures. This concept yields a general time-dependent constitutive model for rubberlike materials. Besides, the short-term rubber hysteresis behaviour (Mullins' effect) is adopted into the present model by implying the rubber hysteresis model of Simo. The experimental characterization of the model parameters – using the eight non-Gaussian chain theory for rubber elasticity as point of departure – as well as the experimental model verification are performed using modified Natural Indonesian Rubber samples. The experimental evidences will be presented in Part II (Septanika, E.G., Ernst, L.J., 1998. Application of the network alteration theory for modeling the time-dependent constitutive behaviour of rubbers. Part II. Further evaluation of the general theory and experimental verification. Mech. Mater. 30, 265–273). The present paper is concerned with the model development.

[1]  I. B. Prettyman,et al.  Stress Relaxation of Natural and Synthetic Rubber Stocks , 1944 .

[2]  A. Wineman,et al.  NUMERICAL SIMULATION OF THE EFFECT OF DAMAGED INDUCED SOFTENING ON THE INFLATION OF A CIRCULAR RUBBER MEMBRANE , 1994 .

[3]  A. Wineman,et al.  On a constitutive theory for materials undergoing microstructural changes , 1990 .

[4]  L. Mullins,et al.  Stress softening in rubber vulcanizates. Part I. Use of a strain amplification factor to describe the elastic behavior of filler‐reinforced vulcanized rubber , 1965 .

[5]  L. Mullins.  Softening of Rubber by Deformation , 1969 .

[6]  V. Giessen,et al.  On improved 3-D non-Gaussian network models for rubber elasticity , 1992 .

[7]  J. C. Simo,et al.  On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects , 1987 .

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

[9]  F. Bueche,et al.  Mullins effect and rubber–filler interaction† , 1961 .

[10]  Jacob Lubliner,et al.  A model of rubber viscoelasticity , 1985 .

[11]  L. J. Ernst,et al.  Application of the network alteration theory for modeling the time-dependent constitutive behaviour of rubbers. Part II. Further evaluation of the general theory and experimental verification , 1998 .

[12]  A. Tobolsky,et al.  Systems Manifesting Superposed Elastic and Viscous Behavior , 1945 .

[13]  F. Bueche.  Molecular basis for the mullins effect , 1960 .

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

[15]  Richard Schapery.  On the characterization of nonlinear viscoelastic materials , 1969 .

[16]  A. Tobolsky,et al.  A New Approach to the Theory of Relaxing Polymeric Media , 1946 .

[17]  The Theory of Permanent Set at Elevated Temperatures in Natural and Synthetic Rubber Vulcanizates , 1946 .

[18]  Sanjay Govindjee,et al.  A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins' effect , 1991 .

[19]  E. Giessen,et al.  On Improved Network Models for Rubber Elasticity and Their Applications to Orientation Hardening in Glassy Polymers , 1993 .

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

[21]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[22]  R. Christensen.  A Nonlinear Theory of Viscoelasticity for Application to Elastomers , 1980 .

[23]  B. Bernstein,et al.  A Study of Stress Relaxation with Finite Strain , 1963 .

[24]  J. F. Besseling,et al.  Mathematical Modelling of Inelastic Deformation , 1994 .

[25]  Kumbakonam R. Rajagopal,et al.  A CONSTITUTIVE EQUATION FOR NONLINEAR SOLIDS WHICH UNDERGO DEFORMATION INDUCED MICROSTRUCTURAL CHANGES , 1992 .

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