A theory of stress softening of elastomers based on finite chain extensibility

In this paper we develop a theory to describe the Mullins effect in rubber–like solids, based on the notion of limiting chain extensibility associated with the Gent model of rubber elasticity. We relate the theory to the mechanisms of network alteration and to the pseudo–elasticity theory of the Mullins effect. The inherently anisotropic nature of the Mullins effect is also discussed.

[1]  M. A. Johnson,et al.  A constitutive equation for the Mullins effect in stress controlled uniaxial extension experiments , 1993 .

[2]  Giuseppe Saccomandi,et al.  Simple Torsion of Isotropic, Hyperelastic, Incompressible Materials with Limiting Chain Extensibility , 1999 .

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

[4]  L. Mullins,et al.  Theoretical Model for the Elastic Behavior of Filler-Reinforced Vulcanized Rubbers , 1957 .

[5]  A. Wineman Torsion of an Elastomeric Cylinder Undergoing Microstructural Changes , 2001 .

[6]  F. Andrieux,et al.  On a Damaged Hyperelastic Medium: Mullins Effect with Irreversible Strain , 1999 .

[7]  Giuseppe Saccomandi,et al.  A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity , 2002 .

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

[9]  A. DeSimone,et al.  A Damage Mechanics Approach to Stress Softening and its Application to Rubber , 2001 .

[10]  Giuseppe Saccomandi,et al.  Constitutive Modelling of Rubber-Like and Biological Materials with Limiting Chain Extensibility , 2002 .

[11]  Millard F. Beatty,et al.  Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With Examples , 1987 .

[12]  D. Owen,et al.  A phenomenological three-dimensional rate-idependent continuum damage model for highly filled polymers: Formulation and computational aspects , 1994 .

[13]  L. Mullins Effect of Stretching on the Properties of Rubber , 1948 .

[14]  Burak Erman,et al.  Structures and properties of rubberlike networks , 1997 .

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

[16]  Millard F. Beatty,et al.  A new phenomenological model for stress-softening in elastomers , 2002 .

[17]  K. Rajagopal,et al.  On The Role of the Eshelby Energy-Momentum Tensor in Materials with Multiple Natural Configurations , 2005 .

[18]  C. Horgan,et al.  PURE AZIMUTHAL SHEAR OF ISOTROPIC, INCOMPRESSIBLE HYPERELASTIC MATERIALS WITH LIMITING CHAIN EXTENSIBILITY , 2001 .

[19]  Giuseppe Saccomandi,et al.  Anti-plane shear deformations for non-Gaussian isotropic, incompressible hyperelastic materials , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  Alexander Lion,et al.  A constitutive model for carbon black filled rubber: Experimental investigations and mathematical representation , 1996 .

[21]  Morton E. Gurtin,et al.  Simple Rate-Independent Model for Damage , 1981 .

[22]  A. Gent A New Constitutive Relation for Rubber , 1996 .

[23]  Carl Eckart,et al.  The Thermodynamics of Irreversible Processes. IV. The Theory of Elasticity and Anelasticity , 1948 .

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

[25]  A. Wineman,et al.  Changes in material symmetry associated with deformation: Uniaxial extension , 1988 .

[26]  R. Ogden,et al.  A pseudo–elastic model for the Mullins effect in filled rubber , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  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 .

[28]  G. Marckmann,et al.  A theory of network alteration for the Mullins effect , 2002 .

[29]  C. Horgan,et al.  Pure Axial Shear of Isotropic, Incompressible Nonlinearly Elastic Materials with Limiting Chain Extensibility , 1999 .

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

[31]  Giuseppe Saccomandi,et al.  Finite thermoelasticity with limiting chain extensibility , 2003 .

[32]  Mary C. Boyce,et al.  Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity , 1996 .

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

[34]  C. Horgan,et al.  Large deformations of a rotating solid cylinder for non-Gaussian isotropic, incompressible hyperelastic materials , 2001 .

[35]  Giuseppe Saccomandi,et al.  A Note on the Gent Model for Rubber-Like Materials , 2002 .

[36]  Millard F. Beatty,et al.  A theory of stress-softening in incompressible isotropic materials , 2000 .

[37]  C. Horgan,et al.  A description of arterial wall mechanics using limiting chain extensibility constitutive models , 2003, Biomechanics and modeling in mechanobiology.

[38]  M. Boyce,et al.  Constitutive models of rubber elasticity: A review , 2000 .

[39]  L. J. Ernst,et al.  Application of the network alteration theory for modeling the time-dependent constitutive behaviour of rubbers. Part I. General theory , 1998 .