The mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string

This paper presents a study of the stress softening effect encountered in uniaxial extension and explores its effect on the small amplitude transverse vibration of a stretched rubber cord. An idealization of the uniaxial stressstrain behavior of a stress softening material is presented, the importance of the deformation history is emphasized, and parameters are introduced to track the deformation history. An extended investigation of a model proposed by Mullins and Tobin to quantify stress softening by introduction of a strain amplification factor is then presented. A major result derived from this model is shown to be consistent with results reported by others. The uniaxial stress softening theory is used to describe the transverse vibration behavior of a rubber string subjected to repeated stretching. This appears to be the first application of the softening model of Mullins and Tobin to a dynamical problem. Analytical results are compared with uniaxial stress-strain and transverse vibration experiments performed with buna-n, neoprene, and silicone rubber cords. Both types of experiments provide a simple and novel method to evaluate the predictive success of our uniaxial theory without the need for a specific constitutive model. The pseudoelastic response found in biological tissues is discussed in light of results obtained in the transverse vibration experiments.

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

[2]  D. O. Stalnaker,et al.  The Poisson Function of Finite Elasticity , 1986 .

[3]  L. Rayleigh,et al.  The theory of sound , 1894 .

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

[5]  H. M. Smallwood.  Limiting Law of the Reinforcement of Rubber , 1944 .

[6]  A. R. Payne,et al.  Stress softening in natural rubber vulcanizates. Part IV. Unfilled vulcanizates , 1966 .

[7]  E. Guth.  Theory of Filler Reinforcement , 1945 .

[8]  A. R. Payne,et al.  Stress softening in natural rubber vulcanizates. Part II. Stress softening effects in pure gum and filler loaded rubbers , 1965 .

[9]  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 .

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

[11]  W. L. Holt,et al.  Behavior of Rubber under Repeated Stresses , 1932 .

[12]  K. J. Smith,et al.  Elasticity of Semicrystalline Polymers1 , 1965 .

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

[14]  A. C. Chow,et al.  On the transverse vibration of a rubber string , 1983 .

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

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

[17]  Yuan-Cheng Fung.  On Pseudo-elasticity of Living Tissues , 1980 .

[18]  H. Bouasse,et al.  Sur les courbes de traction du caoutchouc vulcanisé , 1903 .

[19]  R. Bonart.  X-ray investigations concerning the physical structure of cross-linking in segmented urethane elastomers , 1968 .