Hyperelasticity Model for Finite Element Analysis of Natural and High Damping Rubbers in Compression and Shear

Rate-independent monotonic behavior of filled natural rubber and high damping rubber is investigated in compression and shear regimes. Monotonic responses obtained from tests conducted in both regimes demonstrate the prominent existence of the Fletcher- Gent effect, indicated by high stiffness at low strain levels. An improved hyperelasticity model for compression and shear regimes is proposed to represent the rate-independent instantaneous and equilibrium responses including the Fletcher-Gent effect. A parameter identification scheme involving simultaneous minimization of least-square residuals of uniaxial compression and simple shear data is delineated. The difficulties of identifying a unique set of hyperelasticity parameters that hold for both compression and shear deformation modes are thus overcome. The proposed hyperelasticity model has been implemented in a general purpose finite element program. Finite element simulations of experiments have shown the adequacy of the proposed hyperelasticity model, estimated parameters, and employed numerical procedures. Finally, numerical experiments were conducted to further explore the potential of the proposed model, and estimated parameters in analyzing rubber layers of a base isolation bearing subjected either to compression or to a combination of compression and shear.

[1]  Leonard R. Herrmann,et al.  Nonlinear behavior of elastomeric bearings, I: theory , 1988 .

[2]  C. K. Lim,et al.  EQUIVALENT HOMOGENEOUS FE MODEL FOR ELASTOMERIC BEARINGS , 1987 .

[3]  Leonard R. Herrmann,et al.  Analytical Parameter Study for Class of Elastomeric Bearings , 1989 .

[4]  R. Rivlin.  Large elastic deformations of isotropic materials IV. further developments of the general theory , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  O. H. Yeoh,et al.  Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates , 1990 .

[6]  R. Ogden.  Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  R. E. Whittaker,et al.  Low Strain Dynamic Properties of Filled Rubbers , 1971 .

[8]  John F. Stanton,et al.  Elastomeric Bearings: State‐of‐the‐Art , 1983 .

[9]  Günter Ramberger,et al.  Structural Bearings and Expansion Joints for Bridges , 2003 .

[10]  H. Kawai,et al.  Experimental survey of the strain energy density function of isoprene rubber vulcanizate , 1981 .

[11]  Michel Bercovier,et al.  A finite element method for the analysis of rubber parts, experimental and analytical assessment , 1981 .

[12]  Alan N. Gent,et al.  Relaxation processes in vulcanized rubber. I. Relation among stress relaxation, creep, recovery, and hysteresis , 1962 .

[13]  J. C. Simo,et al.  Penalty function formulations for incompressible nonlinear elastostatics , 1982 .

[14]  J. Z. Zhu,et al.  The finite element method , 1977 .

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

[16]  Athol J. Carr,et al.  Compression behaviour of bridge bearings used for seismic isolation , 1996 .

[17]  H. Alexander,et al.  A constitutive relation for rubber-like materials☆ , 1968 .

[18]  R. Landel,et al.  Stored energy function of rubberlike materials derived from simple tensile data. , 1972 .

[19]  J. S. Hwang,et al.  Analytical Modeling of High Damping Rubber Bearings , 1997 .

[20]  A. M. Abdel-Ghaffar,et al.  MODELING OF RUBBER AND LEAD PASSIVE-CONTROL BEARINGS FOR SEISMIC ANALYSIS , 1995 .

[21]  Stefan L. Burtscher,et al.  Aspects of Cavitation Damage in Seismic Bearings , 2000 .

[22]  L. J. Hart-Smith,et al.  Elasticity parameters for finite deformations of rubber-like materials , 1966 .

[23]  Teck-Yong Lim,et al.  Behavior of Reinforced Steel‐Fiber‐Concrete Beams in Flexure , 1987 .

[24]  Satoshi Fujita,et al.  Research, Development and Implementation of Rubber Bearings for Seismic Isolation , 1990 .

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

[26]  Yozo Fujino,et al.  Three-dimensional finite-element analysis of high damping rubber bearings , 2004 .

[27]  Atef F. Saleeb,et al.  Nonlinear material parameter estimation for characterizing hyper elastic large strain models , 2000 .

[28]  N. Tschoegl.  Constitutive equations for elastomers , 1971 .

[29]  P. R. Pinnock,et al.  The mechanical properties of solid polymers , 1966 .

[30]  J. Yang,et al.  A Review of Methods to Characterize Rubber Elastic Behavior for Use in Finite Element Analysis , 1994 .

[31]  D. Seibert,et al.  Direct Comparison of Some Recent Rubber Elasticity Models , 2000 .

[32]  R. Landel,et al.  The Strain‐Energy Function of a Hyperelastic Material in Terms of the Extension Ratios , 1967 .

[33]  A. G. James,et al.  Strain energy functions of rubber. I. Characterization of gum vulcanizates , 1975 .

[34]  R. Borst,et al.  On the behaviour of rubberlike materials in compression and shear , 1994 .

[35]  A. G. James,et al.  Strain energy functions of rubber. II. The characterization of filled vulcanizates , 1975 .

[36]  Lallit Anand,et al.  A constitutive model for compressible elastomeric solids , 1996 .

[37]  F. Bueche.  Mechanical Degradation of High Polymers , 1960 .

[38]  A. Amin,et al.  Measurement of lateral deformation in natural and high damping rubbers in large deformation uniaxial tests , 2003 .

[39]  Cheng-Hsiung Chang,et al.  Modeling of laminated rubber bearings using an analytical stiffness matrix , 2002 .

[40]  Warren P. Mason,et al.  Introduction to polymer viscoelasticity , 1972 .

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

[42]  Gary K. Patterson,et al.  Mechanical degradation of dilute solutions of high polymers in capillary tube flow , 1975 .

[43]  L. Treloar.  Stress-Strain Data for Vulcanized Rubber under Various Types of Deformation , 1944 .

[44]  Alan N. Gent.  Relaxation Processes in Vulcanized Rubber. II. Secondary Relaxation Due to Network Breakdown , 1962 .

[45]  Large Strain Viscoelastic Constitutive Models for Rubber, Part II: Determination of Material Constants , 1995 .

[46]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[47]  James M. Kelly,et al.  Earthquake-Resistant Design with Rubber , 1993 .

[48]  Shape optimization of a rubber bearing , 1991 .

[49]  A. Gent,et al.  Nonlinearity in the Dynamic Properties of Vulcanized Rubber Compounds , 1954 .

[50]  M. Mooney.  A Theory of Large Elastic Deformation , 1940 .

[51]  Leonard R. Herrmann,et al.  Nonlinear Behavior of Elastomeric Bearings. II: FE Analysis and Verification , 1988 .

[52]  Ch. Tsakmakis,et al.  Finite deformation viscoelasticity laws , 2000 .

[53]  A. Thomas,et al.  Characterization of the Behavior of Rubber for Engineering Design Purposes. 1. Stress-Strain Relations , 1994 .

[54]  Goodarz Ahmadi,et al.  WIND EFFECTS ON BASE-ISOLATED STRUCTURES , 1992 .

[55]  John L. Tassoulas,et al.  BEHAVIOR OF ELASTOMERIC BRIDGE BEARINGS: COMPUTATIONAL RESULTS , 1998 .

[56]  A. Castellani,et al.  ELASTOMERIC MATERIALS USED FOR VIBRATION ISOLATION OF RAILWAY LINES , 1998 .

[57]  B. Häggblad,et al.  Large strain solutions of rubber components , 1983 .

[58]  O. H. Yeoh.  On the Ogden Strain-Energy Function , 1997 .

[59]  R. Rivlin.  Large Elastic Deformations of Isotropic Materials , 1997 .

[60]  O. Yeoh.  Some Forms of the Strain Energy Function for Rubber , 1993 .

[61]  Maura Imbimbo,et al.  F.E. STRESS ANALYSIS OF RUBBER BEARINGS UNDER AXIAL LOADS , 1998 .

[62]  Yoshihiro Yamashita,et al.  Approximated form of the strain energy-density function of carbon-black filled rubbers for industrial applications. , 1992 .

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

[64]  Yoshiaki Okui,et al.  An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification , 2002 .

[65]  D. Nicholson,et al.  Finite Element Analysis of Hyperelastic Components , 1998 .

[66]  S. Peng,et al.  A compressible approach in finite element analysis of rubber-elastic materials , 1997 .

[67]  Yozo Fujino,et al.  CONSTITUTIVE MODEL OF HIGH DAMPING RUBBER MATERIALS , 2002 .

[68]  Christian Rey,et al.  New phenomenological behavior laws for rubbers and thermoplastic elastomers , 1999 .

[69]  R. Ogden,et al.  Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[70]  S. Kawabata,et al.  Strain energy density functions of rubber vulcanizates from biaxial extension , 1977 .