A Recurrence Formula for Viscoelastic Constitutive Equations

  • William W. Feng


The viscoelastic constitutive equations are generally represented by integral equations with kernels. These kernels are functions of current time, an integration limit of the hereditary integral. Therefore, the values of these kernels change as the time increases and the integral must be evaluated from time equals zero to the current time for every increment of time. Thus, as time increases, the required computing time becomes longer and longer. Furthermore, all physical values from time equals zero to the current time must be stored for later evaluations of these integrals. Additionally, for finite deformation viscoelastic problems, the constitutive equation is an integral part of the equilibrium equations that result in a set of nonlinear differential-integral equations. These equations usually can only be solved numerically and iteratively. Hence, computing time and data storage are the main concerns in solving finite deformation viscoelastic problems. The main object of this paper is to develop a method that saves both computing time and data storage in evaluating these integral equations.


Constitutive Equation Data Storage Current Time Relaxation Function Volterra Integral Equation 
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    Feng, W. W., “On Finite Deformation of Viscoelastic Rotating Disks,” Int. J. Non-linear Mechanics, Vol. 20, No. 1, 21–26, 1985.ADSMATHCrossRefGoogle Scholar
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    Christensen, R. M., “A Nonlinear Theory of Viscoelasticity for Application to Elastomers,” J. Appl. Mechanics 47, 762–768, 1980. Trans. ASME Vol. 102, Series E.Google Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • William W. Feng
    • 1
  1. 1.Lawrence Livermore National LaboratoryUniversity of CaliforniaLivermoreUSA

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