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Experimental determination of the relaxation modulus of a linear-isotropic-viscoelastic material

An experimental-data-reduction technique is described to determine more accurately the relaxation modulus of a linear-isotropic-viscoelastic material with the use of a common testing machine

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Abstract

It is well known that the relaxation modulus of a linear-isotropic-viscoelastic material under uniaxial load is the stress history of a unit-step strain history. A unit-stepped strain function cannot be obtained with the common instron testing machine. Instead, an easily obtainable strain function is described from which the relaxation modulus is derived. Experiments were conducted to illustrate this method. Experimental-data-reduction techniques are described. Experimentally measured output stress vs. time is fitted by a ‘smooth’ polynomial using a least-square criterion. Then by differentiation of this polynomial at proper times, the relaxation function is obtained.

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Abbreviations

t, τ1 :

time (s)

σ(t):

stress (Pa, 1 MPa=145 psi)

∈(t):

strain (mm/mm)

E(t) :

relaxation modulus (Pa)

h(t) :

step function

δ(t):

dirac-delta function

ɛ o :

strain (mm/mm)

G ijkl :

generalized relaxation modulus (Pa)

α:

strain rate (1/s)

References

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  4. Christensen, R.M., Theory of Viscoelasticity, An Introduction, Academic Press, New York and London (1971).

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Authors and Affiliations

  1. Mechanical Technology Inc., 12110, Latham, NY

    B. Bhushan (Senior Engineering Scientist)

  2. Department of Civil Engineering, University of Colorado, 80309, Boulder, CO

    F. W. Dauer (Consultant/Research Assistant)

Authors
  1. B. Bhushan
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  2. F. W. Dauer
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Bhushan, B., Dauer, F.W. Experimental determination of the relaxation modulus of a linear-isotropic-viscoelastic material. Experimental Mechanics 18, 421–425 (1978). https://doi.org/10.1007/BF02325058

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  • DOI: https://doi.org/10.1007/BF02325058

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