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Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics

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Summary

Fractional calculus is used to describe the general behavior of materials with memory. An expression for the fractional derivative or the fractional integral is developed in terms of the Stieltjes convolution and the Riesz distribution. The general fractional calculus polynomial operator constitutive equation is reduced to a Stieltjes convolution. A constitutive equation which depends on a memory parameter for an isotorpic viscoelastic material is presented. The proposed creep compliance has an initial response, a primary creep region, a secondary creep region and a tertiary creep region. The corresponding relaxation modulus has a glassy region, a leathery region, a rubbery region and a liquid region.

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  1. Department of Mechanical Engineering, University of Wisconsin-Platterville, 53818, Platteville, WI, U.S.A.

    R. C. Koeller

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Koeller, R.C. Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics. Acta Mechanica 58, 251–264 (1986). https://doi.org/10.1007/BF01176603

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