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Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics. (English) Zbl 0578.73040
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 isotropic 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.

MSC:
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
26A33 Fractional derivatives and integrals
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