Modelling of the hamstring muscle group by use of fractional derivatives. (English) Zbl 1189.35341
Summary: This paper deals with a viscoelastic model of the hamstring muscle group. The model includes fractional derivatives of stretching force and elongation, as well as restrictions on the coefficients that follow from the Clausius-Duhem inequality. On the basis of a ramp-and-hold type of experiment, four rheological parameters have been calculated by numerical treatment ab initio. Riemann-Liouville fractional derivatives were approximated numerically using the Grünwald-Letnikov definition. Obtained results were verified by use of the Laplace transform method. The stretching force in time domain involves Mittag-Leffler-type function.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 92C30 | Physiology (general) |
| 26A33 | Fractional derivatives and integrals |
References:
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