Abstraction and operator characterization of fractal ladder viscoelastic hyper-cell for ligaments and tendons

doi:10.1007/s10483-019-2524-8

Abstract

Abstract: This study investigates the viscoelastic behavior of soft bio-fibres in association with their fractal structures. A spring-dashpot fractal network with the self-similar topology, named the Π-type fractal ladder hyper-cell (FLHC), is abstracted from the micro/nano-structure of ligaments and tendons (LTs). Its constitutive operator is derived by the Heaviside operational calculus, which is of intrinsic fractional order. In terms of this operator, the long-term viscoelastic relaxation of bio-fibres arising from the fractal ladder topology is expounded. In addition, the fractional-order viscoelastic constitutive equation is obtained based on the FLHC of LTs, and its results are consistent with those of available human knee and spinal LT relaxation experiments. Results on the constitutive equation of FLHCs are formulated into two propositions. The multidisciplinary invariance and implications from the fractal ladder pattern of bio-fibres are also discussed.

Key words: ligament and tendon (LT), fractal ladder topology, operator method, stress relaxation

2010 MSC Number:

Jianqiao GUO, Yajun YIN, Gexue REN. Abstraction and operator characterization of fractal ladder viscoelastic hyper-cell for ligaments and tendons. Applied Mathematics and Mechanics (English Edition), 2019, 40(10): 1429-1448.

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