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

作　　者：Jianqiao GUO Yajun YIN Gexue REN 

机构地区：[1]Department of Engineering Mechanics, Tsinghua University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2019年第10期1429-1448,共20页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.11672150);the Beijing Nova Program Interdisciplinary Cooperation Project(No.xxjc201705);the Capital Clinical Special Promotion Project(No.Z161100000516233);the Key Issue of the 12th Five-Year Plan of People’s Liberation Army of China(No.BKJ13J004)

摘　　要：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 -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.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.

关 键 词：LIGAMENT and TENDON (LT) FRACTAL LADDER topology operator method stress relaxation 

分 类 号：O184[理学—数学] O189[理学—基础数学]