Woo S L, Johnson G A, Smith B A
Department of Orthopaedic Surgery, University of Pittsburgh, PA 15213.
J Biomech Eng. 1993 Nov;115(4B):468-73. doi: 10.1115/1.2895526.
Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model.
韧带和肌腱在维持人体结构方面发挥着多种重要功能。尽管有大量文献描述了对这些组织的实验研究，但韧带和肌腱的数学建模对于理解它们的行为也有显著贡献。本文综述了过去20年中韧带和肌腱数学建模的发展情况。韧带和肌腱的数学描述被确定为弹性或粘弹性，并按时间顺序进行了讨论。弹性模型假定韧带和肌腱不表现出与时间相关的行为，因此，它们专注于描述其力学响应的非线性方面。另一方面，粘弹性模型在其数学描述中纳入了与时间相关的效应。特别是，详细讨论了两种粘弹性模型；准线性粘弹性（QLV），在过去20年中被广泛使用，以及最近提出的单积分有限应变（SIFS）模型。
