A composite micromechanical model for connective tissues, I:​ theory

Ault, H. K.<sup>1</sup>; Hoffman, A. H.<sup>1</sup>

Affiliations

¹Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609

Abstract

A micromechanical model has been developed to study and predict the mechanical behavior of fibrous soft tissues. The model uses the theorems of least work and minimum potential energy to predict upper and lower bounds on material behavior based on the structure and properties of tissue components. The basic model consists of a composite of crimped collagen fibers embedded in an elastic glycosaminoglycan matrix. Upper and lower bound aggregation rules predict composite material behavior under the assumptions of uniform strain and uniform stress, respectively. Input parameters consist of the component material properties and the geometric configuration of the fibers. The model may be applied to a variety of connective tissue structures and is valuable in giving insight into material behavior and the nature of interactions between tissue components in various structures. Application of the model to rat tail tendon and cat knee joint capsule is described in a companion paper [2].

Links

DOI: 10.1115/1.2895437

PubMed: 1491576

WoS: A1992HP75200020

History

Received: 1990-01-02

Revised: 1991-04-30

Cited Works (8)

Year	Entry
1988	Ault HK. A Micromechanical Model of Fibrous Soft Tissue [PhD thesis]. Worcester, MA: Worcester Polytechnic Institute; 1988.
1978	Kastelic J, Galeski A, Baer E. The multicomposite structure of tendon. Connect Tissue Res. 1978;6(1):11-23.
1980	Kastelic J, Palley I, Baer E. A structural mechanical model for tendon crimping. J Biomech. 1980;13(10):887-893.
1992	Ault HK, Hoffman AH. A composite micromechanical model for connective tissues, II: application to rat tail tendon and joint capsule. J Biomech Eng. February 1992;114(1):142-146.
1964	Hashin Z, Rosen BW. The elastic moduli of fiber-reinforced materials. J Appl Mech. June 1964;31(2):223-232.
1983	Lanir Y. Constitutive equations for fibrous connective tissues. J Biomech. 1983;16(1):1-12.
1976	Comninou M, Yannas IV. Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibres. J Biomech. 1976;9(7):427-433.
1972	Crisp JDC. Properties of tendon and skin. In: Fung YC, Perrone N, Anliker M, eds. Biomechanics: Its Foundations and Objectives. Symposium on Biomechanics, its Foundations and Objectives; July 29-31, 1970. Englewood Cliff, NJ: Inc., Prentice-Hall International; 1972:141-179.

Cited By (19)

Year	Entry
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
1994	Schwartz MH, Leo PH, Lewis JL. A microstructural model for the elastic response of articular cartilage. J Biomech. July 1994;27(7):865-873.
1999	Arbogast KB, Margulies SS. A fiber-reinforced composite model of the viscoelastic behavior of the brainstem in shear. J Biomech. August 1999;32(8):865-870.
1992	Ault HK, Hoffman AH. A composite micromechanical model for connective tissues, II: application to rat tail tendon and joint capsule. J Biomech Eng. February 1992;114(1):142-146.
1997	Hurschler C, Loitz-Ramage B, Vanderby R Jr. A structurally based stress-stretch relationship for tendon and ligament. J Biomech Eng. November 1997;119(4):392-399.
1999	Soulhat J, Buschmann MD, Shirazi-Adl A. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J Biomech Eng. June 1999;121(3):340-347.
2005	Weiss JA, Gardiner JC, Ellis BJ, Lujan TJ, Phatak NS. Three-dimensional finite element modeling of ligaments: technical aspects. Med Eng Phys. December 2005;27(10):845-861.
1997	Pioletti DP. Viscoelastic Properties of Soft Tissues Application to Knee Ligaments and Tendons [PhD thesis]. Swiss Federal Institute of Technology Lausanne; 1997.
2011	Rigozzi S. Structure and Function in Tendon: Experimental Studies on the Ultrastructural Determinants of Tendon Biomechanical Function [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2011.
2007	Lavagnino M. The Mechanotransduction Response of Tendon Cells to Tensile Loading [PhD thesis]. East Lansing, MI: Michigan State University; 2007.
1996	Levine RE. Heterogeneity of the Medial Collateral Ligament in Uniaxial Tension [PhD thesis]. University of Pittsburgh; 1996.
1997	Wren TAL. Structure-Function Relationships for Soft Skeletal Connective Tissues [PhD thesis]. Stanford University; June 1997.
1998	Derwin KA. A Quantitative Investigation of Structure-Function Relationships in a Tendon Fascicle Model [PhD thesis]. University of Michigan; 1998.
2012	Chiravarambath SS. Finite Element Modeling of Articular Cartilage At Different Length Scales [PhD thesis]. University of Minnesota; April 2012.
1997	Arbogast KB. A Characterization of the Anisotropic Mechanical Properties of the Brainstem [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1997.
2002	Gardiner JC. Computational Modeling of Ligament Mechanics [PhD thesis]. University of Utah; May 2002.
1997	Hurschler C. Collagen Matrix in Normal and Healing Ligaments: Microstructural Behavior, Biological Adaptation, and a Structural Mechanical Model [PhD thesis]. University of Wisconsin – Madison; 1997.
1997	Rapoff AJ. Tensile Fatigue of Intervertebral Disc Annulus and a Probabilistic Rule of Mixtures for Elastic Moduli [PhD thesis]. University of Wisconsin – Madison; August 1997.
2017	Fang F. Composition-Dependent Mechanisms of Multiscale Tendon Mechanics [PhD thesis]. St. Louis, MO: Washington University in St. Louis; August 2017.