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RESEARCH PAPERS

Finite Element Implementation of Anisotropic Quasi-Linear Viscoelasticity Using a Discrete Spectrum Approximation

[+] Author and Article Information
M. A. Puso

Methods Development Group, Lawrence Livermore National Laboratory, Livermore, CA 94550

J. A. Weiss

Orthopedic Biomechanics Institute, The Orthopedic Specialty Hospital, Salt Lake City, UT 84107; Department of Bioengineering, University of Utah, Salt Lake City, UT 84112

J Biomech Eng 120(1), 62-70 (Feb 01, 1998) (9 pages) doi:10.1115/1.2834308 History: Received October 10, 1995; Revised January 03, 1997; Online January 07, 2008

Abstract

The objective of this work was to develop a theoretical and computational framework to apply the finite element method to anisotropic, viscoelastic soft tissues. The quasi-linear viscoelastic (QLV) theory provided the basis for the development. To allow efficient and easy computational implementation, a discrete spectrum approximation was developed for the QLV relaxation function. This approximation provided a graphic means to fit experimental data with an exponential series. A transversely isotropic hyperelastic material model developed for ligaments and tendons was used for the elastic response. The viscoelastic material model was implemented in a general-purpose, nonlinear finite element program. Test problems were analyzed to assess the performance of the discrete spectrum approximation and the accuracy of the finite element implementation. Results indicated that the formulation can reproduce the anisotropy and time-dependent material behavior observed in soft tissues. Application of the formulation to the analysis of the human femur-medial collateral ligament–tibia complex demonstrated the ability of the formulation to analyze large three-dimensional problems in the mechanics of biological joints.

Copyright © 1998 by The American Society of Mechanical Engineers
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