A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.
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January 2013
Research-Article
A Coupled Fiber-Matrix Model Demonstrates Highly Inhomogeneous Microstructural Interactions in Soft Tissues Under Tensile Load
Lijuan Zhang,
Lijuan Zhang
Scientific Computation Research Center
,Rensselaer Polytechnic Institute
,Low Center for Industrial Innovation, CII-4011
,110 8th Street
,Troy, NY 12180
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Spencer P. Lake,
Spencer P. Lake
Department of Biomedical Engineering,
University of Minnesota
,7-105 Nils Hasselmo Hall
,312 Church Street SE
,Minneapolis, MN 55455
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Victor K. Lai,
Victor K. Lai
Department of Chemical Engineering
and Materials Science,
and Materials Science,
University of Minnesota
,421 Washington Ave SE
,Minneapolis, MN 55455
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Catalin R. Picu,
Catalin R. Picu
Scientific Computation Research Center
,Rensselaer Polytechnic Institute
,Low Center for Industrial Innovation
,CII-4011, 110 8th Street
,Troy, NY 12180
;Department of Mechanical
,Aerospace and Nuclear Engineering
,Rensselaer Polytechnic Institute
,Jonsson Engineering Center
,Rm. 2049, 110 8th Street
,Troy, NY 12180
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Victor H. Barocas,
Victor H. Barocas
Department of Biomedical Engineering,
University of Minnesota
,7-105 Nils Hasselmo Hall
,312 Church Street SE
,Minneapolis, MN 55455
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Mark S. Shephard
e-mail: shephard@rpi.edu
Mark S. Shephard
1
Scientific Computation Research Center
,Rensselaer Polytechnic Institute
,Low Center for Industrial Innovation
,CII-4011, 110 8th Street
,Troy, NY 12180
e-mail: shephard@rpi.edu
1Corresponding author.
Search for other works by this author on:
Lijuan Zhang
Scientific Computation Research Center
,Rensselaer Polytechnic Institute
,Low Center for Industrial Innovation, CII-4011
,110 8th Street
,Troy, NY 12180
Spencer P. Lake
Department of Biomedical Engineering,
University of Minnesota
,7-105 Nils Hasselmo Hall
,312 Church Street SE
,Minneapolis, MN 55455
Victor K. Lai
Department of Chemical Engineering
and Materials Science,
and Materials Science,
University of Minnesota
,421 Washington Ave SE
,Minneapolis, MN 55455
Catalin R. Picu
Scientific Computation Research Center
,Rensselaer Polytechnic Institute
,Low Center for Industrial Innovation
,CII-4011, 110 8th Street
,Troy, NY 12180
;Department of Mechanical
,Aerospace and Nuclear Engineering
,Rensselaer Polytechnic Institute
,Jonsson Engineering Center
,Rm. 2049, 110 8th Street
,Troy, NY 12180
Victor H. Barocas
Department of Biomedical Engineering,
University of Minnesota
,7-105 Nils Hasselmo Hall
,312 Church Street SE
,Minneapolis, MN 55455
Mark S. Shephard
Scientific Computation Research Center
,Rensselaer Polytechnic Institute
,Low Center for Industrial Innovation
,CII-4011, 110 8th Street
,Troy, NY 12180
e-mail: shephard@rpi.edu
1Corresponding author.
Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received July 26, 2012; final manuscript received November 16, 2012; accepted manuscript posted December 8, 2012; published online December 27, 2012. Assoc. Editor: James C. Iatridis.
J Biomech Eng. Jan 2013, 135(1): 011008 (9 pages)
Published Online: December 27, 2012
Article history
Received:
July 26, 2012
Revision Received:
November 16, 2012
Accepted:
December 8, 2012
Citation
Zhang, L., Lake, S. P., Lai, V. K., Picu, C. R., Barocas, V. H., and Shephard, M. S. (December 27, 2012). "A Coupled Fiber-Matrix Model Demonstrates Highly Inhomogeneous Microstructural Interactions in Soft Tissues Under Tensile Load." ASME. J Biomech Eng. January 2013; 135(1): 011008. https://doi.org/10.1115/1.4023136
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