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Research Papers

Multiscale Model Predicts Tissue-Level Failure From Collagen Fiber-Level Damage

[+] Author and Article Information
Mohammad F. Hadi

 Department of Biomedical Engineering, University of Minnesota, 7-105 Hasselmo Hall, 312 Church Street SE, Minneapolis, MN 55455hadix004@umn.edu

Edward A. Sander

 Department of Biomedical Engineering, University of Iowa, 1402 Seamans Center, Iowa City, IA 52242edward-sander@uiowa.edu

Victor H. Barocas1

 Department of Biomedical Engineering, University of Minnesota, 7-105 Hasselmo Hall, 312 Church Street SE, Minneapolis, MN 55455baroc001@umn.edu

1

Corresponding author.

J Biomech Eng 134(9), 091005 (Aug 27, 2012) (10 pages) doi:10.1115/1.4007097 History: Received January 31, 2012; Revised June 09, 2012; Posted July 06, 2012; Published August 27, 2012; Online August 27, 2012

Excessive tissue-level forces communicated to the microstructure and extracellular matrix of soft tissues can lead to damage and failure through poorly understood physical processes that are multiscale in nature. In this work, we propose a multiscale mechanical model for the failure of collagenous soft tissues that incorporates spatial heterogeneity in the microstructure and links the failure of discrete collagen fibers to the material response of the tissue. The model, which is based on experimental failure data derived from different collagen gel geometries, was able to predict the mechanical response and failure of type I collagen gels, and it demonstrated that a fiber-based rule (at the micrometer scale) for discrete failure can strongly shape the macroscale failure response of the gel (at the millimeter scale). The model may be a useful tool in predicting the macroscale failure conditions for soft tissues and engineered tissue analogs. In addition, the multiscale model provides a framework for the study of failure in complex fiber-based mechanical systems in general.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 2

Dogbone sample: comparison of the grip force against the total sample stretch (λ) for the experiment (solid line ends at first sample failure) and model (dashed line). Error bars represent the 95% confidence interval for the experimental mean (n = 5). The quadrant defined by the dotted lines represents the 95% confidence interval for the peak experimental force and the 95% confidence interval for the experimental strain at peak force. The center of the quadrant is marked with a red circle. The macroscopic stress in the model for select points (A–D) along the graph is depicted. Two fiber networks illustrating regional differences in the failure mechanics are also shown and shaded to indicate fiber stretch.

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Figure 3

Percentage of intact fibers per element varies at different grip-to-grip sample stretches (λ) for the model dogbone geometry. Percentage of intact fibers were averaged over all RVE networks within each element.

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Figure 4

Elements with nonpercolating networks frame areas of damage for the modeled sample at different grip-to-grip stretches (λ) for the dogbone geometry. A percolating RVE was defined as a network that contained a connected fiber segment that spanned both RVE faces normal to the axis of loading.

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Figure 5

Comparison of broken fiber percentages in elements with and without percolating RVE networks at different grip-to-grip stretches (λ) for the dogbone geometry

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Figure 6

The peak max principal Cauchy stress and the peak max principal Green strain for the dogbone geometry plotted over the deformed finite element mesh at the point of greatest grip force in the model

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Figure 7

Element stretch (along the axis of extension) plotted over the deformed mesh for the model dogbone geometry. The element stretch is also represented via corresponding histograms at a given sample stretch (λ) for the dogbone geometry.

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Figure 8

Notched sample: comparison of the grip force against the total sample stretch (λ) for the experiment (solid line ends at first sample failure) and model prediction (dashed line is the mean result and gray area represents the 95% confidence interval for n = 3 independent simulations). Error bars represent the 95% confidence interval for the experimental mean (n = 5). The quadrant defined by the dotted lines represents the 95% confidence interval for the peak experimental force and the 95% confidence interval for the experimental strain at peak force. The center of the quadrant is marked with a red circle. The macroscopic stress in the model for select points (A–D) along the graph is depicted. Two fiber networks illustrating regional differences in the failure mechanics are also shown and shaded to indicate fiber stretch.

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Figure 9

Percentage of intact fibers per element varies at different grip-to-grip sample stretches (λ) for the notched geometry model. Percentage of intact fibers were averaged over all RVE networks within each element.

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Figure 10

Elements with nonpercolating networks frame areas of damage for the modeled sample at different grip-to-grip stretches (λ) for the notched geometry. A percolating RVE was defined as a network that contained a connected fiber segment that spanned both RVE faces normal to the axis of loading.

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Figure 11

Comparison of broken fiber percentages in elements with and without percolating RVE networks at different notched model grip-to-grip stretches

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Figure 12

Comparison of the model and experiment for the Green strain and collagen fiber alignment (alignment vectors normalized by maximum strength of alignment) at the point of peak grip force for the deformed notch geometry for two independent experimental samples

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Figure 1

Overview of the damage model used in the multiscale simulations. The dogbone domain, which exists on the scale of millimeters, is represented with a 3D finite-element mesh. Within each hexahedral element are eight microscopic fiber networks (RVEs) centered at the Gauss points that govern the stress-strain response of the element. As the FE domain stretches, interconnected fibers in the networks stretch and reorganize to satisfy force equilibrium. Fibers that exceed the critical fiber stretch ratio are effectively removed by reducing their modulus by 10 orders of magnitude.

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