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Research Papers

Microscale Fiber Network Alignment Affects Macroscale Failure Behavior in Simulated Collagen Tissue Analogs

[+] Author and Article Information
Mohammad F. Hadi

e-mail: hadix004@umn.edu

Victor H. Barocas

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

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 22, 2012; final manuscript received January 7, 2013; accepted manuscript posted January 18, 2013; published online February 7, 2013. Editor: Beth Winkelstein.

J Biomech Eng 135(2), 021026 (Feb 07, 2013) (8 pages) Paper No: BIO-12-1502; doi: 10.1115/1.4023411 History: Received October 22, 2012; Revised January 07, 2013; Accepted January 18, 2013

A tissue's microstructure determines its failure properties at larger length scales, however, the specific relationship between microstructure and macroscopic failure in native and engineered soft tissues (such as capsular ligaments, aortic aneurysms, or vascular grafts) has proven elusive. In this study, variations in the microscale fiber alignment in collagen gel tissue analogs were modeled in order to understand their effects on macroscale damage and failure outcomes. The study employed a multiscale finite-element (FE) model for damage and failure in collagen-based materials. The model relied on microstructural representative volume elements (RVEs) that consisted of stochastically-generated networks of discrete type-I collagen fibers. Fiber alignment was varied within RVEs and between layers of RVEs in a macroscopic FE model of a notched dogbone geometry. The macroscale stretch and the microscale response of fibers for each of the differently aligned cases were compared as the dogbone was uniaxially extended to failure. Networks with greater fiber alignment parallel to the direction of extension failed at smaller strains (with a 6–22% reduction in the Green strain at failure), however, at greater grip forces (a 28–60% increase) than networks with fibers aligned perpendicular to the extension. Alternating layers of crisscrossed network alignments (aligned ±45 deg to the direction of extension) failed at smaller strains but at greater grip forces than those created using one fiber alignment type. In summary, variations in microscale structure via fiber alignment produced different macroscale failure trends. To conclude, these findings may be significant in the realm of tissue engineering and in soft tissue biomechanics.

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Fig. 1

(a) Multiscale damage model consisted of a millimeter-scale finite element continuum (in a notched dogbone geometry) with representative volume elements of micrometer-scale collagen fiber networks of varying alignment at each Gauss point. Fibers were allowed to fail when stretched beyond a critical value. The model contained 624 finite elements, with 8 Gauss points per element and with over 500 fibers in each network. The dogbone was fixed at one grip and extended under displacement control from the opposite grip along axis 1 to a final stretch ratio of 1.5. Microscale network fiber alignments were characterized using the orientation tensor Ω and were subsequently rotated relative to the axis of extension. (b) Isotropic networks had initial orientation tensor values of Ω11 = Ω22 = Ω33 = 0.33. (c) Transverse biaxially aligned networks had orientation values of Ω11 = 0.43, Ω22 = 0.13, and Ω33 = 0.43. (d) Uniaxially aligned networks had orientation values of Ω11 = 0.53, Ω22 = 0.23, and Ω33 = 0.23.

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Fig. 2

(a) Macroscopic grip force varied based on model microscale fiber alignments as dogbone samples were uniaxially stretched to failure. (b) The corresponding mechanical work for these deformations also varied by the alignment case. (c)–(e) At the same grip displacement of 7.0 mm, differences in the stress and deformation for each case were apparent.

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Fig. 3

(a) The mean fiber stretch, (b) the mean percentage of failed fibers, and (c) the mean fiber orientation parameter Ω11 varied over the macroscale sample stretch for each fiber alignment case. (d) Fibers were analyzed from a region of notch-adjacent elements. The same region was used to generate the plots in Figs. 7 and 8.

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Fig. 4

A single microscale network in the model experienced distinct fiber stretches and failure at varying grip displacements for each alignment case. The network was selected from a notch-adjacent element.

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Fig. 5

Contour plots of the macroscale (a) peak grip force, (b) displacement at peak grip force, and (c) work were interpolated as functions of the initial network fiber orientation parameter Ω11 and the network rotation. The largest forces occurred when fibers were aligned parallel to extension and the largest prefailure strains when fibers were aligned perpendicular to extension.

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Fig. 6

(a) Macroscopic grip force varied based on differing microscale composite or uniform fiber alignments as dogbone samples were uniaxially stretched to failure. (b) The corresponding mechanical work for these deformations also varied based on the composite or uniform fiber alignment type. (c)–(e) At the same grip displacement of 7.0 mm, differences in the macroscopic Green strain were apparent between the (c) all +45 deg rotated aligned networks, (d) layered ±45 deg networks, and (e) all −45 deg network cases. To illustrate the propagation of failure along the direction of fiber alignment for the (f) all +45 deg and (g) all −45 deg cases, elements with the greatest fiber losses (approximately the top 10%) were removed from plots of notch strains at a grip displacement of 10.8 mm.

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Fig. 7

(a) The mean fiber stretch, (b) the mean percentage of failed fibers, and (c) the mean fiber orientation parameter Ω11 varied over the macroscale sample stretch for each composite or uniform fiber alignment case. Fibers were analyzed from the notch-adjacent elements depicted in Fig. 3.

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Fig. 8

Fiber stretch distributions varied for the (a)–(c) merged, and (d)–(f) rotated aligned network cases at equivalent grip displacements, but were similar at equal grip forces. Fibers were analyzed from the notch-adjacent elements depicted in Fig. 3.

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