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Technical Briefs

An Experimental and Modeling Study of the Viscoelastic Behavior of Collagen Gel

[+] Author and Article Information
Haiyue Li

Department of Mechanical Engineering,
Boston University,
110 Cummington Mall,
Boston, MA 02215

Yanhang Zhang

Associate Professor
Department of Mechanical Engineering,
Department of Biomedical Engineering,
Boston University,
110 Cummington Mall,
Boston, MA 02215
e-mail: yanhang@bu.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received April 16, 2012; final manuscript received March 25, 2013; accepted manuscript posted April 4, 2013; published online April 24, 2013. Assoc. Editor: Stephen Klisch.

J Biomech Eng 135(5), 054501 (Apr 24, 2013) (4 pages) Paper No: BIO-12-1145; doi: 10.1115/1.4024131 History: Received April 16, 2012; Revised March 25, 2013; Accepted April 04, 2013

The macroscopic viscoelastic behavior of collagen gel was studied through relaxation time distribution spectrum obtained from stress relaxation tests and viscoelastic constitutive modeling. Biaxial stress relaxation tests were performed to characterize the viscoelastic behavior of collagen gel crosslinked with Genipin solution. Relaxation time distribution spectrum was obtained from the stress relaxation data by inverse Laplace transform. Peaks at the short (0.3 s–1 s), medium (3 s–90 s), and long relaxation time (>200 s) were observed in the continuous spectrum, which likely correspond to relaxation mechanisms involve fiber, inter-fibril, and fibril sliding. The intensity of the long-term peaks increases with higher initial stress levels indicating the engagement of collagen fibrils at higher levels of tissue strain. We have shown that the stress relaxation behavior can be well simulated using a viscoelastic model with viscous material parameters obtained directly from the relaxation time spectrum. Results from the current study suggest that the relaxation time distribution spectrum is useful in connecting the macro-level viscoelastic behavior of collagen matrices with micro-level structure changes.

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Figures

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Fig. 1

Stress relaxation results of a collagen gel sample at different initial stress levels

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Fig. 2

Relaxation time distribution spectra obtained from biaxial stress relaxation tests of collagen gel under different initial stress levels

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Fig. 3

Effect of relaxation time on relaxation time distribution spectrum for collagen gel at the initial stress level of 25 kPa

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Fig. 4

Simulation results of biaxial tensile—stress relaxation tests of collagen gel at different initial stress levels. Solid lines represent the simulation results. Experiment results were shown in symbols for comparison. Material parameters in the hyperelastic model are C10 = 20 kPa, k1 = 30 MPa, k2 = 1150, γ = 45 deg and κ = 0.333; material parameters in the viscous model are listed in Table 1.

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