Affiliations: [a] Department of Mechanical Engineering, Boston University, Boston, MA, USA | [b] Department of Biomedical Engineering, Boston University, Boston MA, USA
Correspondence:
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Address for correspondence: Yanhang Zhang, Associate Professor, Department of Mechanical Engineering, Boston University, 110 Cummington Mall, Boston, MA 02215, USA. Tel.: +1 617 358 4406; Fax: +1 617 353 5866; E-mail: [email protected].
Abstract: BACKGROUND: Viscoelastic materials contain a continuous spectrum of relaxation time constants that cannot be measured directly from experiments. To model the viscoelastic behavior, discrete Generalized Maxwell model is usually chosen phenomenologically from direct fitting. OBJECTIVE: In the present study, a theoretical framework was developed to determine the continuous spectrum of relaxation time constants, and then applied to study the dynamic rheological behavior of collagen gel using a parallel plate rheometer. METHODS: Frequency sweep tests were performed to determine the storage and loss modulus of collagen gel. To obtain the continuous relaxation spectrum, Tikhonov regularization method was employed to solve the Fredholm integral equations. A Finite Element Model (FEM) was created to simulate the rheological measurement with viscous material parameters obtained from both direct fitting and continuous spectrum. RESULTS: Discrete spectrum obtained by direct fitting method is not unique and highly depends on the specified fitting criteria. Continuous spectrum obtained by Tikhonov regularization effectively eliminates the possibility of getting nonunique solutions. The storage and loss modulus calculated from FEM compared well with the experimental results. CONCLUSIONS: Continuous relaxation spectrum can be determined based on dynamic rheological shear measurements, and incorporated into FEM to study the behavior of viscoelastic materials.
Keywords: Relaxation time constants, continuous spectrum, viscoelastic behavior, oscillatory shear measurements, Tikhonov regularization, Prony series, finite element modeling
DOI: 10.3233/BIR-14032
Journal: Biorheology, vol. 51, no. 6, pp. 369-380, 2014
