Formulation and implementation of a fractional order viscoelastic material model into finite element software and material model parameter identification using in-vivo indenter experiments for soft biological tissues

Demirci, Nagehan
Soft biological tissue material models in the literature are frequently limited to integer order constitutive relations where the order of differentiation of stress and/or strain is integer-valued. However, it has been demonstrated that fractional calculus theory applied in soft tissue material model formulation yields more accurate and reliable soft tissue material models. In this study, firstly a fractional order (where the order of differentation of stress in the constitutive relation is non-integer-valued) linear viscoelastic material model for soft tissues is fitted to force-displacement-time indentation test data and compared with two different integer order linear viscoelastic material models by using MATLAB® optimization toolbox. After the superiority of the fractional order material model compared to integer order material models has been shown, the linear fractional order material model is extended to its nonlinear counterpart in finite deformation regime. The material model developed is assumed to be isotropic and homogeneous. v A user-subroutine is developed for the material model formulated to implement it into the commercial finite element software Msc.Marc 2010. The user-subroutine developed is verified by performing a small strain finite element analysis and comparing the results obtained with linear viscoelastic counterpart of the model on MATLAB®. Finally, the unknown coefficients of the fractional order material model are identified by employing the inverse finite element method. A material parameter set with an amount of accuracy is determined and the material model with the parameters identified is capable of simulating the three different indentation test protocols, i.e., “relaxation”, “creep” and “cyclic loading” protocols with a good accuracy.


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Citation Formats
N. Demirci, “Formulation and implementation of a fractional order viscoelastic material model into finite element software and material model parameter identification using in-vivo indenter experiments for soft biological tissues,” M.S. - Master of Science, Middle East Technical University, 2012.