Date

2023-1-17

Author

Altun, Cem

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Computational biomechanics is an active research area, not only to understand the mechanisms behind the behaviours of biological tissues but also to develop medical techniques for surgeries, rehabilitations, and diseases. The thesis mainly composed of two parts namely, growth-induced instabilities and dispersion-type anisotropic viscoelasticity for soft biological tissues. In the first part of the thesis, planar growth-induced instabilities for a three-dimensional bilayer-type confined tissue is examined. Firstly, a five-field Hu-Washizu type mixed variational formulation for incompressible and inextensible limits is extended for finite growth theory that captures the primary and secondary growth-induced instabilities for anisotropic soft biological tissues. A numerical example is solved by implementing T2P0F0 element on the automated differential equation solver, FEniCS. The influence of fiber stiffness on the critical growth parameter, primary and secondary buckling is investigated. The numerical outcomes of this study will help to understand the fiber stiffness effect on the buckling and post-buckling behavior of bilayer-typed anisotropic soft biological tissues. In the second part of thesis, we proposed five novel formulations for angular-integration based dispersion-type anisotropic viscoelastic constitutive models at finite strains where the formulations use bivariate and planar von Mises density distribution functions. Then, a numerical model validation is conducted for the human myocardium. The proposed models use the generalized structure tensor for the baseline hyperelastic mechanical response to reflect the dispersion characteristics along the fiber and sheet directions of the myocardium. A quadratic free-energy function is defined for the viscous response that is mainly composed of logarithmic elastic and microviscous strains. The density distribution function is introduced in the constitutive equations by defining two types of formulations, namely, local-based and global-based. In the local-based formulations, we use the density distribution as a part of the micro-viscous free-energy functions. In the global-based formulations, the density distribution function enters the equations during the continuous averaging of the stress and tangent moduli expressions. For the five of proposed models, the overstress response has been identified through either nonlinear or linear evolution laws in each orientation direction by using numerical integration, either over the unit micro-sphere or over the unit planar circle. Then, the fitting performances of the proposed models are examined and compared with the cyclic triaxial shear and triaxial shear relaxation experiments of human passive myocardium from the literature. All models are compared, and their pros and cons are discussed. While local-based formulations suffer from the violation of the normalization condition during the averaging integral stage when the nonlinear evolution is used, the global-based formulations are stable and provide high accuracy for both linear and nonlinear evolutions with a sufficient number of integration points. The proposed formulations provide a histological-based flexible calibration capability for any type of anisotropic soft biological tissue that exhibits either elastic or viscous response.

Subject Keywords

anisotropic viscoelasticity, myocardium, fiber dispersion, growth-induced instability

URI

https://hdl.handle.net/11511/101978

Collections

Graduate School of Natural and Applied Sciences, Thesis