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Title:Simulations of deformations and fracture of biological materials
Author(s):Idkaidek, Ashraf
Director of Research:Jasiuk, Iwona
Doctoral Committee Chair(s):Jasiuk, Iwona
Doctoral Committee Member(s):Wagoner Johnson, Amy J.; Elbanna, Ahmed; Kersh, Mariana
Department / Program:Mechanical Sci & Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Finite element method
Extended finite element method
Generalized finite element method
Crack growth
Numerical simulations
Reference Point Indentation
Cortical bone
Bone strength
Bone fracture
Computational surgery
Nonlinear constitutive model
Mathematical models
Abstract:We study deformations and fracture of soft and mineralized biological materials by using a finite element method. More specifically, we predict the deformation of a liver due to the pressure of a surgical tool. Secondly, we model the deformation of a cortical bone due to microindentation. Thirdly, we model the fracture of cortical bone under a uniaxial tensile load by using an extended finite element method. Finally, we evaluate how an arrangement of curved mineral lamellae in bone, at a nanoscale, influences bone’s bending and torsional stiffnesses. First, to advance robotic surgery, we evaluate different numerical algorithms and techniques to simulate the deformation of soft tissue under a surgical tool pressure. We generate a three-dimensional finite element model of a porcine liver which was scanned using Magnetic Resonance Imaging. A nonlinear constitutive law is employed to capture large tissue deformations due to the surgical knife pressure. Effects of implicit versus explicit analyses, element type, and mesh density on computation time are studied. We find that explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents. Bone fracture is a worldwide costly problem. There are various techniques to predict a risk of bone fracture. Clinically, the quality of bone is assessed by measuring bone mineral density and possibly using other imaging methods. These noninvasive techniques provide information on the bone composition and structure, but they do not capture directly mechanical properties of bone. Reference point indentation technique was invented to test bone strength and fracture resistance in vivo by microindentation. However, there is still limited knowledge about the physical interpretation of the indentation instruments’ outputs, and how the measured bone microstructural properties affect the whole bone strength and fracture. There are two types of reference point indentation instruments: Biodent and Osteoprobe (ActiveLife, Santa Barbara, CA). The first instrument involves a cyclic quasi-static indentation and has multiple outputs, while the second involves one loading cycle and has one unique output. This thesis links the reference point indentation instruments’ outputs to actual cortical bone properties by numerically simulating reference point indentations on the bone, using an axisymmetric finite element model with isotropic viscoelastic-plastic constitutive law with continuum damage. The computational models are validated by correlating to experimental results of reference point indentation on bone. Reference point indentation instruments’ outputs relations to bone mechanical properties (Young’s modulus, compressive yield stress, and damage and viscosity constants) and the experimental factors (indenter tip radius, friction coefficient between the indenter and the bone, number of loading cycles, and maximum indentation load) have been developed. We find that the reference point indentation instruments’ outputs are sensitive to the mechanical properties of bone and the experimental factors. Next, this thesis predicts bone’s behavior under external loads by simulating the bone fracture due to remote tensile traction. Fracture analysis of a cortical bone sample from a tibia of a 70 years-old human male donor is conducted computationally using the extended finite element method. The cortical bone microstructure is represented by several randomly arranged osteons. The accuracy of results is investigated by comparing a linear elastic fracture mechanics approach with a cohesive segment approach and varying the finite element model mesh density, element type, damage evolution, and boundary conditions. Microstructural features of cortical bone are assumed to be linear elastic and isotropic. We find that the accuracy of results is influenced by the finite element model mesh density, simulation increment size, element type, and the fracture approach type. Using a relatively fine mesh or small simulation increment size gives inaccurate results compared to using an optimized mesh density and simulation increment size. Also, the mechanical properties of cortical bone phases influence the crack propagation path and speed. Finally, this thesis evaluates the effect of the curved mineral lamellae arrangement in bone, at the nanoscale, on bone’s bending and torsional stiffnesses using three-dimensional finite element models and linear elastic and isotropic material properties. We find that multi-scale circular patterns of curved mineral lamellae, observed by transmission electron microscopy, increase both the bending and torsional stiffness of bone by 7% and 24%, respectively. This research illustrates how computational mechanics can contribute to a better understanding of the deformations and fracture of biological tissues such as liver and bone.
Issue Date:2019-01-02
Rights Information:Copyright 2018 ASHRAF IDKAIDEK
Date Available in IDEALS:2019-08-23
Date Deposited:2019-05

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