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Topology Optimization of Non-Linear Elastic Microstructures
(01. Izmir Institute of Technology, 2023) Güven, Murat; Özdemir, İzzet
Topology optimization (TO) is used in a broad spectrum of engineering disciplines ranging from aerospace to civil engineering. A particular sub-field where topology optimization has been very instrumental is the design of microstructures that yield specific macroscopic properties, such as negative Poisson's ratio and negative magnetic permeability. In this thesis, based on a recently proposed method for nonlinear homogenization, a framework for topology optimization of nonlinear elastic microstructures is developed and implemented as a computer program using the Julia programming language. Following a plane strain formulation, a two-dimensional unit cell with periodic boundary conditions is used in combination with a neo-Hookean elastic material response. By exploiting the symmetry properties of the resulting orthotropic microstructure, it is shown that the computational domain can be reduced, and half of the original discretization is sufficient to carry out the optimization task. The obtained topologies from the developed computer program, the linear and nonlinear response comparison, and the computational gain achieved through domain reduction are presented along with the experiments on proof-of-concept type uni-axial tests.
Numerical Modelling of Failure in 3d Quasi-Brittle Unreinforced Structural Components
(Izmir Institute of Technology, 2022) Kaçmaz, Bekir; Özdemir, İzzet
Concrete has been one of the most commonly used modern structural material with quasi-brittle response. Because of its wide usage, numerical prediction of crack path and failure of structural components made of concrete and reinforced concrete has a great importance. To achieve this goal, a wide range of techniques have been introduced by treating fracture differently. In addition, the development of successful element formulations in analysis of 3D structural components has also been an active research topic. Several formulations have been proposed as an alternative to the conventional Lagrangian elements in recent years. In this thesis, localizing implicit gradient damage model and an isogemetric tetrahedral element are combined to investigate failure of 3D quasi-brittle unreinforced structural components. 10 noded B´ezier tetrahedral element is implemented to commercial finite element software Abaqus through user defined element subroutine, UEL. The implementation is validated by using two benchmark problems with nearly incompressible linear elastic and elasto-plastic material behaviors. After validating the implemented element, the formulation is extended such that localizing implicit gradient damage model is embedded within the isogeometric element formulation. Resulting two field formulation is tested on 3D experimental studies that exhibit complex fracture propagation due to combined torsional and bending moments. The sufficiency of the implemented two field formulation is verified by comparing obtained results with the experimental ones in terms of both force versus displacement responses and resulting crack paths.
Crystal Plasticity Inspired Modelling of Fibre Reinforced Composites
(Izmir Institute of Technology, 2022) Dizman, Emir Aybars; Özdemir, İzzet
There is an increasing demand in carbon fibre reinforced (CFR) composites primarily due to their high strength-to-weight ratio. Although their single-ply behaviour is rather brittle (as compared to metals), by reducing the ply thickness and stacking differently oriented plies, brittleness is suppressed, and a ductile behaviour similar to metals is achieved. In this thesis, a recently proposed material model inspired by crystal plasticity is reconsidered and implemented in an implicit finite element solution framework. To this end, a user-defined element is developed in a geometrically non-linear continuum setting and implemented in commercial finite element software Abaqus through UEL (Userdefined ELement) subroutine. The model is validated by analytical solutions derived for simple shear cases and two experiments for different loading cases from the literature. The model is capable of predicting stress-strain response well in cases where matrix plasticity is dominant. Moreover, a parametric study on the cross-ply shear specimen is conducted to investigate the influence of different material parameters. In the last part, the model is extended by a continuum scale damage in the matrix and degradation in elastic material properties. The predictive capabilities of the damage extended model are assessed by re-analyzing the cross-ply shear test.

Master Degree / Yüksek Lisans Tezleri

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