A NEW TIME DOMAIN BOUNDARY ELEMENT FORMULATION FOR RATE-DEPENDENT INELASTICITY WITH APPLICATION TO HOMOGENIZATION

Date

2023-8-21

Author

Akay, Ahmet Arda

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Effective determination of the homogenized properties of a heterogeneous medium is crucial in multi-scale analysis. The analysis of a heterogeneous medium, such as polymer nano-composites, using the conventional finite element method requires finite element meshes with much smaller element sizes than the dimensions of nano-reinforcements. The finite element analysis of the macroscopic model with such a mesh would be computationally very expensive. For this purpose, in this thesis study, two- and three-dimensional applications of the boundary element method have been discussed. The implementation of linear elasticity to BEM has been examined with the introduction of homogenization techniques using uniform tractions, linear displacement, and periodic displacement boundary conditions. The accuracy of the developed linear elasticity approach with homogenization has been demonstrated through various numerical examples from the literature. Moreover, in mostly heterogeneous Representative Volume Elements (RVEs) with significant differences in material properties between mediums, a third face, often referred to as an interface (or interphase), is observed. The modeling of these regions with BEM is also discussed in this study. Viscoelasticity modeling is first introduced by adapting the Dynamic Correspondence Principle to the developed linear elastic BEM methodology. A comparison study of modeling viscoelasticity with this approach is conducted with FEM and examples from the literature. Domain integration appears in many engineering problems, making effective determination of the domain integral crucial. In conventional Boundary Element Method (BEM) analysis, domain integration is mostly done by using a finite number of internal cells and having BEM solutions in each cell to represent overall behavior. In this thesis study, mesh-free domain integration methods are introduced to developed BEM. The methodology of the Cartesian Transformation Method (CTM) with Moving Least Squares (MLS) and Radial Point Integration (RPIM) interpolation methods are discussed. The developed approach is first validated with a parameter study on mathematical examples. Subsequently, applications on physical engineering problems such as elasticity with body forces, thermoelasticity, and steady-state and transient heat conduction are conducted. Moreover, the developed BEM approach is extended to handle inelastic problems, wherein a new non-iterative rate-dependent inelastic formulation is developed and implemented in BEM. In contrast to the scarce existing rate formulations of inelasticity developed within BEM, the proposed non-iterative formulation exploits the hybrid semi-implicit update of strain-like kinematic history variables. The excellent performance of the proposed approach is demonstrated through comparisons with corresponding analytical and fully implicit finite element results for various boundary-value problems of linear and non-linear viscoelasticity. The limitations of the developed approach are also discussed in its applications to viscoplasticity.

Subject Keywords

Boundary element method, Homogenization, Meshless domain integration, Cartesian transformation method, Radial point interpolation method, Elasticity, Linear viscoelasticity, Non-linear viscoelasticity, Non-linear elastoplasticity, Semi-implicit time integration

URI

https://hdl.handle.net/11511/105339

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Graduate School of Natural and Applied Sciences, Thesis