arXiv subjects

Bilen Emek Abali

Publications and source records attributed to Bilen Emek Abali.

7 recordsLinked to original sources

arXiv2025

Deposition Rates in Thermal Laser Epitaxy: Simulation and Experiment

The modeling of deposition rates in Thermal Laser Epitaxy (TLE) is essential for the accurate prediction of the evaporation process and for improved dynamic process control. We demonstrate excellent agreement between experimental data and a model based on a finite element simulation that describes the temperature distribution of an elemental source when irradiated with continuous wave laser radiation. The simulation strongly depends on the thermophysical constants of the material, data of which is lacking for many elements. Effective values for the parameters may be determined with precision by means of an unambiguous reference provided by the melting point of the material, which is directly observed during the experiments. TLE may therefore be used to study the high temperature thermophysical and optical properties of the elements.

cs.CE↗

arXiv2023

Energy based methods applied in mechanics by using the extended Noether's formalism

Physical systems are modeled by field equations; these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former are axiomatically given and the latter are thermodynamically derived. This approach is useful in thermomechanics and electromagnetism, yet challenges arise once we apply it in damage mechanics for generalized continua. For deriving governing equations, an alternative method is based on a variational framework known as the extended Noether's formalism. Its formal introduction relies on mathematical concepts limiting its use in applied mechanics as a field theory. In this work, we demonstrate the power of extended Noether's formalism by using tensor algebra and usual continuum mechanics nomenclature. We demonstrate derivation of field equations in damage mechanics for generalized continua, specifically in the case of strain gradient elasticity.

physics.class-ph↗

arXiv2022

Determining parameters in generalized thermomechanics for metamaterials by means of asymptotic homogenization

Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized thermomechanics. Strain gradient theory is employed as a higher-order theory with thermodynamics modeled as a first-order theory. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this ``simplest'' model in generalized thermomechanics causes dozens of parameters to be determined. We develop a computational model by using a given microstructure, modeled as a periodic domain, and numerically calculate all parameters by means of asymptotic homogenization. Finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Some example with symmetric and random distribution of voids in a model problem verifies the method and provides an example at which length-scale we need to consider generalized thermoeleasticity in composite materials.

cs.CE↗

arXiv2022

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

A theoretical-computational framework is proposed for predicting the failure behavior of two anisotropic brittle materials, namely, single crystal magnesium and boron carbide. Constitutive equations are derived, in both small and large deformations, by using thermodynamics in order to establish a fully coupled and transient twin and crack system. To study the common deformation mechanisms (e.g., twinning and fracture), which can be caused by extreme mechanical loading, a monolithically-solved Ginzburg--Landau-based phase-field theory coupled with the mechanical equilibrium equation is implemented in a finite element simulation framework for the following problems: (i) twin evolution in two-dimensional single crystal magnesium and boron carbide under simple shear deformation; (ii) crack-induced twinning for magnesium under pure mode I and mode II loading; and (iii) study of fracture in homogeneous single crystal boron carbide under biaxial compressive loading. The results are verified by a steady-state phase-field approach and validated by available experimental data in the literature. The success of this computational method relies on using two distinct phase-field (order) parameters related to fracture and twinning. A finite element method-based code is developed within the Python-based open-source platform FEniCS. We make the code publicly available and the developed algorithm may be extended for the study of phase transformations under dynamic loading or thermally-activated mechanisms, where the competition between various deformation mechanisms is accounted for within the current comprehensive model approach.

cond-mat.mtrl-sci↗

arXiv2021

Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange.

cs.CE↗

arXiv2020

Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

Metamaterials exhibit materials response deviation from conventional elasticity. This phenomenon is captured by the generalized elasticity as a result of extending the theory at the expense of introducing additional parameters. These parameters are linked to internal length scales. Describing on a macroscopic level a material possessing a substructure at a microscopic length scale calls for introducing additional constitutive parameters. Therefore, in principle, an asymptotic homogenization is feasible to determine these parameters given an accurate knowledge on the substructure. Especially in additive manufacturing, known under the infill ratio, topology optimization introduces a substructure leading to higher order terms in mechanical response. Hence, weight reduction creates a metamaterial with an accurately known substructure. Herein, we develop a computational scheme using both scales for numerically identifying metamaterials parameters. As a specific example we apply it on a honeycomb substructure and discuss the infill ratio. Such a computational approach is applicable to a wide class substructures and makes use of open-source codes; we make it publicly available for a transparent scientific exchange.

cs.CE↗

arXiv2018

An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any process---are still missing. Either a very high computational cost is necessary for a direct numerical solution (DNS) or some limiting procedure is used by adding artificial dissipation to the system. These stabilization methods are useful; however, they are often applied relative to the element size such that a local monotonous convergence is challenging to acquire. We need a computational strategy for solving viscous fluid flow using solely the balance equations. In this work, we present a general procedure solving fluid mechanics problems without use of any stabilization or splitting schemes. Hence, its generalization to multiphysics applications is straightforward. We discuss emerging numerical problems and present the methodology rigorously. Implementation is achieved by using open-source packages and the accuracy as well as the robustness is demonstrated by comparing results to the closed-form solutions and also by solving well-known benchmarking problems.

cs.CE↗