| 1. |
- Abali, Bilen Emek, et al.
(författare)
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A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable
- 2021
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Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - : John Wiley & Sons. - 0044-2267 .- 1521-4001. ; 101:9
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Tidskriftsartikel (refereegranskat)abstract
- Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher-order theories, and especially in damage mechanics, such a generalization is difficult to acquire. We exploit the action formalism in order to obtain the governing equations in generalized damage mechanics for metamaterials. Additionally, by using auxilliary variables, the variational formulation is endowed with the first rate of damage variable that is missing in standard approaches. The presented action formalism with auxilliary variables leads directly to the weak form. We implement a finite element method based approach by using open-source computing platform called FEniCS and solve this weak in order to obtain the deformation and damage numerically. Metamaterials simulations are demonstrated for simple geometries in mixed mode (I and II) as well as in mode III.
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| 2. |
- Abali, Bilen Emek, et al.
(författare)
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Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization
- 2021
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer Science and Business Media LLC. - 0935-1175 .- 1432-0959. ; 33:4, s. 993-1009
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Abali, Bilen Emek
(författare)
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An Introduction to Piezoelectric and Thermoelectric Materials
- 2022
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Ingår i: Handbook of Energy Materials. - Singapore : Springer. - 9789811644801 ; , s. 1-18
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Bokkapitel (refereegranskat)abstract
- Materials may demonstrate electromagnetism and thermomechanics coupling. Although we benefit from this coupling in our modern lives, comprehending this coupling is challenging. We intuitively understand that temperature increase causes an expansion in polymers and alloys. Typical example is a plastic water bottle left in the sun, the expansion is visible by naked eyes. Yet it is more abstract to consider that an electric field may create a deformation or even a temperature change. Electromagnetic fields are more abstract since our senses fail to be sensitive to these physical quantities. There are indeed materials with so-called piezoelectric and pyroelectric properties and we use them for sensors and actuators. More confusingly, there is a thermoelectric effect relating electric current and heat flux. In order to set the ideas correctly, we explain these phenomena and introduce to the abstract world of electromagnetism and thermomechanics coupling. Furthermore, we provide an inside look to realize how different types of thermal and electric coupling phenomena work and how to model such materials adequately.
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| 4. |
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| 5. |
- Abali, Bilen Emek, et al.
(författare)
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Cure Kinetics and Inverse Analysis of Epoxy-Amine Based Adhesive Used for Fastening Systems
- 2021
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Ingår i: Materials. - : MDPI. - 1996-1944. ; 14:14
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Tidskriftsartikel (refereegranskat)abstract
- Thermosetting polymers are used in building materials, for example adhesives in fastening systems. They harden in environmental conditions with a daily temperature depending on the season and location. This curing process takes hours or even days effected by the relatively low ambient temperature necessary for a fast and complete curing. As material properties depend on the degree of cure, its accurate estimation is of paramount interest and the main objective in this work. Thus, we develop an approach for modeling the curing process for epoxy based thermosetting polymers. Specifically, we perform experiments and demonstrate an inverse analysis for determining parameters in the curing model. By using calorimetry measurements and implementing an inverse analysis algorithm by using open-source packages, we obtain 10 material parameters describing the curing process. We present the methodology for two commercial, epoxy based products, where a statistical analysis provides independence of material parameters leading to the conclusion that the material equation is adequately describing the material response.
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| 6. |
- Abali, Bilen Emek
(författare)
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Energy based methods applied in mechanics by using the extended Noether's formalism
- 2023
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Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - : Wiley-VCH Verlagsgesellschaft. - 0044-2267 .- 1521-4001. ; 103:12
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Abali, Bilen Emek, et al.
(författare)
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Experimental investigation for modeling the hardening of thermosetting polymers during curing
- 2021
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Ingår i: Polymer testing. - : Elsevier. - 0142-9418 .- 1873-2348. ; 102
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Tidskriftsartikel (refereegranskat)abstract
- During curing of thermosetting polymers, crosslinking results in hardening or stiffening of the material. In electronics, for example in encapsulating integrated circuits (die bonding), thermosets are fully cured in a controlled environment (under UV-light or within a thermal oven) such that the highest stiffness possible has been achieved. In building materials, specifically in thermosets used in fastening systems (adhesive anchoring), hardening occurs at environmental temperature. Daily temperature variations alter the curing process and possibly lead to a lower stiffness. We demonstrate a modeling approach for the mechanical response dependency on the degree of cure by means of rheometer measurements under a specific temperature profile. Precisely, we perform oscillatory rheometric tests and convert the storage and loss moduli to material parameters depending on the degree of cure. Moreover, the temperature dependency as well as chemical shrinkage have been determined by the same experimental protocol. The presented approach has been applied to a commercially available (epoxy) thermoset used as an adhesive. We have observed a hardening after a gelation point of 0.7 and an adequate fit for mechanical response by polynomial functions of degree four.
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| 8. |
- Abali, Bilen Emek, et al.
(författare)
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Influence of microstructure on size effect for metamaterials applied in composite structures
- 2022
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Ingår i: Mechanics research communications. - : Elsevier. - 0093-6413 .- 1873-3972. ; 122
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Tidskriftsartikel (refereegranskat)abstract
- Microstructure related deviation from elastic response is known as "size-effect."Metamaterials - for example modeled by strain gradient elasticity - capture this effect adequately by means of additional parameters to be determined. We employ a methodology based on asymptotic homogenization in order to obtain metamaterials parameters and then present the influence of these additional parameters by using simulations. By means of the finite element method, we solve metamaterials deformation modeled by the strain gradient elasticity. The implementation is established by open-source packages (FEniCS) for a realistic, composite structure with round and oval inclusions.
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| 9. |
- Abali, Bilen Emek
(författare)
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Modeling magnetohydrodynamics and computation of metal smelting
- 2020
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Ingår i: Energy-based mathematical methods for reactive multiphase flows. - : Berlin Mathematics Research Center MATH. ; , s. 12-13
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Ore is a compound including minerals and is found in Earth’s crust. Ore may contain iron, aluminum, copper or even gold. Extracting these metals are called smelting. For aluminum, smelting is driven by electromagnetism, where conductive ore is a viscous melt with high temperatures and is set in motion effected by electromagnetic forces. Simulation of such an application necessitates not only a computational framework but also the consistent set of partial differential equations. Thermomechanics and electromagnetism are both well-studied independently; nevertheless, their interaction is still puzzling.
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| 10. |
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