| 1. |
- Abali, Bilen Emek, et al.
(author)
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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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In: Continuum Mechanics and Thermodynamics. - : Springer Science and Business Media LLC. - 0935-1175 .- 1432-0959. ; 33:4, s. 993-1009
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Journal article (peer-reviewed)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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| 2. |
- Agnelli, Filippo, et al.
(author)
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Design and testing of 3D-printed micro-architectured polymer materials exhibiting a negative Poisson’s ratio
- 2020
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In: Continuum Mechanics and Thermodynamics. - : Springer-Verlag New York. - 0935-1175 .- 1432-0959. ; 32:2, s. 433-449
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Journal article (peer-reviewed)abstract
- This work proposes the complete design cycle for several auxetic materials where the cycle consists of three steps (i) the design of the micro-architecture, (ii) the manufacturing of the material and (iii) the testing of the material. We use topology optimization via a level-set method and asymptotic homogenization to obtain periodic micro-architectured materials with a prescribed effective elasticity tensor and Poisson’s ratio. The space of admissible micro-architectural shapes that carries orthotropic material symmetry allows to attain shapes with an effective Poisson’s ratio below −1−1. Moreover, the specimens were manufactured using a commercial stereolithography Ember printer and are mechanically tested. The observed displacement and strain fields during tensile testing obtained by digital image correlation match the predictions from the finite element simulations and demonstrate the efficiency of the design cycle.
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| 3. |
- Argatov, Ivan, et al.
(author)
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Analysis of the minimal model for the enthalpy relaxation and recovery in glass transition : application to constant-rate differential scanning calorimetry
- 2021
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In: Continuum Mechanics and Thermodynamics. - : Springer. - 0935-1175 .- 1432-0959. ; 33, s. 107-123
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Journal article (peer-reviewed)abstract
- The so-called minimal model is formulated for describing the enthalpy relaxation and recovery in glass transition. The model is based on the Arrhenius law for the enthalpy relaxation, which uses two-dimensional parameters, namely the activation energy and the so-called pre-factor (relaxation time at relatively high temperature). A numerically effective exact analytical solution is obtained for the case of constant-rate differential scanning calorimetry. The developed model is analyzed according to the logic of the model itself without introducing additional simplifying assumptions of thermodynamic nature. For typical range of the model parameters, the resulting differential equation contains a large parameter, which offers an opportunity for the application of asymptotic and approximate techniques. A number of simple approximations have been provided for some thermodynamic quantities of interest.
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| 4. |
- Kari, Leif
(author)
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Effective visco-elastic models of tough, doubly cross-linked, single-network polyvinyl alcohol (PVA) hydrogels : Additively separable fractional derivative-based models for chemical and physical cross-links
- 2020
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In: Continuum Mechanics and Thermodynamics. - : Springer. - 0935-1175 .- 1432-0959.
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Journal article (peer-reviewed)abstract
- An effective fractional derivative-based visco-elastic model of tough, doubly cross-linked, single-network polyvinyl alcohol (PVA) hydrogels, embodying both chemical and physical cross-links, is developed using a Mittag–Leffler relaxation function of order 1/2 while applying only three material parameters that are physically quantifiable, namely frequency for maximum loss modulus, equilibrium elastic modulus and relaxation intensity. The resulting 3-parameter shear modulus model is possible to additively split into chemical and physical parts; the split being the study focus. Physical explanations of the visco-elastic low-, mid- and high-frequency range properties, and their transitions between the frequency ranges, are given mainly in terms of the permanent chemical cross-links and the distinct adhesion–deadhesion processes of the transient physical cross-links. The latter are running from an associated Rouse mode low-frequency behaviour through a maximum adhesion–deadhesion dissipation and to an elastic, fully active cross-link high-frequency behaviour, while the former are displaying essentially an elastic, fully active cross-link behaviour throughout the frequency range. The developed model covers the full frequency range while matching measurements results remarkably well. Furthermore, the model is refined into a 4-parameter model by additively including an Abel relaxation function of order 1/2 to take into account the superimposed Rouse-type behaviour found in the measurements of the chemical cross-links in addition to their dominating elastic response, with the fourth parameter being a chemical Rouse stress intensity factor. The simple, effective visco-elastic models are suitable in predicting the mechanical properties of tough, doubly cross-linked, single-network PVA hydrogels with application potentials in tissue and noise abatement engineering.
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| 5. |
- Laudato, Marco, et al.
(author)
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Analysis of the contact critical pressure of collapsible tubes for biomedical applications
- 2023
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In: Continuum Mechanics and Thermodynamics. - : Springer Nature. - 0935-1175 .- 1432-0959. ; 36:1, s. 217-228
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Journal article (peer-reviewed)abstract
- The onset of self-excited oscillations in airways and blood vessels is a common phenomenon in the human body, connected to both normal and pathological conditions. A recent experimental investigation has shown that the onset of self-excited oscillations happens for values of the intramural pressure close to the contact critical pressure. The goal of this work is to analyse the dependence of the contact critical pressure on the vessel’s geometric parameters. The methodology is based on the implementation of an experimentally validated computational model of a collapsible tube. The results confirm the correlation between the contact critical pressure and the onset of self-excited oscillations in collapsible tubes. Moreover, a set of general equations to compute the contact critical pressure and the corresponding areas of collapsible tubes with arbitrary geometries has been derived.
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| 6. |
- Liu, Yiming, et al.
(author)
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Plate capacitor problem as a benchmark case for verifying the finite element implementation
- 2023
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In: Continuum Mechanics and Thermodynamics. - : Springer Nature. - 0935-1175 .- 1432-0959. ; 35:1, s. 245-265
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Journal article (peer-reviewed)abstract
- In this work, parallel plate capacitors are numerically simulated by solving weak forms within the framework of the finite element method. Two different domains are studied. We study the infinite parallel plate capacitor problem and verify the implementation by deriving analytical solutions with a single layer and multiple layers between two plates. Furthermore, we study the finite parallel plate capacitor problem and verify it by Love’s potential equation and Xiang’s capacitance equation. Moreover, the fringing effect is considered and extended to problems with multiple dielectric layers, such a solution is not possible by means of the existing analytical solutions. Besides, we realize the possibility of choosing different boundary conditions (electric potential boundary conditions and charge density boundary conditions) by changing the weak form. Finally, a transient solution that includes dielectric loss and calculates the quality factor of a capacitor is presented, which may be used in capacitor design. Convergence and consistency of results are demonstrated by comparing the results between analytical and numerical solutions and also the results from different boundary conditions.
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| 7. |
- Molavitabrizi, Danial, et al.
(author)
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Second-order homogenization of 3-D lattice materials towards strain gradient media : numerical modelling and experimental verification
- 2023
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In: Continuum Mechanics and Thermodynamics. - : Springer Nature. - 0935-1175 .- 1432-0959.
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Journal article (peer-reviewed)abstract
- The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being the inclusion) with complex cell topologies. For that, acomputational homogenization scheme based on Mindlin (type II) strain gradient elasticity theory is developed here. The model is based on variational formulation with periodic boundary conditions, implemented in the open-source software FreeFEM to fully characterize the effective classical elastic, coupling, and gradient elastic matrices in lattice materials. Rigorous mathematical derivations based on equilibrium equations and Hill-Mandel lemma are provided, resulting in the introduction of macroscopic body forces and modifications in gradient elasticity tensors which eliminate the spurious gradient effects in the homogeneousmaterial. The obtained homogenized classical and strain gradient elasticity matrices are positive definite, leading to a positive macroscopic strain energy density value—an importantcriterion that sometimes is overlooked. The model is employed to study the size effects in 2-D square and 3-D cubic lattice materials. For the case of 3-D cubic material, the model is verified using full-field simulations, isogeometric analysis, and experimental three-point bending tests.The results of computational homogenization scheme implemented through isogeometric simulations show a good agreement with full-field simulations and mechanical tests. The developed model is generic and can be used to derive the effective second-grade continuum forany 3-D architectured material with arbitrary geometry. However, the identification of the proper type of generalized continua for the mechanical analysis of different cell architectures is yet an open question.
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| 8. |
- Vazic, Bozo, et al.
(author)
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Generalized thermo-mechanical framework for heterogeneous materials through asymptotic homogenization
- 2023
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In: Continuum Mechanics and Thermodynamics. - : Springer Nature. - 0935-1175 .- 1432-0959. ; 35, s. 159-181
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Journal article (peer-reviewed)abstract
- A fundamental understanding of the interaction between microstructure and underlying physical mechanisms is essential, especially for developing more accurate multi-physics models for heterogeneous materials. Effects of microstructure on the material response at the macroscale are modeled by using the generalized thermomechanics. In this study, strain gradient theory is employed as a higher-order theory on the macroscale with thermodynamics modeled as a first-order theory on the microscale. Hence, energy depends only on the temperature such that we circumvent an extension of Fourier’s law and analyze the “simplest” thermo-mechanical model in strain gradient elasticity. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this “simplest” model in generalized thermomechanics creates dozens of parameters to be determined. We develop a thermo-mechanical framework, in which microstructure is modeled as a periodic structure and through asymptotic homogenization approach, higher-order parameters at macroscopic scale are calculated. To illustrate the importance of higher-order parameters in overall thermo-mechanical response of a heterogeneous materials, finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Verification example of a bulk system and several case studies of porous structures demonstrate how such numerical framework can be beneficial in the design of materials with tailored microstructures.
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