| 1. |
- 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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| 2. |
- Agnelli, Filippo, et al.
(författare)
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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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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer-Verlag New York. - 0935-1175 .- 1432-0959. ; 32:2, s. 433-449
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Tidskriftsartikel (refereegranskat)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.
(författare)
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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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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer. - 0935-1175 .- 1432-0959. ; 33, s. 107-123
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Tidskriftsartikel (refereegranskat)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. |
- Argatov, Ivan, et al.
(författare)
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How to define the storage and loss moduli for a rheologically nonlinear material?
- 2017
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer. - 0935-1175 .- 1432-0959. ; 29:6, s. 1375-1387
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Tidskriftsartikel (refereegranskat)abstract
- A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform and the stress decomposition approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous–Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given.
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| 5. |
- dell'Isola, Francesco, et al.
(författare)
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Advances in pantographic structures : design, manufacturing, models, experiments and image analyses
- 2019
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer. - 0935-1175 .- 1432-0959. ; 31:4, s. 1231-1282
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Tidskriftsartikel (refereegranskat)abstract
- In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about the next generation of research in this field. We present an organic scheme of the whole process of design, fabrication, experiments, models and image analyses.
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| 6. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Two-scale modelling of micromorphic continua
- 2009
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer Science and Business Media LLC. - 0935-1175 .- 1432-0959. ; 21:4, s. 297-315
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Tidskriftsartikel (refereegranskat)abstract
- According to their peculiar mechanical properties, the description of cellular materials is of high interest. Modelling aspects to be considered are, e.g. pronounced size depending boundary layer effects as well as a deformation-driven evolution of anisotropy or porosity. In the present contribution, we pay special attention to the description of size-dependent microtopological effects on the one hand. On the other hand, we focus on the relevance of extended continuum theories describing the local deformation state of microstructured materials. We, therefore, introduce a homogenization scheme for two-scale problems replacing a heterogeneous Cauchy continuum on the microscale by a homogeneous effective micromorphic continuum on the macroscale. The transitions between both scales are obtained by appropriate projection and homogenization rules which have to be derived, on the one hand, by kinematic assumptions, i.e. the minimization of the macroscopic displacement field, and, on the other hand, by energetic considerations, i.e. the evaluation of an extended Hill–Mandel condition.
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| 7. |
- Kari, Leif
(författare)
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Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range : Part 2-waveguide solution
- 2017
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Ingår i: Continuum Mechanics and Thermodynamics. - : SPRINGER. - 0935-1175 .- 1432-0959. ; 29:5, s. 1047-1059
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Tidskriftsartikel (refereegranskat)abstract
- The dynamic stiffness of a chemically and physically ageing rubber vibration isolator in the audible frequency range is modelled as a function of ageing temperature, ageing time, actual temperature, time, frequency and isolator dimension. In particular, the dynamic stiffness for an axially symmetric, homogeneously aged rubber vibration isolator is derived by waveguides where the eigenmodes given by the dispersion relation for an infinite cylinder satisfying traction free radial surface boundary condition are matched to satisfy the displacement boundary conditions at the lateral surface ends of the finite rubber cylinder. The constitutive equations are derived in a companion paper (Part 1). The dynamic stiffness is calculated over the whole audible frequency range 20-20,000 Hz at several physical ageing times for a temperature history starting at thermodynamic equilibrium at +25 degrees C and exposed by a sudden temperature step down to -60 degrees C and at several chemical ageing times at temperature +25 degrees C with simultaneous molecular network scission and reformation. The dynamic stiffness results are displaying a strong frequency dependence at a short physical ageing time, showing stiffness magnitude peaks and troughs, and a strong physical ageing time dependence, showing a large stiffness magnitude increase with the increased physical ageing time, while the peaks and troughs are smoothed out. Likewise, stiffness magnitude peaks and troughs are frequency-shifted with increased chemical ageing time. The developed model is possible to apply for dynamic stiffness prediction of rubber vibration isolator over a broad audible frequency range under realistic environmental condition of chemical ageing, mainly attributed to oxygen exposure from outside and of physical ageing, primarily perceived at low-temperature steps.
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| 8. |
- Kari, Leif
(författare)
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Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range
- 2017
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Ingår i: Continuum Mechanics and Thermodynamics. - : SPRINGER. - 0935-1175 .- 1432-0959. ; 29:5, s. 1027-1046
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Tidskriftsartikel (refereegranskat)abstract
- The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.
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| 9. |
- Kari, Leif
(författare)
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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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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer. - 0935-1175 .- 1432-0959.
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Tidskriftsartikel (refereegranskat)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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| 10. |
- Laudato, Marco, et al.
(författare)
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Analysis of the contact critical pressure of collapsible tubes for biomedical applications
- 2023
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Ingår i: Continuum Mechanics and Thermodynamics. - : Springer Nature. - 0935-1175 .- 1432-0959. ; 36:1, s. 217-228
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Tidskriftsartikel (refereegranskat)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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