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Gdańsk University of Technology

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Publications from the year 2022

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  • Od zrównoważonego rozwoju do dewzrostu - paradygmaty krytyczne wobec wzrostu i ich implikacje dla planowania przestrzennego
    • Izabela Mironowicz
    • Robert Skrzypczyński
    2022 Full text SAMORZĄD TERYTORIALNY

    Pomimo ponad trzech dekad wdrażania koncepcji zrównoważonego rozwoju środowisko Ziemi ulega dalszej degradacji i destabilizacji. Sytuacja ta przekłada się na ożywienie antycypowanej już w latach 70. XX w. krytyki założeń leżących u podstaw koncepcji zrównoważonego rozwoju – spośród których kluczowe wydaje się założenie możliwości rozłączenia (decoupling) wzrostu gospodarczego i negatywnego oddziaływania na środowisko. W niniejszym artykule poddajemy pod krytyczną dyskusję wizję decouplingu, a następnie omawiamy trzy alternatywne wobec zrównoważonego rozwoju koncepcje „postwzrostowe” – dewzrost, ekonomię obwarzanka i gospodarkę stacjonarną – oraz wskazujemy na implikacje, jakie płyną z wdrażania postulatów dewzrostu dla teorii i praktyki planowania przestrzennego. Wydaje się, że planowanie przestrzenne powinno z jednej strony zaadaptować się do rysującej się na horyzoncie zmiany paradygmatów, a z drugiej wspierać transformację dewzrostową, co jest możliwe na różne sposoby także z wykorzystaniem już istniejących narzędzi planistycznych.

  • Odbiór zbiorczy z filtracją adaptacyjną RLS w transmisji danych w kanale hydroakustycznym
    • Agnieszka Czapiewska
    • Andrzej Łuksza
    • Ryszard Studański
    • Andrzej Żak
    2022 Full text Przegląd Elektrotechniczny

    Transmisja danych w kanale hydroakustycznych realizowana jest w trudnych warunkach propagacyjnych. Jednym z problemów podczas takiej transmisji są zakłócenia międzysymbolowe (ISI – intersymbol interference) spowodowane głównie przez efekt wielodrogowości. To zjawisko utrudnia, bądź uniemożliwia transmisję danych w takim kanale. Stąd podjęto analizę wpływu zastosowania odbioru zbiorczego oraz filtracji adaptacyjnej RLS (Recursive Least Squares) na poprawę jakości odbioru transmisji danych w kanale hydroakustycznym.

  • Olfactory receptor-based biosensors as potential future tools in medical diagnosis
    • Tomasz Wasilewski
    • Nathália F. Brito
    • Bartosz Szulczyński
    • Marek Wojciechowski
    • Natalia Buda
    • Ana Claudia A. Melo
    • Wojciech Kamysz
    • Jacek Gębicki
    2022 TRAC-TRENDS IN ANALYTICAL CHEMISTRY

    The detection of biomarkers is the future of non-invasive medical diagnosis and screening. Discovery and identification of reliable disease specific volatile organic compounds is dependent on repeatable, accurate analysis of trace level gaseous analytes mainly in breath samples. Natural variety of the olfactory systems and the compounds capable of gas molecules binding creates wide possibilities of acquisition and implementation of the biological elements for construction of the biosensors for different applications, with special emphasis on healthcare and medical areas. Early and fast diagnosis of patient's condition, including respiratory system diseases, as well as on-time launch of suitable treatment are the critical factors influencing on public health and efficiency of clinical trials. Conventional techniques of diagnosis of the respiratory system diseases are usually time-consuming, require centralized laboratories, experienced personnel and expensive equipment. Recently developed biosensors take advantage of micro- and nanotechnology achievements, which significantly improve their metrological parameters. A transfer of the biosensors from scientific laboratories to actual clinic diagnostics is limited and requires overcoming of critical obstacles. Potential use of olfactory receptors and elements mimicking their operation in artificial olfaction for their use in biosensors in disease diagnosis are presented. We review recent progress in olfactory-based biosensors employing different biological units in light of future developments in medical diagnosis with emphasis on examples where biological components have been employed to detect biomarkers. Also, significant advances over the last years were discussed and features of fabrication in the perspective of odorant sensing applications. Pioneering studies that greatly impacted the field of biosensing are critically reviewed along with future challenges to overcome.

  • On a comparison principle and the uniqueness of spectral flow
    • Maciej Starostka
    • Nils Waterstraat
    2022 Full text MATHEMATISCHE NACHRICHTEN

    The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply our result to the existence of non-trivial solutions of boundary value problems of Hamiltonian systems. Secondly, the spectral ow was axiomatically characterised by Lesch, and by Ciriza, Fitzpatrick and Pejsachowicz under the assumption that the endpoints of the paths of selfadjoint Fredholm operators are invertible. We propose a different approach to the uniqueness of spectral flow which lifts this additional assumption. As application of the latter result, we discuss the relation between the spectral flow and the Maslov index in symplectic Hilbert spaces.

  • On a flexomagnetic behavior of composite structures
    • Mohammad Malikan
    • Victor Eremeev
    2022 Full text INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

    The popularity of the studies is getting further on the flexomagnetic (FM) response of nano-electro-magneto machines. In spite of this, there are a few incompatibilities with the available FM model. This study indicates that the accessible FM model is inappropriate when considering the converse magnetization effect that demonstrates the necessity and importance of deriving a new FM relation. Additionally, the literature has neglected the converse FM coefficient in the Lifshitz invariant inside the free energy constitutive relation. This fact inspires us to endeavor and conduct a new characteristic formulation for static analysis of axially compressed piezomagnetic nanobeams comprising the FM effect. This novel FM model is competent and suitable for various boundary conditions, encompassing analytical, semi-analytical, and numerical solving strategies. However, based on the previous FM equation established with respect to Euler-Bernoulli and Timoshenko beams, the governing equations are ill-posed due to the corresponding energy density. Despite that, this error will not remain in the finalized equations in the present model by conjecturing a gradient of the magnetic field and a different formulation. Moreover, the inverse FM parameter will appear in the magnetic field relation. As the literature reported, non-uniform deformed piezomagnetic structures are capable of presenting more outstanding flexomagneticity. In actuality, a non-uniform elastic strain appears as a response to the magnetic field gradient (converse effect) that causes this study to deduce the nanobeam with higher-order shear deformations. Furthermore, the local governing equations will be transferred into the nonlocal phase according to the nonlocal differential, particularly nonlocal integral elasticity which itself is a strong nonlocality. Through this theory, and in regard to the converse FM impact, an analytical expression is applied for computing critical buckling loads within several ends conditions of the nanobeam. Our present results and achievements will hopefully be an effective contribution to theoretical studies on the mechanics of intelligent nanostructures.

  • On Computing Curlicues Generated by Circle Homeomorphisms
    • Justyna Signerska-Rynkowska
    2022 Full text

    The dataset entitled Computing dynamical curlicues contains values of consecutive points on a curlicue generated, respectively, by rotation on the circle by different angles, the Arnold circle map (with various parameter values) and an exemplary sequence as well as corresponding diameters and Birkhoff averages of these curves. We additionally provide source codes of the Matlab programs which can be used to generate and plot the first N points of curlicues of these types and calculating related quantities. Illustrative figures are included as well.

  • On Decision-Making Strategies for Improved-Reliability Size Reduction of Microwave Passives: Intermittent Correction of Equality Constraints and Adaptive Handling of Inequality Constraints
    • Sławomir Kozieł
    • Anna Pietrenko-Dąbrowska
    • Marzieh Mahrokh
    2022 KNOWLEDGE-BASED SYSTEMS

    Design optimization of passive microwave components is an intricate process, especially if the primary objective is a reduction of the physical size of the structure. The latter has become an important design consideration for a growing number of modern applications (mobile communications, wearable/implantable devices, internet of things), where miniaturization is imperative due to a limited space allocated for the electronic circuitry. Optimization-based size reduction is a heavily constrained task, with several acceptance thresholds imposed on electrical characteristics of the system. The challenges are pronounced whenever equality constraints are involved (e.g., related to power split ratio requirements), in which case the feasible space is a thin set, thereby difficult to be explored throughout the optimization process. This feature makes conventional methods, such as penalty function approaches or algorithms with explicit constraint handling, of limited reliability. In this paper, we introduce a novel technique for reliable control of equality constraints in simulation-driven size reduction of microwave components. Our methodology involves an intermittent optimization-based correction of equality constraints. This is essentially a knowledge-based decision-making strategy implemented as a supplementary optimization stage, and launched before each iteration of the core algorithm. Constraint violation is reduced without being detrimental to the remaining figures of merit, in particular, the circuit size and inequality constraints. Meanwhile, inequality constraints are handled using a penalty function approach with adaptive adjustment of penalty coefficients. The proposed technique facilitates exploration of the feasible space, and allows for achieving reduced miniaturization rates in comparison to the benchmark methods, while ensuring a reliable control of the design constraints. These advantages have been demonstrated using four microstrip couplers, with consistent results obtained for all considered circuits.

  • ON DYNAMICS OF ELASTIC NETWORKS WITH RIGID JUNCTIONS WITHIN NONLINEAR MICRO-POLAR ELASTICITY
    • Victor Eremeev
    • Emanuele Reccia
    2022 Full text International Journal for Multiscale Computational Engineering

    Within the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e., static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider a three-dimensional elastic network made of three families of elastic fibers connected through massive rigid joints. Effective elastic properties are inherited from the geometry and material properties of the fibers, whereas the kinetic (inertia) properties are determined by the both fibers and joints. Formulae for microinertia tensors are given.

  • On Earth as in Universe
    • Krzysztof Wróblewski
    2022

    On Earth as in Universe Ślady zostawione na podobraziu przygotowanym własnoręcznie przez Kazimierza Ostrowskiego. Kilka pociągnięć pędzlem ciemną farbą na odwrocie płótna, tu i ówdzie przyklejone włosy do powierzchni gruntu, kurz nagromadzony przez lata - słowem każdy element artefaktu, który trafił do mnie, był kapsułą czasu sprzed około pięćdziesięciu lat. Jedyne co mogłem zrobić, to wpisać drobiny obecności Kazimierza Ostrowskiego w strukturę malowanego obrazu. Odnosząc się luźno do twórczości Kacha użyłem dwóch przetworzonych wzorów opracowanych przez Rogera Penrose'a. Ich bazą są symetrie pięcioosiowe wynikające ze złotego podziału. Zarówno na Ziemi jak i w Kosmosie panuje matematyczny porządek, choć na co dzień tego nie dostrzegamy. Na początku XVII wieku mówił o tym Johanes Kepler w Harmonices Mundi twierdząc, że geometryczne obiekty są modelami całego świata. Ówczesne obserwacje i wnioski Keplera potwierdzają współczesne badania, według których gdy weźmiemy dwie planety z Układu Słonecznego, połączymy ich pozycje linią i będziemy na bieżąco monitorować ich wzajemne położenie, to naszym oczom ukażą się wzory o określonych regularnych kształtach. Na lewym marginesie obrazu umieściłem nawiązanie do symetrii występujących w różnych liściach. W górnym lewym rogu kompozycji znajduje się ponadto detal zaprzeczony z jednego obrazów Hilmy af Klint z cyklu zatytułowanego Ewolucja. Artystka była przekonana, że przemianę napędza zasada polaryzacji występująca w różnych formach, takich jak światło i ciemność, dobro i zło, mężczyzna i kobieta. Jej symboliczne, czy wręcz mistyczne malarstwo jest mi szczególnie bliskie. Znajduję też pewne konotacje pomiędzy dokonaniami Hilmy af Klint i Kazimierza Ostrowskiego - choć jego twórczość miała bardziej charakter alegoryczny. Malarstwo Kazimierza Ostrowskiego w moim przekonaniu spajało i monumentalizowało to, czego doświadczamy na Ziemi z tym co dzieje się we Wszechświecie. Nie opierało się ono wprawdzie na rygorystycznej geometrii, ale rządził nim intuicyjny zmysł porządku, wyczucie równowagi i harmonii. Kachu podobnie jak Lèger „dbał o płaszczyznę” a „kompozycja musiała mieć równowagę od brzegu do brzegu” . Krzysztof Wróblewski Gdańsk, 2022

  • On Improved-Reliability Design Optimization of High-Frequency Structures Using Local Search Algorithms
    • Sławomir Kozieł
    • Anna Pietrenko-Dąbrowska
    • Piotr Płotka
    2022 Full text IEEE Access

    The role of numerical optimization has been continuously growing in the design of high-frequency structures, including microwave and antenna components. At the same time, accurate evaluation of electrical characteristics necessitates full-wave electromagnetic (EM) analysis, which is CPU intensive, especially for complex systems. As rigorous optimization routines involve repetitive EM simulations, the associated cost may be significant. In the design practice, the most widely used EM-driven procedures are by far local (e.g., gradient-based) ones. While typically incurring acceptable expenses that range from dozens to a few hundreds of objective function evaluations, they are prone to failure whenever a decent initial design is not available. Representative scenarios include simulation-based size reduction of compact devices or re-design of structures for operating/material parameters being distant from those at the available design. A standard mitigation approach is the involvement of global search methods, which entails significantly higher computational costs. This paper reviews the recent methodologies introduced to improve the reliability of local parameter tuning algorithms without degrading their computational efficiency. We discuss frequency-based regularization, adaptively adjusted design specification approach, as well as accelerated feature-based optimization. All of these techniques incorporate mechanisms that improve the performance of the search process under challenging scenarios, primarily poor initial conditions. The outline of the mentioned methods is accompanied by illustrative examples including passive microwave circuits and microstrip antennas. Benchmarking against conventional local search is provided as well. Furthermore, the paper discusses the advantages and disadvantages of the reviewed frameworks as well as speculates about future research directions.

  • On proper (1,2)‐dominating sets in graphs
    • Adrian Michalski
    • Iwona Włoch
    • Magda Dettlaff
    • Magdalena Lemańska
    2022 MATHEMATICAL METHODS IN THE APPLIED SCIENCES

    In 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating set of a graph. In particular, we introduce proper (1,2) -domination parameters and study their relations with (1,2) -domination parameters and the classical domination numbers.

  • On reliability assessment of ship machinery system in different autonomy degree; A Bayesian-based approach
    • Ahmad BahooToroody
    • Mohammad Mahdi Abaei
    • Osiris Valdez Banda
    • Jakub Montewka
    • Pentti Kujala
    2022 Full text OCEAN ENGINEERING

    Analyzing the reliability of autonomous ships has recently attracted attention mainly due to epistemic uncertainty (lack of knowledge) integrated with automatic operations in the maritime sector. The advent of new random failures with unrecognized failure patterns in autonomous ship operations requires a comprehensive reliability assessment specifically aiming at estimating the time in which the ship can be trusted to be left unattended. While the reliability concept is touched upon well through the literature, the operational trustworthiness needs more elaboration to be established for system safety, especially within the maritime sector. Accordingly, in this paper, a probabilistic approach has been established to estimate the trusted operational time of the ship machinery system through different autonomy degrees. The uncertainty associated with ship operation has been quantified using Markov Chain Monte-Carlo simulation from likelihood function in Bayesian inference. To verify the developed framework, a practical example of a machinery plant used in typical short sea merchant ships is taken into account. This study can be exploited by asset managers to estimate the time in which the ship can be left unattended.

  • On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
    • Victor Eremeev
    • Leonid Lebedev
    • Violetta Konopińska-Zmysłowska
    2022 Full text MATHEMATICS AND MECHANICS OF SOLIDS

    The problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated and studied. It is proved a theorem of existence and uniqueness of a weak solution for the problem under consideration.

  • On the Bending of Multilayered Plates Considering Surface Viscoelasticity
    • Victor Eremeev
    • Violetta Konopińska-Zmysłowska
    2022

    We discuss the bending resistance of multilayered plates taking into account surface/interfacial viscoelasticity. Within the linear surface viscoelasticity we introduce the surface/interfacial stresses linearly dependent on the history of surface strains. In order to underline the surface viscoelasticity contribution to the bending response we restrict ourselves to the elastic behaviour in the bulk. Using the correspondence principle of the theory of viscoelasticity we present an effective bending relaxation function.

  • On the deformation and frequency analyses of SARS-CoV-2 at nanoscale
    • Shahriar Dastjerdi
    • Mohammad Malikan
    • Bekir Akgöz
    • Ömer Civalek
    • Tomasz Wiczenbach
    • Victor Eremeev
    2022 Full text INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE

    The SARS-CoV-2 virus, which has emerged as a Covid-19 pandemic, has had the most significant impact on people's health, economy, and lifestyle around the world today. In the present study, the SARS-CoV-2 virus is mechanically simulated to obtain its deformation and natural frequencies. The virus under analysis is modeled on a viscoelastic spherical structure. The theory of shell structures in mechanics is used to derive the governing equations. Whereas the virus has nanometric size, using classical theories may give incorrect results. Consequently, the nonlocal elasticity theory is used to consider the effect of interatomic forces on the results. From the mechanical point of view, if a structure vibrates with a natural frequency specific to it, the resonance phenomenon will occur in that structure, leading to the destruction of the structure. Therefore, it is possible that the protein chains of SARS-CoV-2 would be destroyed by vibrating it at natural frequencies. Since the mechanical properties of SARS-CoV-2 are not clearly known due to the new emergence of this virus, deformation and natural frequencies are obtained in a specific interval. Researchers could also use this investigation as a pioneering study to find a non-vaccine treatment solution for the SARS-CoV-2 virus and various viruses, including HIV.

  • On the differential effect of temperature on the Nusselt-Rayleigh relationship in free convection
    • Michał Ryms
    • Grzegorz J. Kwiatkowski
    • Witold Lewandowski
    2022 INTERNATIONAL JOURNAL OF THERMAL SCIENCES

    The aim of and inspiration behind this paper was to explain the reasons, also observed by other researchers, of the discrepancy in the results of experimental free convection, which for small Rayleigh and Nusselt numbers in the initial phase of research can sometimes reach several hundred percent. These discrepancies decrease with increasing heating power and plate surface temperature, in proportion to the increase in Ra and Nu, reaching typical values for this type of research. To explain this phenomenon, a comprehensive theoretical and experimental analysis of the influence of the physical properties of a fluid (air and water) as well as primary (tw and t∞) and secondary (tav and Δt) temperatures on the Rayleigh number was carried out. The impact was found to be unequal. The plate temperature tw is of greater importance, which is much higher than the much lower and almost constant temperature t∞ of the undisturbed area, especially since it causes convective movement, generating differences in fluid density and thus driving the phenomenon. Similarly, the direct contribution of the temperature difference Δt to Ra suggests that it has a greater influence on convective heat transfer than the average temperature of the medium tav. By analysing the effect of each of these temperatures separately, it was possible to show that their mutual, compatible or opposite interaction (tw/t∞) causes a different scattering of results, or may even lead to unusual Rayleigh numbers (Ra temperature dualism). This study led not only to a better understanding of the phenomenon, but even to a prediction of its unusual behaviour, unheard of in typical experimental studies of free convection. For example, if we consider the theoretical convective heat transfer from a plate l = 0.15 m in air in the context of the interaction of tav and Δt, it turns out that for the same Δt = 40 K, the Rayleigh number may assume, depending on tav = (tw + t∞)/2, different values. So, for tw = 50 °C, t∞ = 10 °C and tav = 30 °C, Ra = 1.213.107, whereas for tw = 90 °C, t∞ = 50 °C and tav = 70 °C it is ≈ 1.7 times smaller (Ra = 0.687.107). This hypothetical phenomenon, unheard of in typical experimental studies, which could occur, and maybe even does occur in smelting, thermal energy, etc., forces us to think about the values of Nusselt numbers, heat transfer coefficients and heat fluxes for these two cases. This lies beyond the scope of the present paper, but it is a topic for possible future research.

  • On the Role of Polarimetric Decomposition and Speckle Filtering Methods for C-Band SAR Wetland Classification Purposes
    • Monika Gierszewska
    • Tomasz Berezowski
    2022 Full text IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing

    Previous wetlands studies have thoroughly verified the usefulness of data from synthetic aperture radar (SAR) sensors in various acquisition modes. However, the effect of the processing parameters in wetland classification remains poorly explored. In this study, we investigated the influence of speckle filters and decomposition methods with different combinations of filter and decomposition windows sizes on classification accuracy. We used a C-band Radarsat 2 image acquired over a wetland located in northeast Poland. We processed the SAR data using various speckle filters: boxcar, intensity-driven adaptive-neighborhood (IDAN), improved Lee sigma, refined Lee (in 5×5 to 11×11 pixel window sizes), and a nonlocal NL-SAR. Next, we processed the nonfiltered and filtered data using nine polarimetric decompositions, also in 5×5 to 11×11 pixel window sizes. The extracted polarimetric features were applied as an input dataset in the random forest classification model in single- and multidecomposition scenarios. In the single-decomposition scenario, the Cloude–Pottier decomposition produced the highest (72%) and the Touzi decomposition achieved the lowest (38%) accuracy. The IDAN filter with an 11×11 filter window and a 9×9 decomposition window had the highest, and the nonfiltered data with a 5×5 decomposition window had the lowest accuracy in the multidecomposition scenario. The most important features were the alpha parameter from the Cloude–Pottier decomposition, the polarimetric contribution of the Shannon entropy, and the volume backscattering components. The results stress the importance of appropriate processing parameters in the SAR data classification workflow, and the study guides in selecting the most suitable combination of radar image processing parameters for wetland classification.

  • On the Use of Selected 4th Generation Nuclear Reactors in Marine Power Plants
    • Marta Drosińska-Komor
    • Jerzy Głuch
    • Łukasz Breńkacz
    • Paweł Ziółkowski
    2022 Full text Polish Maritime Research

    This article provides a review of the possibility of using different types of reactors to power ships. The analyses were carried out for three different large vessels: a container ship, a liquid gas carrier and a bulk carrier. A novelty of this work is the analysis of the proposal to adapt marine power plants to ecological requirements in shipping by replacing the conventional propulsion system based on internal combustion engines with nuclear propulsion. The subjects of comparison are primarily the dimensions of the most important devices of the nuclear power plant and the preliminary fitness analysis. It was assumed for this purpose that the nuclear power plant fits in the engine room compartment and uses the space left after the removal of the combustion engines. At the same time, this propulsion provides at all times sufficient energy for port, technological and shipping operations at an economically justifiable speed. For deep-sea vessels, which are supposed to reach null emissions of CO, CO2, NOx, SOx and H2O, this is one of the most reasonable solutions. Finally the paper proves that all the above-mentioned marine functions could be effectively applied in power plants equipped with 4th generation nuclear reactors.

  • On the use of the cumulative strain energy density for fatigue life assessment in advanced high-strength steels
    • Ricardo Branco
    • Rui F. Martins
    • José A.F.O. Correia
    • Zbigniew Marciniak
    • Wojciech Macek
    • J. Jesus
    2022 Full text INTERNATIONAL JOURNAL OF FATIGUE

    In this paper, the applicability of the cumulative strain energy density is explored as a fatigue indicator parameter for advanced high-strength steels subjected to strain-controlled conditions. Firstly, the cyclic stress-strain responses of nine steels, selected from three multiphase families, encompassing different elemental compositions and different heat treatment routes, were studied. Then, the predictive capabilities of the proposed model were compared to those of other strain-based and energy-based approaches. It was found that the cumulative strain energy density decreases as the strain amplitude rises and it can be correlated with the fatigue life via a power function. In addition, the dialectical relationship between the cumulative strain energy and the fatigue life was not significantly affected by the elemental composition or the heat treatment route. Furthermore, the fatigue lives computed through the cumulative strain energy density concept were close to those of the other models but were slightly more conservative.

  • On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
    • Victor Eremeev
    • Francesco dell'Isola
    2022 Full text MATHEMATICS AND MECHANICS OF SOLIDS

    We provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of dilatation only. Such a model has many applications, e.g., to describe phenomena of interest in poroelasticity or in some situations where media with scalar microstructure are necessary. We present an extension of the previous results by Eremeyev et al. (2020 Z angew Math Phys 71(6): 1–16) to the case of domains with edges and when external line forces are applied. Let us note that the interest paid to Lipschitz polyhedra-type domains is at least twofold. First, it is known that geometrical singularity of the boundary may essentially influence singularity of solutions. On the other hand, the analysis of weak solutions in polyhedral domains is of great significance for design of optimal computations using a finite-element method and for the analysis of convergence of numerical solutions.