Alberto Patiño-Vanegas, Carlos R. Payares Guevara, Enrique Pereira-Batista
et al.
The start-up process of water-distribution networks has been extensively investigated in recent years, particularly regarding the pressure surges that may occur during such transient events. In this context, researchers have concentrated on exploring physical formulations capable of describing the behaviour of the two interacting phases—water and air—typically resolved through numerical approaches. This paper presents an analytical solution to the nonlinear mathematical model governing the start-up of water pipelines containing a trapped air pocket. The model adopts the rigid water column approximation for the liquid phase and a polytropic gas law to account for the compressibility of the air. The resulting system can be formulated as a second-order nonlinear differential equation. The analytical approach consists of transforming the governing equation into a first-order linear ordinary differential equation, in which the square of the water front velocity is expressed as a function of the water column length. This transformation yields a closed-form solution expressed as a special integral series. The required integrals are evaluated using binomial expansions and incomplete gamma functions, enabling the derivation of a general solution valid within alternating intervals of monotonic motion. A practical application involving an 800 m pipeline is presented. Furthermore, the proposed solution is validated against experimental measurements, demonstrating the accuracy and effectiveness of the analytical approach in capturing the system’s transient behaviour.
Thermodynamics, Descriptive and experimental mechanics
This article answers the question of whether homogenization of discrete fine-scale mechanical models, such as particle or lattice models, gives rise to an equivalent continuum that is of Cauchy-type or Cosserat-type. The study employs the machinery of asymptotic expansion homogenization to analyze discrete mechanical models with rotational degrees of freedom commonly used to simulate the mechanical behavior of heterogeneous solids. The proposed derivation has general validity in both stationary (steady-state) and transient conditions (assuming wavelength much larger that particle size) and for arbitrary nonlinear, inelastic fine-scale constitutive equations. The results show that the unit cell problem is always stationary, and the only inertia term appears in the linear momentum balance equation at the coarse scale. Depending on the magnitude of the local bending stiffness, mathematical homogenization rigorously identifies two limiting conditions that correspond to the Cauchy continuum and the Cosserat continuum. A heuristic combination of these two limiting conditions provides very accurate results also in the transition from one limiting case to the other. Finally, the study demonstrates that cases for which the Cosserat character of the homogenized response is significant are associated with non-physically high fine-scale bending stiffness and, as such, are of no interest in practice.
In the past couple of years a rich connection has been found between the fields of descriptive set theory and distributed computing. Frequently, and less surprisingly, finitary algorithms can be adopted to the infinite setting, resulting in theorems about infinite, definable graphs. In this survey, we take a different perspective and illustrate how results and ideas from descriptive set theory provide new insights and techniques to the theory of distributed computing. We focus on the two classical topics from graph theory, vertex and edge colorings. After summarizing the up-to-date results from both areas, we discuss the adaptation of Marks' games method to the LOCAL model of distributed computing and the development of the multi-step Vizing's chain technique, which led to the construction of the first non-trivial distributed algorithms for Vizing colorings. We provide a list of related open problems to complement our discussion. Finally, we describe an efficient deterministic distributed algorithm for Brooks coloring on graphs of subexponential growth.
Unilateral transmission refers to the scenario in which the waves transmitted through a system remain in pure tension or pure compression. This transmission phenomenon may occur in systems that exhibit different effective elasticity in compression and tension; i.e. bilinear elasticity. We present a computational investigation of unilateral transmission in the steady-state response of harmonically driven mechanical systems with bilinear coupling. Starting with two bilinearly coupled oscillators, we find that breaking the mirror symmetry of the system, in either elastic or inertial properties, facilitates unilateral transmission by allowing it to occur near a primary resonance. This asymmetry also enables nonreciprocal transmission to occur. We then investigate the nonreciprocal dynamics of the system, including linear stability analysis, with a focus on unilateral transmission. We also extend our discussion to a bilinear periodic structure, for which we investigate the influence of the number of units and energy dissipation on unilateral transmission. We report on the existence of stable nonreciprocal unilateral transmission near primary and internal resonances of the system, as well as other nonreciprocal features such as period-doubled and quasiperiodic response characteristics.
In this paper, the size-dependent nonlinear bending of microbeams subjected to mechanical loading is studied using a finite element formulation. Based on the von Kármán nonlinear relationship and the third-order shear deformation theory, a size-dependent nonlinear beam element is derived by using the modified couple stress theory (MCST) to capture the microstructural size effect. The element with explicit expressions for the element vector of internal forces and tangent stiffness matrix is derived by employing the transverse shear rotation as a variable. Nonlinear bending of microbeams under different mechanical loading is predicted with the aid of Newton–Raphson iterative method. Numerical investigation shows that the derived element is efficient, and it is capable of giving accurate results by several elements. The obtained results reveal the importance of the micro-size effect on the nonlinear behavior of the microbeams, and the deflections are overestimated when the microstructural effect is ignored. The effects of the material length scale parameter, boundary conditions and loading type on the bending response of the microbeams are studied and highlighted.
Mechanical engineering and machinery, Descriptive and experimental mechanics
Andrey Kozelkov, Andrey Kurkin, Vadim Kurulin
et al.
Verification problems and numeric simulation of cavitation processes with the help of LOGOS computational fluid dynamics software are presented in this article. The Volume of Fluid method realized within LOGOS allowing numerical simulation of double-phase problems with a free surface is used for numeric simulation. Cavitation is resolved by updating the method with the account for interphase mass exchange; its condensation and evaporation parameters are calculated with the use of the Schnerr–Sauer and Zwart–Gerber–Belamri cavitation models. Numerical simulation results of most actual test problems considering turbulence and having reliable numerical data are presented, including simulations of flow around cylinders with flat and hemispherical end surfaces for various cavitation numbers. Numerical simulation results are presented for the process of rotation of a VP1304 screw propeller in the cavitational mode. Numerical experiments prove the operability of the implemented method.
Thermodynamics, Descriptive and experimental mechanics
We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are approximated using neural networks and solved through a training process. The loss function is chosen as the residuals of the boundary integral equations. Regularization techniques are adopted to efficiently evaluate the weakly singular and Cauchy principle integrals in boundary integral equations. Potential problems and elastostatic problems are mainly concerned in this article as a demonstration. The proposed method has several outstanding advantages: First, the dimensions of the original problem are reduced by one, thus the freedoms are greatly reduced. Second, the proposed method does not require any extra treatment to introduce the boundary conditions, since they are naturally considered through the boundary integral equations. Therefore, the method is suitable for complex geometries. Third, BINN is suitable for problems on the infinite or semi-infinite domains. Moreover, BINN can easily handle heterogeneous problems with a single neural network without domain decomposition.
Markus Sudmanns, Athanasios P. Iliopoulos, Andrew J. Birnbaum
et al.
Mesoscale simulations of discrete defects in metals provide an ideal framework to investigate the micro-scale mechanisms governing the plastic deformation under high thermal and mechanical loading conditions. To bridge size and time-scale while limiting computational effort, typically the concept of representative volume elements (RVEs) is employed. This approach considers the microstructure evolution in a volume that is representative of the overall material behavior. However, in settings with complex thermal and mechanical loading histories careful consideration of the impact of modeling constraints in terms of time scale and simulation domain on predicted results is required. We address the representation of heterogeneous dislocation structure formation in simulation volumes using the example of residual stress formation during cool-down of laser powder-bed fusion (LPBF) of AISI 316L stainless steel. This is achieved by a series of large-scale three-dimensional discrete dislocation dynamics (DDD) simulations assisted by thermo-mechanical finite element modeling of the LPBF process. Our results show that insufficient size of periodic simulation domains can result in dislocation patterns that reflect the boundaries of the primary cell. More pronounced dislocation interaction observed for larger domains highlight the significance of simulation domain constraints for predicting mechanical properties. We formulate criteria that characterize representative volume elements by capturing the conformity of the dislocation structure to the bulk material. This work provides a basis for future investigations of heterogeneous microstructure formation in mesoscale simulations of bulk material behavior.
Photoacoustic (PA) technology can provide information on both the physical structure and chemical composition of bone, showing great potential in bone assessment. However, due to the complex composition and porous structure of cancellous bone, the PA signals generated and propagated in cancellous bone are complex and difficult to be directly used in cancellous bone analysis. In this paper, a photoacoustic differential attenuation spectrum (PA-DAS) method is proposed. By eliminating the PA spectrum of the optical absorption sources, the propagation attenuation characteristics of cancellous bone are studied theoretically and experimentally. An analytical solution for the propagation attenuation of broadband ultrasound waves in cancellous bone is given by applying high-frequency and viscous corrections to Biot's theory. An experimental system of PA-DAS with an eccentric excitation differential detection system is established to obtain the PA-DAS of cancellous bone and its acoustic propagation characteristic on the rabbit osteoporosis model. The PA-DAS quantization parameter slope is further extracted to quantify the attenuation of high and low frequency components. The results show that the PA-DAS can distinguish osteoporotic bone from normal bone, enabling quantitative assessment of bone mineral density and the diagnosis of osteoporosis.
Sergey S. Andreyko, Natalya Litvinovskaya, Artem Papulov
et al.
The use of the new mining technology on the Third potash bed at the Starobinsk potash salt deposit is accompanied by the displacement of the undermined rocks. The displacement is accompanied by the foliation. The gas accumulates in the resulting foliation. The gas accumulations in the roof or the floor rocks can be the cause of a rockburst. A rockburst poses a threat to the miners’ lives, breaks driving and wide equipment and stops the working activity of the mines. Therefore, the study of the underworking effect on the gas content and the gas-dynamic characteristics are relevant problems in mining science. Thus, the purpose of this work is the study of the underworking effect on the gas content and the gas-dynamic characteristics. The <i>τ</i> criterion was used for testing the data samples. At the second stage of the comparative statistical analysis, two hypotheses H<sub>0</sub> and H<sub>1</sub> were accepted which were later subjected to verification using Student’s <i>t</i>-test. The gas parameters are changed by the camera floor and are not changed by other places. Therefore, the effect of the rock underworking leads to the formation of the additional foliation of the floor and, accordingly, to the free gases’ redistribution along the stratigraphic section and, ultimately, to the significant changes of the free gas content, the starting gas release and the gas pressure. The validity of the effect of the undermining can be the intensive gas releases repeatedly recorded in the process of drilling research holes into the soil with the ejection of a piece of the rock.
Thermodynamics, Descriptive and experimental mechanics
The present study focuses on the optimum design effectiveness in heat removal for small surfaces. Pin-fin made of solid and porous cylindrical shape forming chevron is investigated numerically using the finite element method. The design consists of 3-chevron and 5-chevron configurations connected to a heated block with fluid circulating between the chevron and above them. Variable Reynolds number and pin-fins height ranging from 2 mm to 8 mm are investigated. The full Navier–Stokes equation combined with the energy equation was solved in the presence of the solid pin-fins. The Darcy–Brinkman model with the effective energy equation is used in the presence of the porous pin-fins. The system is solved for Reynolds numbers ranging from 50 to 1000, thus remaining in the laminar regime. Results revealed that the best performance evaluation criterion is higher for the 8 mm porous pin-fins regardless of their permeability. If one ignores the pressure drop and friction contribution, a solid pin-fin having a height of 4 mm showed the best heat absorption mechanism.
Thermodynamics, Descriptive and experimental mechanics
It has long been known that plane wave solutions of the cubic nonlinear Schrödinger Equation (NLS) are linearly unstable. This fact is widely known as modulation instability (MI), and sometimes referred to as Benjamin–Feir instability in the context of water waves. In 1978, I.E. Alber introduced a methodology to perform an analogous linear stability analysis around a sea state with a known power spectrum, instead of around a plane wave. This analysis applies to second moments, and yields a stability criterion for power spectra. Asymptotically, it predicts that sufficiently narrow and high-intensity spectra are unstable, while sufficiently broad and low-intensity spectra are stable, which is consistent with empirical observations. The bifurcation between unstable and stable behaviour has no counterpart in the classical MI (where all plane waves are unstable), and we call it Landau–Alber bifurcation because the stable regime has been shown to be a case of Landau damping. In this paper, we work with the realistic power spectra of ocean waves, and for the first time, we produce clear, direct evidence for an abrupt bifurcation as the spectrum becomes narrow/intense enough. A fundamental ingredient of this work was to look directly at the nonlinear evolution of small, localised inhomogeneities, and whether these can grow dramatically. Indeed, one of the issues affecting previous investigations of this bifurcation seem to have been that they mostly looked for the indirect evidence of instability, such as an increase in overall extreme events. It is also found that a sufficiently large computational domain is crucial for the bifurcation to manifest.
Thermodynamics, Descriptive and experimental mechanics
У місті Вейхай (провінція Шаньдун, Китай) відбулося «Онлайн-відео роуд-шоу», присвячене підбору зарубіжних талантів високо класу. Понад 20 підприємців і кілька українських науковців із захопленням спілкувалися через онлайн-відео, обговорюючи стикування технологій у сферах сільського господарства, медичного лікування, автоматизації тощо. Було розпочато нову спробу хмарного міжнародного роуд-шоу – прелюдію до «China Weihai International Talents, Innovation and Entrepreneurship Conference».
Захід був організований Вейхайським муніципальним бюро кадрових ресурсів та соціального забезпечення та проведення Управлінням людських ресурсів та соціального забезпечення (Weihai Talent Work). Після чисельних відборів і поєднання з виробничою ситуацією та реальними потребами парку підприємств було визначено план заходів для онлайн-стикування з українською командою науковців. Україна має міцну науково-дослідну базу, достатній запас висококласних талантів та потужну технічну силу. У спільних роботах брали участь п'ять академіків і спеціалістів, які зацікавили підприємства Вейхаю своїми технічними досягненнями.
The dynamics of materials failure is one of the most critical phenomena in a range of scientific and engineering fields, from healthcare to structural materials to transportation. In this paper we propose a specially designed deep neural network, DyFraNet, which can predict dynamic fracture behaviors by identifying a complete history of fracture propagation - from cracking onset, as a crack grows through the material, modeled as a series of frames evolving over time and dependent on each other. Furthermore, this model can not only forecast future fracture processes but also backcast to elucidate the past fracture history. In this scenario, once provided with the outcome of a fracture event, the model will elucidate past events that led to this state and will predict the future evolution of the failure process. By comparing the predicted results with atomistic-level simulations and theory, we show that DyFraNet can capture dynamic fracture mechanics by accurately predicting how cracks develop over time, including measures such as the crack speed, as well as when cracks become unstable. We use GradCAM to interpret how DyFraNet perceives the relationship between geometric conditions and fracture dynamics and we find DyFraNet pays special attention to the areas around crack tips, which have a critical influence in the early stage of fracture propagation. In later stages, the model pays increased attention to the existing or newly formed damage distribution in the material. The proposed approach offers significant potential to accelerate the exploration of the dynamics in material design against fracture failures and can be beneficially adapted for all kinds of dynamical engineering problems.
Thermophoresis is a transport phenomenon induced by a temperature gradient. Very small objects dispersed in a fluid medium and in a temperature gradient present a non homogeneous steady density. Analysing this phenomenon within the theoretical scenario of non interacting Brownian motion one can assume that those particles are driven by a spatially dependent mechanical force. This implies the existence of a potential which was derived in a previous work. From this potential the qualitative properties of the force and the Soret coefficient were obtained. Nevertheless a quantitative correlation between the theory and the experimental data were not consistently proved. Here it is presented a methodology to match this theory with the experimental data, which it is used to analyse the experimental information of sodium docecyl sulfate (SDS) micelles.
Midas Segers, Aderik Voorspoels, Takahiro Sakaue
et al.
Mechanical properties of nucleic acids play an important role in many biological processes which often involve physical deformations of these molecules. At sufficiently long length scales (say above $\sim 20-30$ base pairs) the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites gets coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model which clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables which describe the twist and bending of the molecule. Differently from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior which matches experimental data.
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov–Galerkin projections) if a mixed velocity–pressure formulation is considered, possibly hampering the evaluation of reliable solutions in real-time. Dealing with fluid–structure interactions entails even greater difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning, in a nonintrusive way, both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD, enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid–structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.
Thermodynamics, Descriptive and experimental mechanics
Flow separation control over a wall-mounted hump model was studied experimentally to assess the performance of fluidic oscillators (sweeping jet actuators). An array of fluidic oscillators was used to control flow separation. The results showed that the fluidic oscillators were able to achieve substantial control over the separated flow by increasing the upstream suction pressure and downstream pressure recovery. Using the data available in the literature, the performance of the fluidic oscillators was compared to other active flow control (AFC) methods such as steady blowing, steady suction, and zero-net-mass-flux (ZNMF) actuators. Several integral parameters, such as the inviscid flow comparison coefficient, pressure drag coefficient, and modified normal force coefficient, were used as quality metrics in the performance comparison of the AFC methods. These quality metrics indicated the superiority of the steady suction method, especially at lower excitation amplitudes that is followed by the fluidic oscillators, steady blowing, and the ZNMF actuators, respectively. An aerodynamic figure of merit (AFM) was also constructed using the integral parameters and AFC power usage. The AFM results revealed that, for this study, steady suction was the most efficient AFC method at lower excitation amplitudes. The steady suction loses its efficiency as the excitation amplitude increases, and the fluidic oscillators become the most efficient AFC method. Both the steady suction and the fluidic oscillators have an AFM > 1 for the range tested in this study, indicating that they provide a net benefit when the AFC power consumption is also considered. On the other hand, both the steady blowing and ZNMF actuators were found to be inefficient AFC methods (AFM < 1) for the current configuration. Although they improved the flow field by controlling flow separation, the power requirement was more than their benefit.
Thermodynamics, Descriptive and experimental mechanics
Theoretical analyses and experiments have been carried out to investigate fracture behavior of glassy polymers. Our birefringence measurements quantify the local stress buildup at cut tip during different stages of drawing. Based on polymethyl methacrylate (PMMA), bisphenol A polycarbonate (PC) and polyethylene terephthalate (PET), we find several key results beyond the existing knowledge base. (1) The inherent fracture and yield strengths sigma_F(inh) and sigma_Y(inh) differ little in magnitude from the breaking and yield stress (sigma_b and sigma_y). (2) Stress intensification (SI) near a pre-through-cut builds up deviates from the theoretical description of linear elastic fracture mechanics (LEFM) upon approaching the cut tip. (3) SI meets a natural cutoff below which stress ceases to increase. (4) The stress stip at cut tip shows a trend of approximate linear increase with the far-field load s0 for all three polymers and different cut size a. (5) A characteristic length scale P emerges from the linear relation between stip and KI. For these glassy polymers, P is on the order of 0.1 mm. (6) Fracture toughness of brittle polymers is characterized by critical stress intensity factor K_Ic = sigma_F(inh)(2*pi*P)1/2, revealing relevance of the two crucial quantities. (7) The critical energy release rate GIc for brittle glass polymers such as PMMA is determined by the product of its work of fracture wF (of uncut specimen) and P. (8) The elusive fractocohesive length Lfc defined in the literature as G_Ic/w_F naturally arises from the new expression for G_Ic as stated in (7), i.e., it is essentially P. These results suggest that a great deal of future work is required to acquire additional understanding with regards to fracture and failure behaviors of plastics.