Numerical Implementation Research Articles

A rational multiscale nonlinear constitutive model for freeze–thaw rocks under triaxial compression

The stability and durability of rocks in cold regions are significantly impacted by the degradation of mechanical properties caused by freeze–thaw (F–T) environment. In this work, we shall propose a rational multiscale nonlinear constitutive model based on thermodynamics, micromechanics, and fractional calculus theory to describe the complete deformation and failure process of F–T rocks under triaxial compression. The F–T rocks at the mesoscale are regarded as consisting of porous matrix and cracks, while porous matrix is composed of the micropores and elastic solid grains at the microscale. According to experimental observations, we assume the F–T action mainly causes micropores growth and cracks opening, and mechanical damage is resulted from the initiation and propagation of cracks. In this context, the effects of F–T and mechanical damage on effective elastic properties of rocks can be quantitatively analyzed by using the two-step Mori–Tanaka (M-T) homogenization method. After subtly deriving the total free energy function of F–T rocks under compression, we systematically develop specific criteria for describing open cracks closure deformation, mechanical damage evolution and frictional sliding induced plastic distortion. Note that to correctly capture the plastic deformation characteristics, the non-orthogonal flow rule based on fractional differential calculations is employed. Following that, analytical analyses and numerical implementation of the proposed model are conducted. The performance of the model is evaluated by the simulations with experimental data on two kinds of F–T rocks, and discussions on parameters sensitivity and effects of fractional order are followed.

Investment–consumption optimization with transaction cost and learning about return predictability

In this paper, we investigate an investment–consumption optimization problem in continuous-time settings, where the expected rate of return from a risky asset is predictable with an observable factor and an unobservable factor. Based on observable information, a decision-maker learns about the unobservable factor while making investment–consumption decisions. Both factors are supposed to follow a mean-reverting process. Also, we relax the assumption for perfect liquidity of the risky asset through incorporating proportional transaction costs that are incurred in trading the risky asset. In such way, a form of friction posing liquidity risk to the investor is examined. Dynamic programming principle coupled with an Hamilton–Jacobi–Bellman (HJB) equation are adopted to discuss the problem. Applying an asymptotic method with small transaction costs being taken as a perturbation parameter, we determine the frictional value function by solving the first and second corrector equations. For the numerical implementation of the proposed approach, a Monte-Carlo-simulation-based approximation algorithm is adopted to solve the second corrector equation. Finally, numerical examples and their economic interpretations are discussed.

Viscoelastic Fractional Model with a Non-Uniform Time Discretization for Laminated Glass: Experimental Validation

We discuss a novel approach, based on fractional calculus with a non-uniform time discretization, to numerically simulate interlayer viscoelastic behaviour and associated time-dependent deformation of laminated glass. Reference is made to the classic example of a simply supported laminated glass beam under long-duration loads. The fractional model is compared with some results obtained using the widely used finite element software ABAQUS 2021, which for the viscoelastic properties of the polymeric interlayer, utilizes the more traditional approach based on the Wiechert model and approximation via Prony series of the relaxation function and a uniform discretization of time for the numerical solution. The model is also validated through the comparison with experimental test. The novel approach based on fractional calculus presents two main advantages: 1) the definition of the model parameters from experimental data is simplified; and 2) the numerical implementation is easier and computationally more efficient. When a long observation time is considered, the use of a non-uniform time discretization presents the great advantage of not neglecting any part of the relaxation function. Use of traditional uniform time discretization requires the use of large time steps making it impossible to describe all the changes of the relaxation curve within the large time interval. Practical examples will be presented using viscoelastic models for Trosifol® Extra Stiff (PVB) and SentryGlas® interlayers. This methodology also shows potential to advance next generation standards for the design of structural laminated glass.

Performance Evaluation of Physical Properties on Zinc Sulfide (ZnS)-based Field Effect Transistor

The paper presents the performance evaluation of physical properties on Zinc Sulfide (ZnS)-based Field Effect Transistor. The most famous III-V compound-based semiconductor devices have several affected to the environment and the toxic contents are directly responded to the society. Due to the lack of technology on nontoxic compound-based semiconductor device fabrications, the novel device with II-VI compound materials are challenging issues for the environments. The specific objectives of doing research on fabrication of II-VI compound-based semiconductor devices in advanced laboratories are to emphasize the numerical modeling of the device structure and designing the FET based on ZnS material, to contribute the mathematical model for physical characteristics of the FET structure and the modification of the device structure will be easily established by using numerical simulation. The mathematical analyses on physical properties of device structure with ZnS material are confirmed and observed the several properties of electrical and electronic characteristics. The detailed implementations for ZnS-based FET devices are performed and evaluated the performance of the developed FET devices. There are two steps analyses in physical properties of ZnS-based FET devices with numerical implementation by MATLAB languages. The results observed in this study could be confirmed with the recent works from several research laboratories and the developed ZnS-based FET devices could be utilized in high performance wide band applications on switching in the power electronics and amplification purposes in modern amplifier design in real world applications.

Staggered finite volume algorithms for dynamic analysis of saturated soil with low permeability and incompressible pore fluid by using OpenFOAM

Biot dynamic theory forms the basis of dynamic analysis for soil-pore fluid coupling, whose formulations can be simplified by u-p approximation for low frequency phenomena without loss of accuracy. In the past decades, fully-coupled approach and segregated method were two common strategies for Finite Volume (FV) solutions to Biot dynamic theory. However, both methods encounter problems that limit their applicability when soil permeability and pore fluid compressibility reduce to a relatively low level. Under this circumstance, fully-coupled approach requires mixed formulation to satisfy Babuška-Brezzi condition, which complicates numerical implementation. On the other hand, segregated method suffers from divergence and instability, and shows poor performance in computation efficiency. In this article, two staggered FV algorithms incorporating operator splitting technique are devoted to overcoming the aforementioned shortcomings, and they are implemented on the open-source, broadly used and versatile platform for FV calculation, OpenFOAM. Through comparing the computed results of the two algorithms with solutions in the literature, both of the proposed algorithms are shown to reasonably reflect the dynamic responses of porous media. By conducting stability analyses based on the numerical cases, the two algorithms are shown to enlarge the stability region and enable larger time steps for computation.

FE modeling to generate composite RVEs with high volume fractions and various shapes of inclusions

This work proposes a novel multi-step dynamic FE compression method to generate Representative Volume Elements (RVEs) of composites containing a variety of inclusions. This method is actualized through a sequential and four-stage procedure: (1) Sparse and periodic inclusions exhibiting a predefined orientation distribution are generated by implementing a modified random sequential adsorption algorithm, (2) Sparse inclusions undergo biaxial compression into the region of the targeted RVE via a dynamic FE analysis, (3) Periodic inclusions are compressed into the region utilizing a dynamic FE analysis with periodic boundary conditions, and (4) Positions and orientations of the compressed inclusions are extracted and the RVE in computer-aided design format is then generated. The proposed method confers advantages from four distinct perspectives: (1) applicability to various inclusion geometries, including ellipses, lobules, polygons, kidneys and stars, (2) ability to generate periodic RVEs of composites with high inclusion volume fractions (up to 80.0% for circular inclusions), (3) simple and straightforward numerical implementation without explicitly considering inclusion intersection check and (4) capacity to predefine inclusion orientation distribution. Statistical analyses utilizing multiple spatial descriptors, i.e., inclusion orientation angle, local volume fraction, Voronoi cell area, nearest-neighbor distance and orientation, second order intensity function, radial distribution function and two-point probability function, confirm randomness of inclusion distribution in the generated RVEs. The elastic properties and damage behaviors of composites via the FE homogenization method are predicted based on the generated RVEs and are compared with those of available experimental data, the literature and the mean-field homogenization models to demonstrate effectiveness of the proposed multi-step dynamic FE compression method.

A Revisit of Electromagnetic Wave Scattering by a Metal Isotropic Body in a Lossless Environment with Magnetic Sensor Excitation.

This paper investigates the electromagnetic fields being scattered by a metal spherical object in a vacuum environment, providing a numerical implementation of the obtained analytical results. A time-harmonic magnetic dipole source, far enough, emits the incident field at low frequencies, oriented arbitrarily in the three-dimensional space. The aim is to find a detailed solution to the scattering problem at spherical coordinates, which is useful for data inversion. Based on the theory of low frequencies, the Maxwell-type problem is transformed into Laplace's or Poisson's interconnected equations, accompanied by the proper boundary conditions on the perfectly conducting sphere and the radiation conditions at infinity, which are solved gradually. Broadly, the static and the first three dynamic terms are sufficient, while the terms of a higher order are negligible, which is confirmed by the field graphical representation.

Lining up a positive semi-definite six-point bootstrap

In this work, we initiate a positive semi-definite numerical bootstrap program for multi-point correlators. Considering six-point functions of operators on a line, we reformulate the crossing symmetry equation for a pair of comb-channel expansions as a semi-definite programming problem. We provide two alternative formulations of this problem. At least one of them turns out to be amenable to numerical implementation. Through a combination of analytical and numerical techniques, we obtain rigorous bounds on CFT data in the triple-twist channel for several examples.

PEAK Mood, Mind, and Marks: a pilot study of an intervention to support university students' mental and cognitive health through physical exercise.

Regular exercise has the potential to enhance university students' mental and cognitive health. The PEAK Mood, Mind and Marks program (i.e., PEAK) is a neuroscience-informed intervention developed using the Behaviour Change Wheel to support students to exercise three or more times per week to benefit their mental and cognitive health. This pilot study assessed the impact of PEAK on exercise, mental and cognitive health, and implementation outcomes. PEAK was delivered to 115 undergraduate university students throughout a 12-week university semester. The primary outcome was weekly exercise frequency. Secondary outcomes were: time spent engaged in moderate-vigorous exercise, sedentary behaviour and perceived mental health and cognitive health. All were measured via online self-report questionnaires. Qualitative interviews with 15 students investigated influences on engagement, the acceptability and appropriateness of PEAK, and its mechanisms of behaviour change. Paired t-tests, Wilcoxon Signed-Rank tests and template analysis were used to analyse quantitative and qualitative data, respectively. On average, 48.4% of students engaged in the recommended frequency of three or more exercise sessions per week. This proportion decreased towards the end of PEAK. Sedentary behaviour significantly decreased from baseline to end-point, and moderate-vigorous exercise significantly increased among students' who were non-exercisers. Mental wellbeing, stress, loneliness, and sense of belonging to the university significantly improved. There were no significant changes in psychological distress. Concentration, memory, and productivity significantly improved. Sixty-eight percent of students remained engaged in one or more components of PEAK at end-point. Qualitative data indicated students found PEAK to be acceptable and appropriate, and that it improved aspects of their capability, opportunity, and motivation to exercise. Students are receptive to an exercise-based program to support their mental and cognitive health. Students exercise frequency decreased; however, these figures are likely a conservative estimate of students exercise engagement. Students valued the neuroscience-informed approach to motivational and educational content and that the program's goals aligned with their academic goals. Students identified numerous areas PEAK's content and implementation can be optimised, including use of a single digital delivery platform, more opportunities to connect with peers and to expand the content's cultural inclusivity.

Modelling of Multicomponent Fluid Flow in Deforming and Reacting Porous Rock

We propose a coupled hydro-chemo-mechanical model and its 1D numerical implementation. We demonstrate its application to model filtration of a multicomponent fluid in deforming and reacting host rocks, considering changes in the densities, phase proportions and chemical compositions of coexisting phases. We presented 1D numerical implementation on the example of soapstone formation from serpentinite during H₂O-СО2 fluid filtration with low concentration of СО2 coupled with viscous deformation of mineral matrix, considering MgO-SiO2-H₂O-СО2 system. The numerical results show porosity wave propagation by viscous (de)compaction mechanism accompanied with the formation of an elongated zone with higher filtration properties. After the formation of such a channel, the formation and propagation of reaction fronts occurs associated with the transformation of the mineral composition of the original rock. During H2O-CO2 fluid filtration, starting from 1 weight percent of dissolved CO2, carbonization of hydrated serpentinite starts, specifically antigorite transforms to magnesite and talc.

Homogenization of partial differential equations with Preisach operators

The current work deals with initial boundary value parabolic problems with Preisach hysteresis whose the density functions are allowed to depend on the variable of space. The model contains nonlinear monotone operators in the diffusion term, arising from an energy. Thanks to the properties of Preisach hysteresis operators and to the sigma-convergence method, we obtain the convergence of themicroscopic solutions to the solution of the homogenized problem. The effective operator is obtained in terms of a solution of a nonlinear corrector equation addressed in the usual sense of distributions, leading in an approximate scheme for the homogenizedcoefficient which is an important step towards the numerical implementation of the results from the homogenization theory beyond the periodic setting.

A Permeability Model for Fractured Granite and its Numerical Implementation

A Permeability Model for Fractured Granite and its Numerical Implementation

A parameter-free and monolithic approach for multiscale simulations of flow, transport, and chemical reactions in porous media

Traditional approaches for transport in porous media rely on empirical hydrodynamic/transport parameters to quantify the interfacial exchange terms between fluid and solid, which leads to considerable uncertainties and also to a narrow application range of each method for realistic investigations of porous media. A parameter-free approach for flow, transport, and chemical reactions in porous media is presented in this paper. This approach adopts a novel, single-domain set of equations that are rigorously derived based on the elementary conservation laws describing the physical, continuous domain. The impact of the solid on nearby fluid being directly quantified in terms of the quantity to be solved, this avoids the introduction of empirical parameters. Various transport problems including external, conjugate, and reactive processes are properly formulated in this context, with the coupling between fluid and porous structures at different scales naturally solved in a monolithic manner. All these equations remain simple in terms of their numerical implementation, with solid structures represented by the porosity field on a background mesh. The application of the present method in both pore-scale and representative elementary volume (REV-scale) simulations are checked by performing a series of test cases, including interfacial momentum/heat/mass transport, conjugate heat/mass transfer, chemical reactions, and two practical applications containing reacting interfaces. An overall first-order convergence rate has been observed in both spatial and temporal accuracy tests.

The ϕ4 Oscillons in a Ball: Numerical Approach and Parallel Implementation

The ϕ4 Oscillons in a Ball: Numerical Approach and Parallel Implementation

Regularization errors introduced by the one-fluid formulation in the solution of two-phase elliptic problems

This manuscript discusses the structure of the errors in the solution of elliptic problems introduced by the regularization of the fluid properties discontinuity in a small region of finite size. By using a multiscale approach, the problem of the error calculation is splitted into an outer problem, where the regularization region is replaced by a sharp interface, and an inner local one dimensional problem that eventually imposes effective jump conditions across the interface for the outer problem. Except in some particular cases, the use of regularization techniques introduces first order errors in the solution imposing an error flux jump that is proportional to the tangential Laplacian of the averaged solution and an error jump that is proportional to the normal flux, both multiplied by a prefactor that depends on the averaging rule used. In general, the optimal averaging procedure is shown to depend on the structure of the problem at hand. The errors introduced by standard arithmetic and harmonic averages are obtained for various analytical and numerical examples which are used to discuss the nature of the errors introduced and the importance of first order errors in the solution. The influence of the ratio between the regularization thickness and the grid size is also investigated in numerical implementations of the one-fluid model.

Geometrically exact 3D arbitrarily curved rod theory for dynamic analysis: Application to predicting the motion of hard-magnetic soft robotic arm

Magnetorheological elastomers are active materials which can be actuated by the applied magnetic field. Hard magnetic soft (HMS) materials, a type of magnetorheological elastomers, show great potential in the fields of biomedical engineering and soft robotics, due to their short response time, remote operation, and shape programmability. To exploit its potential, a series of theoretical frameworks of HMS rods have been developed, but they are mainly limited to the static rod models or classical curved rod models that fail to consider the effect of the “initial curvature” on the distribution of the stress. In this work, we develop a curved rod theory to predict the 3D dynamic motion of the rod-like HMS robotics under large deformation. Based on the geometrically exact rod theory, we include the heterogeneous initial length of the longitudinal fiber caused by “initial curvature” into our model and obtain the reduced balance equations of the HMS robotics. As a result, the “tension-bending” and “shear-torsion” coupling effects of curved rods emerge in the present model. A numerical implementation of our model based on the classical Newmark algorithm is presented. To validate our model, three numerical examples, including the dynamic snap-through behavior of a bistable arch, are performed and compared with the simulation or experiment results reported in literatures, which show a good agreement. Finally, we experimentally study the 2D and 3D static and dynamic motion of a quarter arc HMS robotic arm under an applied magnetic field of 10 mT, and our model gives a satisfactory prediction, especially for static deformation.

Unbounded Domain Modeling in Axisymmetric Rotor Wake Analysis

Mitigating the effects of wind turbine wakes is a central part of wind farm design. This paper proposes a spectral solver for the axisymmetrical Ainslie wake model based on modified Laguerre basis functions over the semi-infinite radial domain and a marching scheme in the downstream direction. This orthogonal basis promises fast convergence and a low number of DOFs for discretizing the continuity and axial momentum equation, promising a computationally efficient method. The numerical implementation of the model could not be finished in time; preliminary results are presented but still show non-negligible conservation errors. The focus of this work lies, therefore, on a detailed derivation of the method and a discussion of the sources of numerical errors in the nonlinear terms, and due to the truncation of the spectral basis, a comparison of the solver outputs to other methods remains part of the ongoing work.

Implementation of Multi Extension in Blockchain-Based IoT Platform for Industrial IoT Devices

The rise of the Internet of Things (IoT) has led to the creation of technologies to improve human life. IoT involves integrating the Internet with the physical world, spanning applications like smart homes, industries, supply chains, academia, and more. By the end of 2020, around 212 billion IoT devices were globally deployed, presenting substantial opportunities for manufacturers and diverse applications. There have been numerous implementations of IoT across various fields, including Blockchain IoT (B-IoT), Artificial Intelligence of Things (AIoT), Digital Twin, and new communication protocols like the Matter protocol. We conducted a comprehensive testing of the blockchain (B-IoT) extension system on various bandwidths and scenarios, such as blockchain API execution time, speed, retention performance, and smart contract vulnerability testing. Our testing has been successful, and several messaging systems were used. Kafka was recommended to overcome the pending transaction problem caused by unprocessed messages. Our smart contract exhibited high severity. The Artificial Intelligence of Things extension, tested on real environments for person and vehicle counters, has shown successful results. Digital Twin, integrated into the IoT platform to perform and control 3D assets such as the postgraduate PENS building, has demonstrated efficient performance. Matter protocol achieved an average task execution speed of 0.48 tasks per second. Matter P2P communication was also successfully tested in this research by implementing the Access Control List (ACL) command.

Simhypo-sand: a simple hypoplastic model for granular materials and SPH implementation

This paper introduces a new hypoplastic model characterized by a simple and elegant formulation. It requires only 7 material parameters to depict salient mechanical behaviors of granular materials. The numerical implementation employs an explicit integration method, enhanced by a best-fit stress correction algorithm in a smoothed particle hydrodynamics code. The performance of this model in capturing soil behavior across a range of scenarios is demonstrated by conducting various numerical tests, including triaxial and simple shear at low strain rates, as well as granular collapse, rigid penetration and landslide process at high strain rates.

Inversion of the attenuated momenta ray transform of planar symmetric tensors

We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ray transform. The problem is recast as an inverse boundary value problem for a system of transport equations, which we solve by an extension of Bukhgeim’s A-analytic theory. The method of proof is constructive. To illustrate the reconstruction method, we present results obtained in the numerical implementation for the non-attenuated case of one-tensors.