Continuum Methods Research Articles

Hydro-mechanical modeling of cohesive crack propagation of concrete lining in high internal pressure tunnels

High pressure tunnels with concrete lining have been extensively utilized in project practice. However, due to the characteristic of concrete being susceptible to cracking under tension, the lining inevitably develops cracks under high internal water pressure, posing a serious threat to the operation of tunnels. This study aims at developing a hydro-mechanical numerical model of cohesive crack propagation of concrete lining in high internal pressure tunnels. In this regard, the determination of cohesive element parameters is elucidated, the contact simulation within the software ABAQUS is improved to accurately characterize the interface between lining and surrounding rock, and the numerical calculation process in ABAQUS is realized using indirect coupled method. The simulation results align well with the physical model test and engineering monitoring data, demonstrating that the proposed method can accurately simulate the hydraulic interactions of high pressure tunnel. Additionally, a comparison with calculation models employing tie constraints to simulate the lining-surrounding rock interface is conducted. Finally, comparison with traditional continuum method reveals that while both methods exhibit consistent overall trends. It is recommended to choose the proposed method when describing the discontinuous propagation process of cracks, which cannot be simulated by the continuum analysis method.

Stochastic hazard assessment framework of landslide blocking river by depth-integrated continuum method and random field theory

AbstractLandslide-induced barrier dams pose a threat to the safety of humans, livestock and nearby infrastructures. The efficient assessment of landslide blocking river is crucial for disaster prevention and mitigation solutions. This study proposes a novel stochastic assessment framework to evaluate the landslide blocking river through the prediction of their deposition depths and considering the heterogeneity of shear strength parameters on the potential sliding surface. The depth-integrated continuum method (DICM) is used to simulate the landslide runout process. Using an enhanced Karhunen-Loève expansion (KLE) method, the spatial variations in soil's shear strength parameters are modeled by random fields to incorporate the effects of soil's spatial heterogeneity on the landslide deposition pattern. Subsequently, the multi-response surrogate model is constructed to relate the random field variables to the deposition depths based on extreme gradient boosting (XGBoost). To improve the performance of the surrogate model, principal component analysis (PCA) and sliced inverse regression (SIR) methods are employed for the dimension reduction of output and input variables, respectively. Furthermore, the algorithm for river blockage identification is developed to search for the deposition ridges. To demonstrate the capability of the stochastic assessment framework, an example of the first Baige landslide in Tibet, China is simulated, and the affected region and deposition depths of the landslide are predicted to calculate the probability of river damming. The presented methodology provides a practical means for improving the landslide blocking river prediction and new insights for early warning and risk mitigation.

Implicit hydromechanical representation of fractures using a continuum approach

Fractures control fluid flow, solute transport, and mechanical deformation in crystalline media. They can be modeled numerically either explicitly or implicitly via an equivalent continuum. The implicit framework implies lower computational cost and complexity. However, upscaling heterogeneous fracture properties for its implicit representation as an equivalent fracture layer remains an open question. In this study, we propose an approach, the Equivalent Fracture Layer (EFL), for the implicit representation of fractures surrounded by low-permeability rock matrix to accurately simulate hydromechanical coupled processes. The approach assimilates fractures as equivalent continua with a manageable scale (≫1 μm) that facilitates spatial discretization, even for large-scale models including multiple fractures. Simulation results demonstrate that a relatively thick equivalent continuum layer (in the order of cm) can represent a fracture (with aperture in the order of μm) and accurately reproduce the hydromechanical behavior (i.e., fluid flow and deformation/stress behavior). There is an upper bound restriction due to the Young's modulus because the equivalent fracture layer should have a lower Young's modulus than that of the surrounding matrix. To validate the approach, we model a hydraulic stimulation carried out at the Bedretto Underground Laboratory for Geosciences and Geoenergies in Switzerland by comparing numerical results against measured data. The method further improves the ability and simplicity of continuum methods to represent fractures in fractured media.

Reproducing the Solvatochromism of Merocyanines by PCM Calculations.

Polarizable continuum methods (PCM) have been widely employed for simulating solvent effects, in spite of the fact that they either ignore specific interactions in solution or only partially reproduce non-specific contributions. Examples of three solvatochromic dyes with a negative, a positive and a reverse behavior illustrate the achievements and shortcomings of PCM calculations and the causes for their variable success. Even when qualitatively mimicking non-specific solvent effects, departures of calculated values from experimental data may be significant (20-30%). In addition, they can utterly fail to reproduce an inverted behavior that is caused by significant specific contributions by the solvent. As shown through a theoretical model that rationalizes and predicts the solvatochromism of phenolate merocyanines based on DFT (Density Functional Theory) descriptors in the gas phase, PCM shortcomings are to be held responsible for its eventual failure to reproduce experimental data in solution.

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

Seismic performance analysis and control method of composite coupled shear wall with steel plate-fiber reinforced concrete coupling beams

This paper based on the study of steel plate-fiber reinforced concrete coupling beam components, designs a basic model of composite coupled shear walls with steel plate-fiber reinforced concrete coupling beams. The seismic performance of this model was numerically simulated using the ABAQUS finite element software, analyzing the stress distribution of various parts and the development pattern of plastic hinges in the structure. It also examines how factors such as axial compression ratio, coupling beam cross-sectional dimensions, single-sided wall limb aspect ratio, and total floor height affect the seismic performance of this type of coupled shear wall, providing a reasonable range for axial compression ratios and coupling ratios for composite coupled shear walls with steel plate-fiber reinforced concrete coupling beams. Based on the obtained reasonable axial compression ratio and coupling ratio, and using the analytical solution of the continuum method, a method for controlling the seismic performance of coupled shear wall structures was proposed. Results show that the composite coupled shear walls with steel plate-fiber reinforced concrete coupling beams exhibit high load-bearing capacity and lateral stiffness under inverted triangular horizontal loads, with good displacement ductility and strong energy dissipation capability, making it an excellent seismic performance coupled shear wall system. As the axial compression ratio increases, the displacement corresponding to the yield point and peak point of the structure gradually decreases, and the displacement ductility coefficient shows a trend of first increasing and then decreasing; it is recommended that when designing steel plate-fiber reinforced concrete coupling beam-coupled shear walls, the axial compression ratio should not exceed 0.3. Numerical analysis of coupling ratio-related parameters indicates that in high-intensity seismic design areas, the range of coupling ratios should be between 45% and 60%.

Subspace graph networks for real-time granular flow simulation with applications to machine-terrain interactions

Granular flows interacting with rigid bodies are key to machine-terrain interactions in robotics and related fields, and still pose several open problems. Continuum methods and deep learning, separately and in combination, show promise. This research advances machine learning methods for modeling rigid body-driven granular flows, for terrestrial industrial machine and planetary rover (where gravity is an important factor) applications. The original contribution of this research is the application of a subspace machine learning simulation approach for these engineering problems. To generate training datasets, a high-fidelity continuum method, the material point method (MPM) is utilized. Principal component analysis (PCA) is used to reduce the dimensionality of data. It is shown that the first few (8 in our datasets) principal components of our high-dimensional data keep almost the entire variance in data. A graph network simulator (GNS) is trained to learn the underlying subspace dynamics. The learned GNS is then able to predict particle positions and interaction forces with good accuracy, averaging 6×10−5 and 3×10−6 mean squared position error and 7% and 17% mean percentage force error, for excavation and wheel data, respectively. More importantly, PCA significantly enhances the time and memory efficiency of GNS in both training and rollout. This enables GNS to be trained using a single desktop graphics processing unit (GPU) with moderate video random-access memory (VRAM). This also makes the GNS real-time on large-scale 3D physics configurations (700x faster than our continuum method), which is the first demonstration of such significantly accelerated high-fidelity granular flow engineering simulations.

Study on copper-to-copper bonding of three-dimensional integrated circuits using the quasicontinuum method

Cu-Cu bonding presents an attractive approach to bottom-up manufacturing, facilitating nanoparticle production, linking, and restoration. The ramifications of varying bonding depths and orientations exhibit distinct characteristics. At the same time, investigations into the material composition of nanoscale bonded pairs involve scrutiny of atomic slippage, strain distribution, and the force-displacement profile. The methodology simulates the Cu-Cu bonding process by implementing the quasi-continuum (QC) approach, constituting a multifaceted mixed molecular dynamics technique integrating atomistic and continuum methods. The analysis of results reveals variations in the Contact effect induced by the four orientations, along with discrepancies in the atomic slippage observed in distinct directions. Notably, a pronounced distinction is discernible in the directional movement. Specifically, the strained regions on the flat surface of the lower substrate, characterized by the directionality of X[001]-Y[110], exhibit a notably broader range of atomic slip compared to regions strained by alternative orientations. Furthermore, the directional alignment of X[110]-Y[111] illustrates that irrespective of whether the lower substrate’s surface is flat or rough, the orientation of atomic slip diverges. In conclusion, our study employed a quasi-continuous method to explore the bonding efficacy of copper-to-copper interfaces on flat and irregular substrate surfaces. Through this approach, we scrutinized the distributions of strain, stress, average Newtonian force, and atom differential arrangement direction across different orientations.

What Is the Black Hole Spin in Cyg X-1?

We perform a detailed study of the black hole spin of Cyg X-1, using accurate broadband X-ray data obtained in the soft spectral state by simultaneous NICER and NuSTAR observations, supplemented at high energies by INTEGRAL data. We use the relativistic disk model kerrbb together with different models of the Comptonization high-energy tail and the relativistically broadened reflection features. Unlike most previous studies, we tie the spin parameters of the disk and relativistic broadening models, thus combining the continuum and reflection methods of spin determination. We also consider a likely increase of the disk color correction due to a partial support of the disk by large-scale magnetic fields. We find that such models yield a spin parameter of a*=0.87−0.03+0.04 if the disk inclination is allowed to be free, with i=39°−1+1 . Assuming i = 27.°5, as determined by optical studies of the binary, worsens the fit but leads to similar values of the spin, a*=0.90−0.01+0.01 . In addition, we consider the presence of a warm Comptonization layer on top of the disk, motivated by successful modeling of soft X-ray excesses in other sources with such a model. This dramatically lowers the spin, to a * ≲ 0.1, consistent with the spin measurements from black hole mergers. On the other hand, if the natal spin of Cyg X-1 was low but now a * ≈ 0.9, a period of effective supercritical accretion had to take place in the past. Such accretion could be facilitated by photon advection, as proposed for ultraluminous X-ray sources.

Energy transfer efficiency and rock damage characteristics of a hydraulic impact hammer with different tool shapes

The energy transfer efficiency and damage characteristics are the theoretical basis for the selection and optimization of hydraulic impact hammer tools. In this paper, quarter three-dimensional models of the piston-tool-rock system are established based on the continuum and discontinuum element method. The incident and reflected stress waves and rock damage characteristics obtained from the simulation model are in good agreement with experimental and theoretical results. The effects of piston impact velocity, tool shape, rock strength, confining pressure and repeated impacts on rock damage zone and energy transfer efficiency between tool and rock are analyzed. The force-penetration curves and penetration coefficients under different impact velocities, rock strength, and confining pressure conditions are obtained. The results illustrate that the energy transfer efficiency and penetration coefficient increase with the increase of rock strength, confining pressure and tip area of tool, but decrease with the increase of impact velocity. Based on the simulation results, a prediction formula for penetration force with consideration of the shape of the tool tip is proposed and the calculation accuracy is verified. Finally, the proportion of energy actually used for rock fracturing is analyzed.

Black Hole Spin Measurements in LMC X-1 and Cyg X-1 Are Highly Model Dependent

The black hole spin parameter, a *, was measured to be close to its maximum value of 1 in many accreting X-ray binaries. In particular, a * ≳ 0.9 was found in a number of studies of LMC X-1. These measurements were claimed to take into account both statistical and systematic uncertainties. We perform new measurements using a recent simultaneous observation by NICER and NuSTAR, providing a data set of high quality. We use the disk continuum method together with improved models for coronal Comptonization. With the standard relativistic disk model and optically thin Comptonization, we obtain values of a * similar to those obtained before. We then consider modifications to the standard model. Using a color correction of 2, we find a * ≈ 0.64–0.84. We then consider disks with dissipation in surface layers. To account for that, we assume the standard disk is covered by a warm and optically thick Comptonizing layer. Our model with the lowest χ 2 then yields a*≈0.40−0.32+0.41 . In order to test the presence of such effects in other sources, we also study an X-ray observation of Cyg X-1 by Suzaku in the soft state. We confirm the previous findings of a * > 0.99 using the standard model, but then we find a weakly constrained a*≈0.82−0.74+0.16 when including an optically thick Comptonizing layer. We conclude that determinations of the spin using the continuum method can be highly sensitive to the assumptions about the disk structure.

Improved alpha shape-based continuum method for long-term density propagation

Improved alpha shape-based continuum method for long-term density propagation

A multi-segment alpha shape-based continuum method for long-term density propagation with bifurcation

A multi-segment alpha shape-based continuum method for long-term density propagation with bifurcation

A State-of-the-Art Review on Computational Modeling of Dynamic Soil–Structure Interaction in Crash Test Simulations

The use of nonlinear, large-deformation, dynamic finite element analysis (FEA) has become a cornerstone in crash test simulations, playing a pivotal role in evaluating the safety performance of critical civil infrastructures, including soil-embedded vehicle barrier systems. This review paper offers a detailed examination of numerical modeling methodologies employed for simulating dynamic soil–structure interactions in crash test simulations, with a particular focus on dynamic impact pile–soil interaction. This interaction is a critical determinant in assessing the effectiveness of soil-embedded barrier systems during vehicular impacts. Our extensive review methodically categorizes and critically evaluates four prevalent modeling methodologies: the lumped parameter method, the subgrade reaction method, the modified subgrade reaction approach, and the direct or mesh-based continuum method. We explore each methodology’s underlying philosophy, strengths, and shortcomings in accurately simulating the dynamic interaction between soil and piles under impact loading. This technical review aims to provide a thorough understanding of the critical and distinctive aspects of modeling soil’s dynamic responses under impact loading conditions. Moreover, this paper is envisioned to serve as a foundational reference for future research endeavors, steering the advancement of innovative simulation techniques for tackling the dynamic impact soil–structure interaction problem.

Exploring the influence of size-related factors on geocell-reinforced soil response using coupled continuum-discontinuum analysis

Size-related factors, such as the dimensions and cell count of geocell, play a crucial role in determining the effectiveness of soil reinforcement. In this study, a 3D coupled framework that leverages the strengths of both continuum and discontinuum methods was developed to investigate the influence of pocket size and multi-cell configuration on geocell-reinforced soils. To unveil the impact of size-related factors on soil-geocell interactions, reinforced soils containing various geocell configurations (single large-sized cell, multiple small-sized cells), as well as geocell-free soils subjected to increasing levels of confining pressure were extensively examined. This thorough investigation aimed to establish correlations between macroscopic responses and underlying micromechanical mechanisms. Our findings revealed that the presence of the geocell not only enhances the densification of interparticle contacts and reduces the number of floating particles that contribute minimally to load support, but also facilitates the concentration of force chains within the geocell structure. This leads to an increase in elastic stiffness along the loading axis. These observations highlight that the geocell's confining mechanism enhances both the load-carrying capacity and the infill rigidity, thereby preventing lateral soil spreading. In essence, the geocell serves to increase the soil's ability to withstand load and maintain its structural integrity laterally.

Континуум «массового» и «элитарного» в музыкальной культуре постиндустриальной эпохи

The article comprehends the problem of the continuum of «mass» and «elite» in musical culture. The authors note that the continuum method is becoming one of the most important methodological principles in the approach to its understanding and allows us to analyze all aspects from the perspective of established and constantly developing cultural objects with certain boundaries. One of the most important characteristics of the continuum is the mobility of its contours, the content of which is determined by the specifics of the categories that fix a certain state of culture, its properties in the endless process of cultural development. It seems that in the XX-early XXI centuries «mass» and «elite» can be attributed to them, the dialectic of which determines the peculiarities of the development of musical culture in the chronotype of the post-industrial era, becomes its peculiar sign, since the essence of culture is always manifested through certain of its texts. The «mass» in the musical culture of the post-industrial era dominates and leads to the deformation not only of the artistic and aesthetic completeness of the development of musical art forms in all their diversity, but also to the distortion of the socially regulating role of music as a cultural phenomenon.

A method for calculation of lateral displacements of buildings under distributed loads

Lateral displacement is a vary important parameter that we need to calculate when structures are subjected to lateral loads like earthquake and wind loads. In this study, a method is proposed for lateral displacement calculation of structures with different structural systems in different planes. This method is based on the continuum system calculation model. The method suggested in the literature for only top displacement in the case of uniform loading, is developed in this study for the calculation of displacements at each storey level and also in both uniform and triangular loading conditions. At the end of the study, twenty-eight storey building with shear wall-frame bearing system, which was taken from the literature, was solved with the presented method and Finite Element Method. The shear walls were modelled with three different element types for the analysis with the Finite Element Method with structural engineering program used. The results, obtained from the Continuum Method and Finite Element Method were presented in tables and by figures. Thus, the compatibility of the proposed method with the classical Finite Element Method was investigated. From the compared results of the method and the literature or finite element models it was seen that the method used for the case of uniform or triangular distributed loading gives very close results.

(Invited) Multiscale Modeling of Heterogeneous Interfaces for Hydrogen Production

Improving performance of hydrogen production devices requires a detailed understanding of physicochemical processes at solid-gas and solid-liquid interfaces. However, probing behavior of these interfaces under working conditions remain a significant challenge for both simulations and experimental techniques. In this talk, I will provide an overview of our strategy for simulating heterogeneous interfaces within the HydroGEN Advanced Water Splitting Materials Consortium, ranging from first-principles calculations of chemical reactivity to machine learning approaches for accelerating theory-experiment integration and continuum methods for understanding microstructure effects. In particular, I will discuss how computational models can be used to elucidate mechanisms of interface chemical reactions and mass transport, as well as the formation of new phases and their impacts on materials stability and performance. I will also show how simulations have been integrated with experimental probes, such as X-ray spectroscopy, to obtain new understanding of materials interfaces under operating conditions. Finally, I will discuss how this understanding is being used to guide new strategies for improving materials functionality for hydrogen production.This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

First X-Ray Polarization Measurement Confirms the Low Black Hole Spin in LMC X-3

X-ray polarization is a powerful tool to investigate the geometry of accreting material around black holes, allowing independent measurements of the black hole spin and orientation of the innermost parts of the accretion disk. We perform X-ray spectropolarimetric analysis of an X-ray binary system in the Large Magellanic Cloud, LMC X-3, that hosts a stellar-mass black hole, known to be persistently accreting since its discovery. We report the first detection of the X-ray polarization in LMC X-3 with the Imaging X-ray Polarimetry Explorer, and find the average polarization degree (PD) of 3.2% ± 0.6% and a constant polarization angle of −42° ± 6° over the 2–8 keV range. Using accompanying spectroscopic observations by NICER, NuSTAR, and the Neil Gehrels Swift observatories, we confirm previous measurements of the black hole spin via the X-ray continuum method, a ≈ 0.2. From polarization analysis only, we found consistent results with low black hole spin, with an upper limit of a < 0.7 at a 90% confidence level. A slight increase in the PD with energy, similar to other black hole X-ray binaries in the soft state, is suggested from the data but with a low statistical significance.

On Topology Optimisation Methods and Additive Manufacture for Satellite Structures: A Review

Launching satellites into the Earth’s orbit is a critical area of research, and very demanding satellite services increase exponentially as modern society takes shape. At the same time, the costs of developing and launching satellite missions with shorter development times increase the requirements of novel approaches in the several engineering areas required to build, test, launch, and operate satellites in the Earth’s orbit, as well as in orbits around other celestial bodies. One area with the potential to save launching costs is that of the structural integrity of satellites, particularly in the launching phase where the largest vibrations due to the rocket motion and subsequent stresses could impact the survival ability of the satellite. To address this problem, two important areas of engineering join together to provide novel, complete, and competitive solutions: topology optimisation methods and additive manufacturing. On one side, topology optimisation methods are mathematical methods that allow iteratively optimising structures (usually by decreasing mass) while improving some structural properties depending on the application (load capacity, for instance), through the maximisation or minimisation of a uni- or multi-objective function and multiple types of algorithms. This area has been widely active in general for the last 30 years and has two main core types of algorithms: continuum methods that modify continuous parameters such as density, and discrete methods that work by adding and deleting material elements in a meshing context. On the other side, additive manufacturing techniques are more recent manufacturing processes aimed at revolutionising manufacturing and supply chains. The main exponents of additive manufacturing are Selective Laser Melting (SLM) (3D printing) as well as Electron Beam Melting (EBM). Recent trends show that topology-optimised structures built with novel materials through additive manufacturing processes may provide cheaper state-of-the-art structures that are fully optimised to better perform in the outer-space environment, particularly as part of the structure subsystem of novel satellite systems. This work aims to present an extended review of the main methods of structural topology optimisation as well as additive manufacture in the aerospace field, with a particular focus on satellite structures, which may set the arena for the development of future satellite structures in the next five to ten years.