Elastic Model Research Articles

Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model

Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model

Analysis of mechanical response and failure characteristics of tunnels crossing active faults considering axial force and geometrical nonlinearity

Tunnels subjected to active fault dislocation may experience significant damage. This paper establishes a novel methodology and solution procedure for analyzing the mechanical response and failure characteristics of tunnels subjected to active fault dislocation based on an elastic foundation beam model. The proposed methodology includes axial, transverse, and vertical soil-tunnel interaction terms, in addition to geometrical nonlinearity and axial force terms in the governing equation. This approach has a significantly extended application range, effectively addressing the problems encountered in tunnels crossing active faults with diverse crossing angles, dip angles, and fault types. The proposed methodology is verified by comparison to a 3D FEM model with various fault types, experimental tests, and on-site case, and the results are in excellent quantitative and qualitative agreement with the numerical, experimental, and on-site results. When fault displacement is below 0.5m, disregarding geometric nonlinearity results in calculation errors of approximately 10% to 17% for peak axial force (Nmax), 18% to 22% for peak shear force (Vmax), and 20% to 30% for peak bending moment (Mmax). Finally, the responses caused by different factors, i.e., fault type, fault displacement, tunnel stiffness, and tunnel diameter, are investigated in detail to better understand tunnels crossing active faults. The results show that amongst the various fault types, the Vmax and the Mmax experienced by tunnels subjected to oblique slip-fault dislocation surpass those of other fault types, accompanied by the most extensive failure range. The augmentation of fault displacement, tunnel stiffness, and tunnel diameter precipitates a corresponding escalation in the Nmax, Vmax, Mmax, and failure range. Under oblique-slip fault dislocation, the tunnel undergoes an initial phase of shear failure, followed by tension-bending failure, delineated by distinct fault displacement thresholds of 0.1m and 0.2m, respectively. The proposed methodology provides the advantage of reliable stability analysis and design of tunnels crossing active faults.

Modeling microgel swelling: Influence of chain finite extensibility.

Microgels exhibit the ability to undergo reversible swelling in response to shifts in environmental factors that include variations in temperature, concentration, and pH. While several models have been put forward to elucidate specific aspects of microgel swelling and its impact on bulk behavior, a consistent theoretical description that chains throughout the microscopic degrees of freedom with suspension properties and deepens into the full implications of swelling remains a challenge yet to be met. In this work, we extend the mean-field swelling model of microgels from Denton and Tang [J. Chem. Phys. 145, 164901 (2016)] to include the finite extensibility of the polymer chains. The elastic contribution to swelling in the original work is formulated for Gaussian chains. By using the Langevin chain model, we modify this elastic contribution in order to account for finite extensibility effects, which become prominent for microgels containing highly charged polyelectrolytes and short polymer chains. We assess the performance of both elastic models, namely for Gaussian and Langevin chains, comparing against coarse-grained bead-spring simulations of ionic microgels with explicit electrostatic interactions. We examine the applicability scope of the models under a variation of parameters, such as ionization degree, microgel concentration, and salt concentration. The models are also tested against experimental results. This work broadens the applicability of the microgel swelling model toward a more realistic description, which brings advantages when describing the suspensions of nanogels and weak-polyelectrolyte micro-/nanogels.

Simulation of stress in a blood vessel due to plaque sediments in coronary artery disease.

Atherosclerosis is a cardiovascular disease mainly caused by plaque deposition in blood vessels. Plaque comprises components such as thrombosis, fibrin, collagen, and lipid core. It plays an essential role in inducing rupture in a blood vessel. Generally, Plaque could be described as three kinds of elastic models: cellular Plaque, hypocellular Plaque, and calcified Plaque. The present study aimed to investigate the behavior of atherosclerotic plaque rupture according to different lipid cores using Fluid-Structure Interaction (FSI). The blood vessel was also varied with different thicknesses (0.05, 0.25, and 0.5 mm). In this study, FSI simulation with a cellular plaque model with various thicknesses was investigated to obtain information on plaque rupture. Results revealed that the blood vessel with Plaque having a lipid core represents higher stresses than those without a lipid core. Blood vessels' thin thickness, like a thin cap, results in more considerable than Von Mises stress. The result also suggests that even at low fracture stress, the risk of rupture due to platelet decomposition at the gap was more significant for cellular plaques.

Development in the Study of Mechanical Prop-erties and Damage Constitutive Models of Rub-ber-Reclaimed Concrete

Advances in rubber-reinforced concrete technology and its applications in engineering are cru-cial for the thorough recycling and safe disposal of waste tire rubber and construction debris. Rubber-reinforced concrete (RAC) is a concrete material produced by substituting some fine and coarse aggregates with waste rubber particles and recycled aggregates. The incorporation of waste rubber particles endows RAC with distinctive mechanical properties and a distinct damage constitutive model. The mechanical properties of rubber recycled concrete mainly in-clude compressive strength, tensile strength, flexural strength, and elastic modulus. Compared to traditional concrete, RAC exhibits slightly lower compressive and flexural strengths but sig-nificantly enhanced tensile strength. This is due to the changes in mechanical properties caused by the softness and elastic properties of rubber particles. In addition, the addition of rubber particles can also improve the energy absorption capacity and impact resistance of concrete. On the other hand, in order to describe the damage behavior of rubber recycled con-crete, some constitutive models were studied. Common models include linear elastic model, plastic model, and damage model. The linear elastic model is suitable for describing the be-havior of rubber recycled concrete during the elastic stage; The plastic model is suitable for describing its deformation behavior during the plastic stage; The damage model can better describe the fracture and failure behavior of rubber recycled concrete, including shear damage, tensile damage, and compression damage. Tailored to the unique characteristics of RAC, these models consider the stiffness of rubber particles and the deformation characteristics of the binding materials, enabling accurate predictions of the stress-strain behavior of RAC. In conclusion, rubber-reinforced concrete possesses excellent mechanical and durability proper-ties, which can be accurately described and predicted using appropriate constitutive models. These findings are crucial for advancing the application and development of rubber-reinforced concrete.

Finite element modelling of pipe piles driven in low-to-medium density chalk under monotonic axial loading

Percussive driving in low-to-medium density chalk creates a thin annulus of fully de-structured ‘putty’ chalk around pile shafts and an outer annular zone where fracturing is more intense than in the natural chalk. This damage and the related generation, and subsequent equalisation, of excess pore pressures impacts the piles’ time-dependent axial loading behaviour, as do other ageing processes. This paper presents finite element analyses of open steel tubular piles driven for the recent ALPACA and ALPACA Plus research projects under monotonic axial loading to failure after extended ageing periods. A nonlinear elastic stiffness model with a nonlocal deviatoric strain-based Mohr-Coulomb failure criterion was employed, with different sets of properties to represent the de-structured, fractured chalk and intact chalk. It is shown that the piles’ axial responses are mainly controlled by the puttified chalk annuli. A simplified but efficient means is adopted to impose pre-loading chalk effective stress conditions that explicitly capture the effects of installation damage and subsequent ageing. The potential for strain-softening in the brittle chalk is examined and the effective stress paths developed in representative chalk elements throughout the loading are considered in conjunction with the mobilisation of accumulated deviatoric strains. The simulations indicate 264% higher shaft capacity in compression than in tension, which is mainly attributed to the internal chalk plug.

RVE determination and developement of an anisotropic elastic model for auxetic sheet metal

This article deals with the development of an elastic tetragonal model for the 2D auxetic rotating units structures in the framework of orthogonal transformations. The existing anisotropy in the structure was first determined by numerical simulations on the samples with different pattern orientation angles. A suitable representative volume element (RVE), which correctly represents the mechanical properties of the whole structure both in macroscale and in microscale, was then proposed by implementation of the kinematic periodic boundary conditions. In the next step, with the help of the orthogonal transformations relations, an anisotropic elastic model was developed, which correctly reflects the present tetragonal symmetry in the structure. Finally, the model parameters were identified and validated with the help of the corresponding experiments

Energy‐principle‐based analysis of elastic instability in polymer cylinders subject to surface tension

AbstractAn elastic instability model of polymer cylinder subject to surface tension is studied by energy functional analysis. The no‐classical boundary conditions and equilibrium equation are derived by introducing stress double harmonic function. The criteria of instability with surface tension contribution are deduced by substituting stress solution into boundary conditions. The results show that the criterion equation of elastic instability is relevant to the radius and intrinsic scale and instable wavelength or wavenumber of cylinder. Therefore, the relation between shear modulus and surface tension has the same trend comparing with the result of Barrierès' et al. This study provides insights into the instability of polymer and has important implications for the development of nanoscale cylindrical element in micro electro mechanical systems (MEMS) or nano electro mechanical systems (NEMS).

Robotica: decoupled elastostatic stiffness modeling of hybrid robots

Abstract A decoupling method is proposed for the elastic stiffness modeling of hybrid robots based on the rigidity principle, screw theory, strain energy, and Castigliano’s second theorem. It enables the decoupling of parallel and serial modules, as well as the individual contributions of each elastic component to the mechanism’s stiffness performance. The method is implemented as follows: (1) formulate limb constraint wrenches and corresponding limb stiffness matrix based on the screw theory and strain energy, (2) formulate the overall stiffness matrix of parallel and serial modules corresponding to end of the hybrid robots based on the rigidity principle, principle of virtual work, the wrench transfer formula, and strain energy methods, and (3) obtain and decouple the overall stiffness matrix and deflection of the robot based on the Castigliano’s second theorem. Finally, A planar hybrid structure and the 4SRRR + 6R hybrid robot are used as illustrative examples to implement the proposed method. The results indicate that selectively enhancing the stiffness performance of the mechanism is the most effective approach.

MinActionPath2: path generation between different conformations of large macromolecular assemblies by action minimization.

Recent progress in solving macromolecular structures and assemblies by cryogenic electron microscopy techniques enables sampling of their conformations in different states that are relevant to their biological function. Knowing the transition path between these conformations would provide new avenues for drug discovery. While the experimental study of transition paths is intrinsically difficult, in-silico methods can be used to generate an initial guess for those paths. The Elastic Network Model (ENM), along with a coarse-grained representation (CG) of the structures are among the most popular models to explore such possible paths. Here we propose an update to our software platform MinActionPath that generates non-linear transition paths based on ENM and CG models, using action minimization to solve the equations of motion. The new website enables the study of large structures such as ribosomes or entire virus envelopes. It provides direct visualization of the trajectories along with quantitative analyses of their behaviors at http://dynstr.pasteur.fr/servers/minactionpath/ minactionpath2_submission.

Anisotropic functionally graded nano-beam models and closed-form solutions in plane gradient elasticity

This study delves into the investigation of exact analytical solutions for the plane stress and displacement fields within linear homogeneous anisotropic nano-beam models of gradient elasticity. It focuses on solving the Helmholtz equation, which encompasses a second-order non-homogeneous linear partial differential equation in plane gradient elasticity theory, utilizing polynomial series-type solutions. The analysis centers on the utilization of gradient Airy stress functions to derive stress fields in the gradient theory. The research yields closed-form analytical solutions for Airy stress functions, stress, and strain fields in both classical and gradient theories. The study considers five distinct types of two-dimensional functionally graded cantilever beams with various boundary conditions: a cantilever anisotropic nano-beam subjected to a concentrated force at the free end, a cantilever anisotropic nano-beam under a uniform load, a simple anisotropic nano-beam under a uniform load, a propped cantilever anisotropic nano-beam under a uniform load, and a fixed end cantilever anisotropic nano-beam under a uniform load. General analytical solutions for the gradient stress and displacement fields of two-dimensional and one-dimensional anisotropic nano-beams under different boundary conditions are provided. The study showcases significant strain gradient size effects at the nano-scale through the derived analytical solutions for anisotropic beams. Additionally, it demonstrates that the strain gradient theory results for the limit case of the gradient coefficient c precisely align with results for isotropic and anisotropic materials in elasticity theory and classical theory. Furthermore, real-world applications are discussed, considering stress and displacement fields in real anisotropic materials such as TiSi2 single crystals and orthotropic materials, which are special cases of anisotropic materials like wood and epoxy as documented in the literature.

Hybrid method for hydraulic transient analysis of liquid pipe networks based on characteristic lines and equivalent circuits

Water hammer poses a significant concern in the transportation of pipelines and pipe networks. Due to the passage of reflection of water hammer waves at nodes, a large number of high-frequency pressure fluctuation signals appear in the pipe network, demanding an intensive computational workload. A novel hybrid method based on characteristic lines and equivalent circuits is proposed for the accurate and fast simulation of pipe networks. Multiple methods are employed for the simulation of pipelines and pipe networks, followed by a comparative analysis. The accuracy of the hybrid method is validated by comparing the proposed method with simulation results of commercial software. The hybrid method reduces the significant computational workload inherent in the classic method of characteristics and enhances the accuracy at high frequencies in the state-of-the-art elastic water column model. A trade-off between simulation accuracy and computation speed is achieved by adjusting the time step. The accuracy of calculating higher-frequency pressure fluctuations is further validated with an increase in the pipe diameter and a corresponding reduction in the friction loss. Generally, this method enables the simultaneous descriptions of high-frequency characteristics and nonlinear friction loss, enhancing calculation speed with little impact on the accuracy. The results demonstrate that the proposed model can be utilized for the transient analysis of pipe networks, providing support for predicting system performance and designing optimal strategies.

Study of fluid-elastic instability of the spatially bent tube structure in fast reactor intermediate heat exchanger

This study conducts a numerical simulation investigation on the flow field characteristics and fluid-elastic instability of the spatially bent tube structure in the intermediate heat exchanger (IHX) of a fast reactor. The inherent frequencies of the unique structure of the IHX spatially bent tube are calculated by using the wet modal method. They are employing Computational Fluid Dynamics (CFD) in conjunction with a fluid-structure coupling model, establishing an elastic tube model. Considering the bundle concentric circles arrangement, the “transition” arrangement is selected as the model to simulate the fluid-elastic instability. By the analysis of critical flow velocity, displacement, and the main vibration direction, the results indicate that the fluid-elastic instability of the tube bundle with a transition arrangement is mainly manifested by more severe vibrations in the bent tube segment. The instability flow velocity in the straight tube segment, ranging from 4.64 to 4.84 m/s, is greater than the instability flow velocity of 2.85 m/s in the bent tube segment. This study provides theoretical support for the design and operation of the intermediate heat exchanger in fast reactors, offering references for considering tube bundle arrangement and fluid-elastic instability in engineering practice.

Separation of source, attenuation and site parameters of 2 moderate earthquakes in France: an elastic radiative transfer approach

Summary An accurate magnitude estimation is necessary to properly evaluate seismic hazard, especially in low to moderate seismicity areas such as Metropolitan France. However, magnitudes of small earthquakes are subject to large uncertainties caused by major high-frequency propagation effects which are generally not properly considered. To address this issue, we developed a method to separate source, attenuation and site parameters from the elastic radiative transfer modeling of the full energy envelopes of seismograms. The key feature of our approach is the treatment of attenuation -both scattering and absorption- in a simple but realistic velocity model of the Earth’s lithosphere, including a velocity discontinuity at the Moho. To reach this goal, we developed a 2-step inversion procedure, allowing first to extract attenuation parameters for each source-station path from the whole observed energy envelope using the Levenberg-Marquardt and grid-search algorithms, then to determine site amplification and the source displacement spectrum from which the moment magnitude Mw is extracted. In the first step, we use the forward modeling procedure of Heller et al. (2022) in order to simulate energy envelopes by taking into account the full treatment of wave polarization, the focal mechanism of the source and the scattering anisotropy. The inversion procedure is then applied to the 2019 ML 5.2 Le Teil and 2014 ML 4.5 Lourdes earthquakes which both occurred in southern France. Data from 6 stations are selected for each event. The inversion results confirm a significant variability in the attenuation parameters (scattering and absorption) at regional scale and a strong frequency dependence. Scattering appears to be stronger towards the French Alps and Western Pyrenees. Absorption is stronger as frequency increases. Although not very resolvable, the mechanism of scattering appears to be forward or very forward. By inverting the source spectrum, we determine moment magnitudes Mw of 5.02 ± 0.17 for the Le Teil earthquake and 4.17 ± 0.15 for the Lourdes earthquake.

Using Artificial Intelligence to Predict Mortality in AKI Patients: A systematic review/Meta-Analysis

Abstract Background Acute kidney injury (AKI) is associated with increased morbidity/mortality. With artificial intelligence (AI), more dynamic models for mortality prediction in AKI patients have been developed using machine learning (ML) algorithms. The performance of various ML models were reviewed in their ability to predict in-hospital mortality (IHM) for AKI patients. Methods A literature search was conducted through Pubmed, Embase, and Web of Science Databases. Included studies contained variables regarding the efficacy of the AI model (AUC, accuracy, sensitivity, specificity, negative predictive value (NPV), and positive predictive value (PPV)). Only original studies which consisted of cross-sectional studies, prospective and retrospective studies were included, while reviews and self-reported outcomes were excluded. There was no restriction on time and geographic location. Results 8 studies with 37 032 AKI patients were included with a mean age of 65.3 years. The IHM was 18.0% in the derivation and 15.8% in the validation cohorts. The pooled (95% CI) AUC was observed to be highest for Broad Learning System (BLS) Models: [0.852 (0.820–0.883) and Elastic Net Final Model (ENF) [0.852 (0.813–0.891)] and lowest for proposed clinical model (PCM) [0.765 (0.716–0.814)]. The pooled (95% CI) AUC of BLS and ENF did not differ significantly from other models except PCM [Delong's test P = 0.022]. PCM exhibited the highest NPV, which supports this model's use as a possible rule out tool. Conclusion Our results show that BLS & ENF Models are equally effective as other ML models, in predicting in-hospital mortality with variability across all models. Additional studies are needed.

An enhanced quasi-3D HSDT for free vibration analysis of porous FG-CNT beams on a new concept of orthotropic VE-foundations

The original primary objective of this study is to conduct a comprehensive investigation into the free vibration behavior of beams with porosity, reinforced by carbon nanotubes (CNTs). These beams are supported by an arbitrary orthotropic variable elastic foundation (AOVEF). The focus lies on understanding how the presence of porosity and CNT reinforcement, coupled with the complex support provided by the AOVEF, influences the vibration characteristics of the beams. In addition, we intend to examine the impact of a number of micromechanical models on the vibration properties of these beams. Four carbon nanotube variables are introduced to symbolize several CNT variations. CNTs’ mechanical properties are examined through a variety of micromechanical models. Shear deformation effects are considered into account in the framework of higher-order shear deformation (HSDT) beam theory. The equations of motion are constructed using Hamilton’s concept and the equation system for the FG-CNT beam with supported ends is solved via the Navier methodology. A new approach in elastic foundation modeling is the Arbitrarily Orthotropic Variable Elastic (AOP-VE) foundation. It builds on the Winkler layer concept but introduces the idea of a variable response along the length of the beam foundation. Unlike the Winkler-Pasternak model, AOP-VE allows for control over the directional properties of the Pasternak foundation. The study looks into multiple aspects, involving various distribution kinds of CNTs, the impact of Winkler and Pasternak factors, mode values, side-to-length ratio, porosity, and angle variation. The results indicate that these parameters have a major effect on the inherent vibration features of FG-CNT beams. The study results in various novel findings that improve the understanding of the subject topic and set a standard for future studies.

Simulation of fretting wear in steel wires under variable coefficient of friction and variable wear coefficient

In this paper, the fretting wear behaviour of steel wires working in coal mining technology is studied numerically. In past studies, the fretting process of steel wires was carried out numerically considering that the coefficient of friction (COF) and wear coefficient (WC) are constant parameters. However, it has been noticed experimentally that COF increases up to a certain number of fretting cycles and then becomes constant, i.e. a steady-state stage, depending on the loading conditions. This increase in COF during the fretting process is also known as the running-up stage. The fretting wear model is modified to evaluate the influence of the varying coefficient of friction (VCOF), which is associated with the variable wear coefficient (VWC), so the influence of VWC is also considered. The subroutine UMESHMOTION used to implement the wear law is also modified to study the effect of VCOF and VWC. Therefore, in this study, the numerical results of a three-dimensional finite element (FE) model are compared, with analytical results of contact area and contact stresses, and with experimental results of peak wear depth. After validating the FE model, the wear scar, the increasing wear depth, wear volume, and the decreasing contact stress with increasing fretting cycles are determined numerically considering VCOF and VWC using cycle jump approach. The energy dissipation effect of frictional force and fretting amplitude is also studied for varying interaction properties of fretting wear models. The numerical simulations are performed by considering both elastic and plastic material properties to analyse the influence of varying interaction properties on fretting wear models at the running-up stage. The results indicate that the VWC model exhibits comparable impacts on both the elastic and plastic models. The results also show that the VWC fretting wear model leads to higher wear scar, wear volume, and wear depth values at the running-up stage as well as at the steady state stage, which are close to the experimental data.

Chromatin phase separation and nuclear shape fluctuations are correlated in a polymer model of the nucleus

ABSTRACT Abnormal cell nuclear shapes are hallmarks of diseases, including progeria, muscular dystrophy, and many cancers. Experiments have shown that disruption of heterochromatin and increases in euchromatin lead to nuclear deformations, such as blebs and ruptures. However, the physical mechanisms through which chromatin governs nuclear shape are poorly understood. To investigate how heterochromatin and euchromatin might govern nuclear morphology, we studied chromatin microphase separation in a composite coarse-grained polymer and elastic shell simulation model. By varying chromatin density, heterochromatin composition, and heterochromatin-lamina interactions, we show how the chromatin phase organization may perturb nuclear shape. Increasing chromatin density stabilizes the lamina against large fluctuations. However, increasing heterochromatin levels or heterochromatin-lamina interactions enhances nuclear shape fluctuations by a “wetting”-like interaction. In contrast, fluctuations are insensitive to heterochromatin’s internal structure. Our simulations suggest that peripheral heterochromatin accumulation could perturb nuclear morphology, while nuclear shape stabilization likely occurs through mechanisms other than chromatin microphase organization.

Γ-convergence of a discrete Kirchhoff rod energy

This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove Γ-convergence to the continuous model. This discrete energy is given by the bending and torsion energy of an interpolating conforming polynomial curve and provides a simple formula for the bending energy depending in each discrete segment only on angle and adjacent edge lengths. For the liminf-inequality, we need to introduce penalty terms to ensure arc-length parametrization in the limit. For the recovery sequence a discretization with equal Euclidean distance between consecutive points is constructed. Particular care is taken to treat the interaction between bending and torsion by employing a discrete version of the Bishop frame.

Effect of steel fibers and the fiber-concrete adhesion stress on the nonlinear shear behavior of beams

In this article, a theoretical model in nonlinear elasticity is presented to analyze the influence of the percentage of steel fibers and the effect of the fiber-concrete bond stress on the shear force at the rupture of beams subjected to the combined effect of bending moment, normal force, and shear force. For a given beam section, it is defined by a succession of layers of concrete and longitudinal steel elements. Each layer is defined by its height hi, width bi, and position relative to one end of the section YGi. Each longitudinal steel element is also defined by its cross-sectional area and position relative to one end of the section. The steel fibers are defined by volume percentages of 0.5%, 1%, 1.5%, and 2%, taking into account the mechanical nonlinearity of the materials. This model is based on the multilayer analysis of sections and an iterative solution procedure for each layer and each section, considering a given longitudinal deformation state and shear stress. The global equilibrium of the sections is analyzed under the assumption of flat longitudinal deformations but with, in principle, an interdependence of longitudinal normal stresses and shear stresses. In this study, using the principle of virtual work, equilibrium equations for deformations and stresses, as well as partial compatibility equations between concrete deformations and mean deformations, are derived. Comparative examples between ordinary reinforced concrete beams with variable shapes and reinforcement details, and those reinforced with steel fibers, are presented to demonstrate the accuracy of the proposed model for simulating the nonlinear shear response of beams.