Estimation Of Modulus Research Articles

Dark energy reconstruction analysis with artificial neural networks: Application on simulated Supernova Ia data from Rubin Observatory

In this paper, we present an analysis of Supernova Ia (SNIa) distance moduli (μ(z)) and dark energy using an Artificial Neural Network (ANN) reconstruction based on LSST simulated three-year SNIa data. The ANNs employed in this study utilize genetic algorithms for hyperparameter tuning and Monte Carlo Dropout for predictions. Our ANN reconstruction architecture is capable of modeling both the distance moduli and their associated statistical errors given redshift values. We compare the performance of the ANN-based reconstruction with two theoretical dark energy models: ΛCDM and Chevallier–Linder–Polarski (CPL). Bayesian analysis is conducted for these theoretical models using the LSST simulations and compared with observations from Pantheon and Pantheon+ SNIa real data. We demonstrate that our model-independent ANN reconstruction is consistent with both theoretical models. Performance metrics and statistical tests reveal that the ANN produces distance modulus estimates that align well with the LSST dataset and exhibit only minor discrepancies with ΛCDM and CPL.

Influence of initial state and residual stresses on the modulus-density relationship of geomaterials: insights from multiple experimental setups

ABSTRACT Quality control in pavement construction traditionally relies on density measurements of geomaterials. With the introduction of modulus measurement methods, a shift has occurred due to the operational advantages of modulus-estimating devices over conventional density measurement techniques. Modulus-based methods also provide valuable information for the mechanistic-empirical (ME) design of pavement layers. However, a challenge emerges as a single modulus measurement does not directly correspond to a specific density measurement, leading to concerns about replacing density measurements in quality control processes. While it is generally accepted that a geomaterial's modulus primarily depends on its moisture content and density or void ratio, this study explores the complex relationship between modulus and density, particularly in field scenarios with consistent moisture content. Using three different laboratory-scale test set-ups, characterised by unique loading and boundary conditions, the research highlights the significant role of a geomaterial's initial state in obtaining accurate modulus estimates. The results reveal that identical densities can exhibit variations in modulus due to differences in initial densities and the development of residual lateral stresses. These variations in field conditions often stem from different paving or spreading techniques, emphasising the need for a comprehensive approach when establishing density-modulus correlations..

A model-based approach for joint estimation of track irregularities and track support modulus from trackside measurements in railway turnouts

ABSTRACT The paper proposes a model-based approach for the concomitant estimation of track modulus, track irregularity, and dynamic loading by combining an analytical model of a beam on an elastic foundation with vibration data collected by a trackside measurement system. The model is empirically extended to incorporate the effects of dynamic wheel/rail interaction forces when both short wavelength defects (in the rail surface) and medium-long wavelength track irregularities (e.g. hanging sleepers, differential ballast settlement) are present. The power spectral density of the rail vertical acceleration is then exploited in combination with the extended model to estimate track parameters using least squares. The proposed method is validated on vibration data collected in a turnout of the Danish railway infrastructure over a period of 2.5 years. The obtained results show that changes over time in track modulus and track irregularities, and consequently in dynamic wheel/rail contact forces, can be efficiently monitored from trackside measurements.

SLM-printed lattice structures with tapered vertical struts: Design, simulation and experimentation

This study, designed new lattice structures using vertical struts that taper off. The degree of tapering was controlled using a parameter called “α”. To fabricate these structures, 3D-printing technology known as SLM (selected laser melting) was used. These lattice structures were also simulated using finite element analysis (FEA) and tested experimentally. The used material was 316L stainless steel. Stress–strain curves provided insights into their deformation behavior, revealing a noteworthy occurrence: the unloading modulus exceeded the loading modulus. The mechanical properties of these absolute and density-normalized lattice structures, demonstrated improvement with higher values of the shape parameter α. Yield stress increased by 31 %, loading modulus by 21 %, and energy absorption by 33 %. Specific yield stress improved by 24 %, and specific energy absorption increased by 27 %. While simulation and experimental results exhibited a correlation, they differed significantly in modulus estimation, with simulations overestimating it by more than 30 %.

Valorisation of bamboo stalk waste: eco-friendly synthesis and characterisation of activated carbon monolith

ABSTRACT In contemporary waste management, the escalating volumes of bamboo stalk waste present a pressing environmental challenge, necessitating innovative and sustainable solutions. This research examined the properties of activated carbon monolith (ACM) derived from bamboo stalk (BS) using a facile method. Polystyrene resin and KOH were employed as an eco-binder and activator in the monolith synthesis, respectively. Analytical methods were employed to characterise the mechanical, morphological, elemental, and textual profiles of the monolith obtained. The study's results indicated the creation of a monolith characterised by a rough, amorphous shape firmly secured by the binder. It revealed a BET surface area measuring 265 m2/g and a pore diameter of 2.8 nm. The monolith displayed various irregular void pores, forming a mesoporous morphological network, along with sporadically distributed slivery-white dot-like particles on its heterogeneous surface. EDX analysis also revealed the BS-ACM is largely composed of carbon (77%), potassium (11%), oxygen (8%), and trace amounts of aluminium, gold, iron, and plutonium. The compressive strength test indicated a peak force of 21,536 N before any significant signs of appreciable deformation were observed, with the subsequent estimation of Young's modulus at 8.34 MPa. Beyond advancing bamboo waste valorisation, the research aligns with circular economy principles and sustainable practices, presenting a promising pathway for developing eco-friendly materials and contributing to a more sustainable and resource-efficient future.

Estimation of Effective Bulk Modulus of Metamaterial Composites with Coated Spheres Using a Reduced Micromorphic Model

Estimation of Effective Bulk Modulus of Metamaterial Composites with Coated Spheres Using a Reduced Micromorphic Model

Most frequent value analysis of distance measurements to M87

Abstract We reanalyze the recent compilation of distance measurements to M87 by collecting the data from published literature. Different from the traditional statistical methods, based on the principle of minimum information loss, we use a robust most frequent value (MFV) procedure to estimate the distance to M87, irrespective of the Gaussian or non-Gaussian distributions. The MFV-based robust estimate for the M87 distance modulus is given by $31.09^{+0.04}_{-0.03}$(statistical)$^{+0.05}_{-0.07}$ (systematic) mag corresponding to a 68.27% confidence interval, whereas the result of combining the two uncertainties in quadrature is $31.09^{+0.06}_{-0.08}$ mag. We also construct the error distributions of M87 distance moduli values according to the weighted mean, median, and MFV, which is non-Gaussian. This demonstrates that the MFV method offers a more accurate and robust estimate of the distance to M87 compared to methods that depend on the unfulfilled assumption of Gaussianity.

Estimation of cement paste stiffness and UHPC elastic modulus through measured phase-property upscaling

The elastic stiffness of bulk concrete materials results from the complex interaction of aggregates, voids, and hydrated cement (which can have multiple hardened phases at multiple length scales). Given the complexities associated with understanding the arrangement of these particles within bulk concrete volumes, estimations for elastic modulus often rely on empirical correlations with unit weight and compressive strength. Such estimations are inherently scale-dependent and fail to capture variability in mix designs, particularly the variability found in specialty concrete mixes. To develop a scale-independent method for estimating elastic modulus from mix-design volume fraction information, this study explores a novel bottom-up approach using cement paste phase stiffness values determined through micro-mechanical experimentation and randomized Monte-Carlo spring arrangement simulations. Statistical representations of cement paste phase stiffness distributions and bulk volume fraction data are combined to provide estimations for elastic stiffness in both the composite cement paste and bulk concrete containing fine aggregate and fibers. Resulting a priori estimations of UHPC cement paste stiffness from the micro-mechanical upscaling simulations were within 4% of measured values (based on mix-design and void volume fraction information alone) for a selected sample of mix proportions. When applied to the two UHPC mixes containing fibers and fine aggregate, upscaling simulations consistently overpredicted the measured elastic modulus, likely due to the aggregate-cement interfacial transition zone (ITZ) properties that were not captured in the micro-mechanical testing.

Experimental and numerical based model formulation for estimation of subgrade resilient modulus using the repeated load CBR test considering in situ state of stress

Characterizing subgrade in terms of resilient modulus is a crucial aspect of flexible pavement design. This paper proposes a methodology and predictive model to estimate the resilient modulus with better consideration of subgrade soils’ in situ stress state using a simple Repeated Load CBR (RLCBR) test. RLCBR tests were conducted on eight subgrade soils at three moisture contents. Numerical studies were conducted by simulating the CBR test in the commercial package LS-DYNA® to understand the stress state under plunger loading concerning field conditions. A new model was proposed for the characterization of subgrade soils based on laboratory RLCBR tests and the FEM, considering the stress state experienced by subgrade soils in the field. The proposed model was validated using data from four other soils and showed good agreement. The study model showed a better predictive capacity for the low plastic subgrade soils than previously developed models. Practicing engineers can use the developed model for estimating the subgrade resilient modulus at the recommended stress state for mechanistic pavement design while understanding the soil’s load-deformation behavior.

Ulyanov inequalities for the mixed moduli of smoothness in mixed metrics

Abstract In this paper, mixed moduli of smoothness of functions of two variables are studied. We prove Ulyanov-type inequalities between mixed moduli of smoothness of positive orders in different metrics. Estimates for the mixed moduli of smoothness of the derivative of a function are also obtained in terms of the mixed moduli of smoothness of the function itself.

Reloading Modulus Estimation Based on Static and Dynamic Plate Load Tests Carried out on Unpaved Forest Roads

Reloading Modulus Estimation Based on Static and Dynamic Plate Load Tests Carried out on Unpaved Forest Roads

A New Rank Estimator for Least Squares Estimation of Weibull Modulus

The Weibull distribution is widely used in reliability analysis to evaluate the failure behavior and lifetime characteristics of various systems and components. One of the most commonly used methods for estimating the parameters of the Weibull distribution is the ordinary least squares (OLS) technique, which is based on fitting a linear regression model to the transformed data. This paper proposes a new rank estimator for ordinary least squares estimation of Weibull modulus, a key parameter used as a measure of variability in the data. The new rank estimator is a quadratic function of the order statistic number, with three parameters that are optimized by Monte Carlo simulations. Using relative efficiency as a criterion, the performance of the new rank estimator is compared with three commonly used rank estimators, mean, median and hazen rank estimators, which are linear functions of the order statistic number. The results show that the new rank estimator has a significant advantage over the other rank estimators for any sample size between 3 and 150. The findings also imply that other nonlinear functions, such as cubic polynomials, could be applied to further improve the efficiency of the parameter estimators of the ordinary least squares method.

Computational comparison study of virtual compression and shear test for estimation of apparent elastic moduli under various boundary conditions.

Virtual compression tests based on finite element analysis are representative noninvasive methods to evaluate bone strength. However, owing to the characteristic porous structure of bones, the material obtained from micro-computed tomography images in the finite-element model is not uniformly distributed. These characteristics cause differences in the apparent elastic moduli depending on the boundary conditions and affect the accuracy of bone-strength evaluation. Therefore, this study aimed to evaluate and compare the apparent elastic moduli under various, virtual-compression and shear-test boundary conditions. Four, nonuniform models were constructed with increasing model complexity. For representative boundary conditions, two, different, testing directions, and constrained surfaces were applied. As a result, the apparent elastic moduli of the nonuniform model varied up to 55.2% based on where the constrained surface was located in the single-end-cemented condition. Additionally, when connectivity in the test direction was lost, the accuracy of the apparent elastic moduli was low. A graphical comparison showed that the equivalent-stress distribution was more advantageous for analyzing load transferability and physical behavior than the strain-energy distribution. These results clearly show that the prediction accuracy of the apparent elastic moduli can be guaranteed if the boundary condition on the constraint and loading surfaces of the nonuniform model are applied symmetrically and the connectivity of the elements in the testing direction is well maintained. This study will aid in precision improvement of bone-strength-indicator determination for osteoporosis prevention.

Demonstrating a Quartz Crystal Microbalance with Dissipation (QCMD) to Enhance the Monitoring and Mechanistic Understanding of Iron Carbonate Crystalline Films.

This paper reports the real time monitoring of siderite deposition, on both Au- and Fe-coated surfaces, using the changes in frequency and dissipation of quartz crystal microbalance with dissipation (QCMD). In an iron chloride solution saturated with carbon dioxide, buffered with sodium bicarbonate to pH 6.8, roughly spherical particles of siderite formed within 15 min, which subsequently deposited on the QCMD crystal surface. Imaging of the surface showed a layer formed from particles ca. < 0.5 μm in diameter. Larger particles are clearly deposited on top of the lower layer; these larger particles are >1 μm in diameter. Monitoring of the frequency clearly differentiates the formation of the lower layer from the larger crystals deposited on top at later times. The elastic moduli calculated from QCMD data showed a progressive dissipation increase; the modeling of the solid-liquid interface using a flat approximation resulted in a poor estimation of elastic and storage moduli. Rather, the impedance modeled as a viscoelastic layer in contact with a semi-infinite liquid, where a random bumpy surface with a Gaussian correlator is used, is much more accurate in determining the elastic and storage moduli as losses from the uneven interface are considered. A further step considers that the film is in fact a composite consisting of hard spherical particles of siderite with water in the vacant spaces. This is treated by considering the individual contributions of the phases to the losses measured, thereby further improving the accuracy of the description of the film and the QCMD data. Collectively, this work presents a new framework for the use of QCMD, paired with traditional approaches, to enhance the understanding of crystal deposition and film formation as well as quantify the often evolving mechanical properties.

Discovering 3D hidden elasticity in isotropic and transversely isotropic materials with physics-informed UNets

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5 % for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5 %. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. Statement of significanceElasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity–the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics.

Indirect estimation of resilient modulus (Mr) of subgrade soil: Gene expression programming vs multi expression programming

Accurate prediction of resilient modulus (MR) in compacted subgrade soil is crucial for planning secure and environmentally friendly flexible pavement systems. This research assembled a dataset of 2813 data points from twelve compacted soils. The dry density, confining stress, deviator stress, number of freeze-thaw cycles, and moisture content were among the important variables considered for determining the MR. Subsequently, this study employs ensemble machine learning methodologies, specifically gene expression programming (GEP) and multi-expression programming (MEP), to investigate the subject further. The precision and anticipatory proficiency of both the GEP and MEP models are assessed through statistical evaluations, encompassing crucial metrics (R, RMSE, MAE, RSE, RRMSE, and ρ). The GEP and MEP models align well with validation criteria, underscoring their robustness in predicting novel data and showcasing their broad applicability. The GEP model consistently outperformed the MEP model, with higher coefficient of regression (R2) values in both training (0.992 vs. 0.983) and testing (0.981 vs. 0.972) phases, demonstrating its superior predictive accuracy and robustness. In summary, the GEP model consistently outperforms the MEP model in accuracy and prediction, making it the preferred choice for subgrade soil MR prediction. Sensitivity analysis was done, which ranked the parameters by their influence: dry density (26.6 %), confining stress (22.7 %), weighted plasticity index (15.3 %), moisture content (13.5 %), deviator stress (12.5 %), and freeze and thaw cycles (9.4 %). This research aims to enhance the utilization of GEP and MEP in civil engineering for more accurate and efficient MR prediction, ultimately reducing time and costs.

Uniform estimates for local properties of analytic functions in a complete Reinahrdt domain

Using recent estimates of maximum modulus for partial derivatives of the analytic functions with bounded $\mathbf{L}$-index in joint variables we describe maximum modulus of these functions at the polydisc skeleton with given radii by the maximum modulus with lesser radii. Such a description is sufficient and necessary condition of boundedness of $\mathbf{L}$-index in joint variables for functions which are analytic in a complete Reinhardt domain. The vector-valued function $\mathbf{L}$ is a positive and continuous function in the domain and its values at a point is greater than reciprocal of distance from the point to the boundary of the Reinhardt domain multiplied by some constant.

Shear modulus of sand-rubber mixtures: element testing and constitutive modeling

In this study, a series of resonant column tests was conducted to measure the shear modulus of sand-rubber mixtures at small strain amplitudes (i.e. between 10−4% and 10−2%), considering different rubber percentages and confining stress levels. The results were then combined with data obtained by dynamic hollow cylinder tests to investigate shear modulus degradation of the mixtures over a wider shear strain range. Based on the test results, a new expression was proposed to improve the prediction of maximum shear modulus of sand-rubber mixtures using the modified equivalent void ratio concept. A new constitutive model was also developed for estimation of strain-dependent shear modulus of the mixtures based on the modified hyperbolic framework. The shear modulus of the mixtures was found to be a function of rubber percentage, confining stress, the modified equivalent void ratio and the relative shear stiffness of rubber and sand. The experimental data and the developed models showed that the shear modulus decreased with rubber percentage and increased with confining stress. Moreover, the reference shear strain of the modified hyperbolic model increased with both rubber percentage and confining stress while its curvature coefficient increased more considerably with rubber percentage compared to the confining stress.

Advancement in Fabrication and Characterization Techniques of Nanocomposites.

Advancements in the field of materials research have unveiled numerous unparalleled features, such as mechanical properties, clinical advances, interfacial strengthening, and porosities, providing a wide range of applications. The employment of any material begins with fabrication and characterization, demanding expertise for the effective execution of the investigation. This review encompasses the details of the working principles of some significant and frequently used fabrication and characterization techniques for various material categories, including pellets and coatings. The discussion begins with techniques for fabricating materials for various applications. A brief overview of coating synthesis methods can provide intriguing information for researchers in the field of coating fabrication. The report highlights the portrayal of morphological and physiochemical analysis techniques, followed by the estimation of the elastic modulus using nanoindentation and dynamic modulus mapping testing for the materials. Additionally, the review covers theoretical models for observing the elastic moduli of the materials. The review depicts tribological investigations of the materials, aiming to provide insight into fretting wear, pin-on-disc, and microscratch testing. The fundamentals of electrochemical characterization are presented, including the appraisal of linear polarization and potentiodynamic polarization as well as electrochemical impedance spectroscopy. Furthermore, the magnetic behavior was examined by using a vibrating sample magnetometer (VSM), and the estimation of magnetic domains in the materials was conducted through magnetic force microscopy. Thus, the report suggests that readers, especially beginners, can gain a comprehensive understanding of the extensive prospects associated with the fundamental principles of material synthesis and characterization.

Lower average estimate for the minimum modulus on circles foran entire function of genus zero

The article was written based on the materials of the joint report of the authors, made by them at the Sixth International Conference “Functional spaces. Differential operators. Problems of mathematical education,” dedicated to the centenary of the birth of Corresponding Member of the Russian Academy of Sciences, Academician of the European Academy of Sciences L.D.Kudryavtsev. For an entire function represented by a canonical product of genus zero with positive roots, the following result is proved. For any \(\delta\in(0,1/3]\), the minimum modulus of such a function exceeds on average the maximum of its modulus raised to the power \(-1-\delta,\) on any segment whose end ratio is equal to \(\exp(&#x0D; 2/\delta).\) The main theorem is illustrated by two examples. The first of them shows that instead of the exponent \(-1-\delta\) it is impossible to take \(-1.\) The second example demonstrates the impossibility of replacing the value \(\exp(2/\delta)\) by the value\(28/(15\delta)\) in the theorem for small \(\delta.\)