Isotropic Parameters Research Articles

Fractional Viscoelastic Analysis of Transversely Isotropic Surrounding Rock Along Shallow Buried Elliptical Tunnel

ABSTRACTThis study introduces the fractional order Merchant model to analytically solve the stress and displacement fields of the transversely isotropic viscoelastic surrounding rock along shallow elliptical tunnels. First, the stress and displacement solutions of fractional order viscoelastic and transversely isotropic half planes under arbitrary loads are obtained using the Laplace transform and the elastic‐viscoelastic correspondence principle. Second, based on the above half plane solution and the solution of the deep buried elliptical tunnel problem, the Schwarz alternating method is introduced to obtain the analytical solution of the shallow buried elliptical tunnel. A MATLAB program is developed, and the accuracy of the theory and program in this study is verified by comparing it with the results of ABAQUS. Finally, the effects of transversely isotropic parameters, tunnel burial depth, and viscoelastic parameters on the stress and displacement of tunnel surrounding rock are analyzed.

Prediction of flanking sound transmission through cross-laminated timber junctions with resilient interlayers

While the low weight and high bending stiffness of cross-laminated timber (CLT) are key to its popularity, these properties also contribute to poor acoustic performance. Notably flanking sound transmission is a critical factor, driving the need for vibration reduction solutions such as resilient interlayers in the junction design. However, due to the complex material behavior of CLT and resilient interlayers, the improvement related to these solutions is difficult to predict. In this research, an analytical model with low computational cost is developed to evaluate the vibration reduction index Kij for CLT junctions with resilient interlayers. The CLT panels are considered as thin orthotropic plates with homogenized material properties. Three potential material models are proposed for the interlayer: it is considered as a thin plate, a thick flexible layer with out-of-plane motion governed by shear or distributed springs. The prediction model is experimentally validated for junctions consisting of CLT panels, with and without resilient interlayers. For junctions without interlayers, the predicted and experimentally determined vibration reduction index Kij correspond most closely when the junction is realized with stiff connectors. In this case, the predictions are moderately accurate with deviations below 5 dB in 1/3 octave bands up to approximately 2000 Hz for both corner and coplanar transmission paths. For junctions with resilient interlayers, the shear interlayer model exhibits the best performance with deviations of less than 5 dB in most 1/3 octave bands. For frequencies below 1000 Hz, the accuracy of the simplified spring model is comparable to that of the thick layer model. Simulations with equivalent isotropic material parameters yield slightly inferior predictions than for orthotropic parameters if the degree of orthotropy of the panels is high.

Dynamic analysis of fractional poroviscoelastic reinforced subgrade under moving loading

This paper conducts the dynamic analysis of fractional poroviscoelastic reinforced subgrade under moving loading. Based on the Biot theory and transversely isotropic (TI) parameter expression of the geogrid reinforced subgrade, the governing equations of the poroelastic reinforced subgrade are established in the wavenumber domain by the double Fourier transform. Considering the viscosity of the soil skeleton and the flow-dependent viscosity between the soil skeleton and pore water, the governing equations are extended to the fractional poroviscoelastic medium by introducing the Zener viscoelastic model, fractional calculus theory and the dynamic elastic-viscoelastic correspondence principle. Combining boundary conditions and interlayer continuity conditions, the extended precise integration method (PIM) and double Fourier integral transform are employed to obtain the solution of fractional poroviscoelastic reinforced subgrade in the spatial domain. After the numerical validation, a sensitivity analysis of the relaxation time, permeability, reinforcement ratio and the load velocity are conducted.

Modeling of LCF Behaviour on AISI316L Steel Applying the Armstrong-Frederick Kinematic Hardening Model.

The combination of kinematic and isotropic hardening models makes it possible to model the behaviour of cyclic elastic-plastic steel material, though the estimation of the hardening parameters and catching the influence of those parameters on the material response is a challenging task. In the current work, an approach for the numerical simulation of the low-cycle fatigue of AISI316L steel is presented using a finite element method to study the fatigue behaviour of the steel at different strain amplitudes and operating temperatures. Fully reversed uniaxial LCF tests are performed at different strain amplitudes and operating temperatures. Based on the LCF test experimental results, the non-linear isotropic and kinematic hardening parameters are estimated for numerical simulation. On comparing, the numerical simulation results were in very good agreement with those of the experimental ones. This presented method for the numerical simulation of the low-cycle fatigue on AISI316 stainless steel can be used for the approximate prediction of the fatigue life of the components under different cyclic loading amplitudes.

Assessment of Anisotropic Elastic Parameters Using Laboratory Triaxial and In-Situ Pressuremeter Tests in Opalinus Clay

AbstractOpalinus Clay is a stratified shale that exhibits anisotropic deformation properties. In this work, the transversely isotropic deformation parameters of Opalinus Clay are summarized from recent undrained triaxial test campaigns. Relatively consistent values are found for Poisson’s ratios representing different orientations, regardless of the lithofacies and the effective confining stresses used in the tests. Pressuremeter tests were performed at the Mont Terri Rock Laboratory in two boreholes perpendicular and parallel to bedding, respectively. The elastic moduli normal to the borehole wall (borehole moduli) are determined using unloading data obtained at multiple diametric caliper axes and exhibit strong anisotropy for the tests in the borehole parallel to bedding. The anisotropic borehole moduli are predicted based on Amadei and Savage’s (Int J Rock Mech Min Sci 28:383–396, 1991. https://doi.org/10.1016/0148-9062(91)90077-Y) analytical solution using the laboratory-derived Poisson’s ratios and the shear modulus derived from pressuremeter tests in the borehole perpendicular to bedding. The prediction overestimates the magnitude of the borehole moduli but underestimates their anisotropic ratio compared to that from pressuremeter measurement. Drilling a borehole parallel to the bedding of Opalinus Clay is known to induce a local borehole damage zone preferentially developed normal to bedding. The results from a finite element analysis that incorporates this local damage are in better agreement with the pressuremeter measurement.

Transversely isotropic effects on the coupled thermo‐hydro‐mechanical performance for layered saturated media

AbstractIn this manuscript, a novel transformed differential quadrature solution to the coupled thermo‐hydro‐mechanical (THM) problem of layered transversely isotropic (TI) saturated media is proposed, accompanied by a sensitivity analysis of pertinent parameters. Initially, the THM governing equations that encompass the transverse isotropy characteristics of thermal, permeable, and mechanical properties are introduced. Subsequently, utilizing the transformed differential quadrature method (TDQM), the discretized algebraic equations in the transformed domain are derived. Boundary conditions related to stresses, displacements, and temperatures are defined leveraging integral transform techniques and the stress‐strain relationship, while algebraic equations for continuity conditions across adjacent layers are incorporated. The global matrix equation is assembled and solved. After verifying the proposed TDQM solution, a sensitivity analysis on the complex transversely isotropic parameters is conducted to identify the principal factors influencing THM coupling behaviors, thereby simplifying the parameters for discussion in practical engineering applications.

Effect of thermal cycling on the isotropic consolidation and triaxial shear behavior of lateritic clay

It is crucial to comprehend soil thermomechanical behavior while designing underground energy structures to ensure safety. Studies on the soil response to thermal cycles in terms of the generation of thermal-induced volume change and pore water pressure are rare, and relevant research on how these responses might affect soil consolidation parameters and shear strength is very limited. To experimentally investigate the effect of thermal cycling under drained and undrained conditions on the isotropic consolidation parameters and triaxial shear strength of lateritic clay, this paper employs a temperature-controlled triaxial apparatus to conduct a series of isotropic mechanical consolidation and thermal consolidation tests, as well as undrained triaxial shear tests. The thermal response in volume change and pore water pressure are discussed, and the changes in the consolidation parameters, the preconsolidation pressure, and the shear strength are identified. It is concluded that increments of irreversible contraction of lateritic clay are observed during thermal cycling under drained conditions and further lead to a slight increase in the preconsolidation pressure. Nevertheless, thermal cycling hardly affects the swelling and compression index. The shear strength increases after being subjected to thermal cycling under drained conditions, which can be attributed to the increase in cohesion. When drainage is not allowed during thermal cycling, the generation of pore water pressure occurs during temperature variations and completely dissipates after the thermal cycling phase, and its reversibility is unaffected by the stress level and number of cycles. Furthermore, thermal cycling has little effect on the consolidation parameters, preconsolidation pressure, and shear strength. This study provides new insights into the mechanisms controlling the response of clay to thermal cycling.

Combined anisotropic and cyclic constitutive model for laser powder bed fusion fabricated aluminum alloy

This study presents new methods to effectively model the anisotropic yielding and hardening behavior of laser powder bed fusion fabricated aluminum alloy under both monotonic and cyclic loading conditions. The proposed model combines the yield surface-interpolation method to accurately describe the anisotropic hardening rates in various directions, with the Chaboche kinematic hardening rule to precisely reflect the cyclic characteristics. For numerical implementation of the combined anisotropic and cyclic constitutive model, a fully implicit stress integration algorithm based on return mapping method is provided. Moreover, the multiple parameters associated with the model are categorized and identified in an uncoupled manner. The isotropic and cyclic hardening parameters are determined by an inverse method, and the stability of the optimization outcomes is validated by applying different starting points for the parameters. Particularly, the back-stress effect on the identification of anisotropic parameters associated with the stress invariant-based Hill48 yield function is considered for the first time. This consideration leads to an improved prediction accuracy compared to the identification of anisotropic parameters without considering back-stress effect. The combined anisotropic and cyclic constitutive model, along with the calibrated parameters, are proven capable of accurately reproducing the intricate deformation behavior of laser powder bed fusion fabricated AlSi10Mg.

Absolute Configuration of 12S-Deoxynortryptoquivaline from Ascidian-Derived Fungus Aspergillus clavatus Determined by Anisotropic NMR and Chiroptical Spectroscopy.

Tryptoquivalines are highly toxic metabolites initially isolated from the fungus Aspergillus clavatus. The relative and absolute configuration of tryptoquivaline derivates was primarily established by comparison of the chemical shifts, NOE data, and ECD calculations. A de novo determination of the complete relative configuration using NMR spectroscopy was challenging due to multiple spatially separated stereocenters, including one nonprotonated carbon. In this study, we isolated a new tryptoquivaline derivative, 12S-deoxynortryptoquivaline (1), from the marine ascidian-derived fungus Aspergillus clavatus AS-107. The correct assignment of the relative configuration of 1 was accomplished using anisotropic NMR spectroscopy, while the absolute configuration was determined by comparing calculated and experimental ECD spectra. This case study highlights the effectiveness of anisotropic NMR parameters over isotropic NMR parameters in determining the relative configuration of complex natural products without the need for crystallization.

The germanides ScTGe2 (T = Fe, Co, Ru, Rh) – crystal chemistry, 45Sc solid-state NMR and 57Fe Mössbauer spectroscopy

Abstract The TiMnSi2-type (space group Pbam) germanides ScTGe2 (T = Fe, Co, Ru, Rh) were synthesized from the elements by arc-melting. Single crystals were grown by annealing sequences of the arc-melted buttons in an induction furnace. The structures of ScFeGe2, ScRuGe2 and ScRhGe2 were refined from single-crystal X-ray diffraction data. In ScRuGe2, the ruthenium atoms have distorted octahedral germanium coordination (242–268 pm Ru–Ge). Three trans-face-sharing octahedra form a sub-unit which is condensed via common edges in c direction and connected via common corners with four adjacent blocks, forming a three-dimensional [RuGe2 type] substructure. The two crystallographically independent scandium sites have coordination numbers 15 (Sc1@Ge8Ru4Sc3) and 17 (Sc2@Ge7Ru6Sc4). Electronic band structure calculations for ScCoGe2 and ScRuGe2 show a net charge transfer from the scandium to the transition metal and germanium atoms, leading to a description with polyanionic networks Sc δ+[TGe2]δ−. The two crystallographically independent Sc sites are easily distinguishable by 45Sc magic-angle spinning (MAS)-NMR spectroscopy. Isotropic chemical shift values and nuclear electric quadrupolar interaction parameters were deduced from an analysis of the triple-quantum (TQ)-MAS NMR spectra. The electric field gradient parameters deduced from these experiments are in good agreement with quantum-chemical calculations using the Wien2k code. Likewise, the two crystallographically independent iron sites in ScFeGe2 could be discriminated in the 57Fe Mößbauer spectra through their isomer shifts and quadrupole splitting parameters: δ = 0.369(1) mm s−1 and ∆E Q = 0.232(2) mm s−1 for Fe1 and δ = 0.375(2) mm s−1 and ∆E Q = 0.435(4) mm s−1 for Fe2 (data at T = 78 K).

Elastic Behavior of Transversely Isotropic Cylindrical Rock Samples under Uniaxial Compression Considering Ideal and Frictional Boundary Conditions

Conceptualizing sophisticated measurement set-ups as well as testing and evaluation procedures for laboratory experiments on anisotropic rocks requires a basic understanding of the potential specimen behavior. The focus of the present work was therefore to investigate the influence of different transversely isotropic parameters and their ratios on the elastic behavior of cylindrical rock samples in uniaxial compression tests. Parameter sets corresponding to soft anisotropic rocks were chosen based on naturally observed ranges for the five elastic transversely isotropic constants. Analytical results for the radial and vertical strain distributions around the sample circumference and a comparison with finite element simulations are presented. Further, the effect of interface friction between samples and loading platens was analyzed within the numerical models. The results suggest that radial strains around cylindrical anisotropic samples are rarely uniform except for specific combinations of parameters and isotropy plane inclinations. The effect of interface friction was found to have a clear influence on the developing elastic stress and strain distributions for samples with inclined isotropy planes. Nevertheless, no significant influence of frictional boundary conditions on the back-calibrated values of the elastic parameters could be identified, suggesting that friction-reducing measures in uniaxial compression tests on transversely isotropic samples with predominantly linear behavior are not required.

Comparison of the continuum damage and fracture mechanics in fatigue assessment of components containing residual stresses

In the present study, the fatigue crack growth life of standard and smooth notched specimens containing residual stresses are evaluated based on the continuum damage and fracture mechanics approaches. It is indicated that fatigue crack growth lives assessed by the continuum damage model are closer to the experimental results, with a difference of <10% in the specimens containing residual stresses. The total stress intensity factor range is used to consider the effects of residual stresses in the estimation of fatigue crack growth life based on the fracture mechanics. It is found that in existing residual stresses, the stress intensity factor K is not a proper parameter to evaluate crack tip zone. Fatigue crack initiation life is experimentally obtained based on assessing variations of the slope of unloading curve in the force-displacement diagram of fatigue experiments. The cycle including a change in the slope is considered as fatigue crack initiation event. Isotropic and kinematic hardening parameters of ASTM A516 pressure vessel steel are considered in finite element analyses. Tensile residual stresses are introduced into the notched specimens by employing four-point-bending with a magnitude of around 90% of the yield stress of the material. The results indicate that at least 65% of the fatigue life of the specimens is decreased due to the presence of tensile residual stresses. Tensile residual stresses are measured using the hole-drilling technique.

Thermodynamic property of sandwich cylindrical shell structure with metallic wire mesh: Numerical modeling and experimental analysis

As a new addition to lightweight composite structures, the sandwich cylindrical shell with a metallic wire mesh core has emerged as a promising solution for thermodynamic performance analysis at elevated temperatures. The intricate interwoven cellular formations within the metallic wire mesh pose difficulties for thermo-mechanical modeling and property evaluation. First, the constitutive models employed to characterize hysteresis phenomena were presented, comprising isotropic elasticity, Bergstrom-Boyce model, Ogden hyper-elasticity, and parameter identification through mechanical examinations at varying temperatures. Second, the finite element modeling of cylindrical shell structures was determined for modal and steady-state dynamic analyses. Third, the experimental procedures were carried out, including the preparation of the sandwich cylindrical shell and the dynamic testing platform. The first-order natural frequency of the cylindrical shell structure is close to the resonance frequency of the dynamic test results, with a maximum error of 6.5%, demonstrating the accuracy of the simulation model. When compared to the solid-core cylindrical shell, the average insertion loss of the sandwich cylindrical shell structure within the frequency range of 10–1000 Hz at room temperature is up to 11.09 dB. Furthermore, at elevated temperatures, the average insertion loss of the sandwich cylindrical shell decreases but fluctuates as the temperature changes.

Application of continuum damage mechanics in fatigue assessment of A516 steel specimens considering residual stresses

The present study evaluates the effects of tensile residual stresses on fatigue behaviour of ASTM A516 pressure vessel steel specimens. In this regard, fatigue specimens containing a smooth notch region are studied. A damage coupled elastic-plastic constitutive material model is developed to investigate effects of residual stresses on fatigue life. Isotropic and kinematic hardening parameters of the material are experimentally determined. Additionally, the damage model parameters are specified from fatigue experiments conducted on standard specimens in different stress ratios. Tensile residual stresses are introduced into the smooth notched specimens through employing four-point-bending method. The hole drilling technique is utilized to measure the residual stress magnitudes. The results indicate that about two third of fatigue life of the specimens is decreased due to the existed tensile residual stresses. Furthermore, fatigue crack initiation and propagation behaviour in the specimens containing residual stress are studied based on the developed continuum damage model.

Hyperfine-Resolved Rotational Spectroscopy of Phenyl Radical.

We present an analysis of the hyperfine-resolved rotational spectrum of gas-phase phenyl radical, c-C6H5, between 9 and 35 GHz. The isotropic and anisotropic hyperfine parameters of all five protons and the electronic spin-rotation fine structure parameters are accurately determined from this study, which allow detailed insight into the distribution and interactions of the unpaired electron in this prototypical σ-radical. The implications for laboratory and astronomical investigations of phenyl that are reliant on a precise centimeter-wave catalog are discussed, as are the prospects for detecting and assigning the hyperfine-resolved rotational spectra of other large, weakly polar hydrocarbon chain and ring radicals.

Displacement based Simulation and Material Calibration based on Digital Image Correlation Part II - Application

An alternative approach to calibrate material models is proposed. The entire displacement field of a specimen measured with a DIC system was converted into boundary conditions by the Envyo® mapping software. These boundary conditions were imposed on all nodes in the corresponding LS-DYNA® simulation model. In this way a digital twin of the specimen geometry and the experimental kinematics was obtained. Considering the local stress equilibrium over the entire specimen and the equilibrium of global force integrated over many hypothetical cross sections, LS-OPT® was used to iteratively determine the isotropic model parameters of the tested material. A new tensile specimen geometry is introduced to get the most out of a single test. The findings suggest that, at present, convergence in iterative parameter optimization cannot be attained without prior filtering and smoothing of the DIC input data in time and space, despite the utilization of the chosen material model.

Amplitude variation with incidence and azimuth stepwise inversion with coherence-attribute constraints for anisotropic parameters

With the development of 5D (3D + offset + azimuth) seismic technology, the stable acquisition of anisotropy information from wide-azimuth seismic data has become a key scientific problem in the seismic inversion of fractured reservoirs. The amplitude variation with incidence and azimuth (AVAZ) inversion method using wide-azimuth seismic data is an effective way to predict the anisotropic information of the subsurface medium. However, the conventional AVAZ inversion method suffers from too many parameters to be estimated, large variation in contribution, and inversion instability. Therefore, an AVAZ inversion method with coherence-attribute constraints is developed to solve the problem of unstable inversion of anisotropic parameters. First, we use seismic coherence attributes to build a fracture-probability-distribution model containing anisotropic information of the subsurface medium, which can be used to simulate large-scale subsurface fractures and faults. Then, it is added to the objective function as an anisotropic information constraint to improve the reliability and stability of the anisotropic inversion. Furthermore, an AVAZ inversion method in a Bayesian framework is implemented by using wide-azimuth seismic data. Gaussian distribution and a smoothing background model are added to the objective function to improve the reasonableness and stability of the inversion. In addition, we develop a stepwise optimization inversion method for isotropic and anisotropic parameters, prioritizing the inversion of parameters that contribute significantly to the reflection coefficient, and then using the results of the previous inversion as the initial values for the next inversion step to achieve multiparameter inversion. This method can reduce the number of the estimated parameters and thus improve the stability of the inversion of the anisotropic parameters. Field data examples indicate that this method produces suitable inversion results even at moderate levels of noise. Therefore, we can conclude that the proposed method has good applicability and stability in predicting the anisotropy parameters of fractured shale reservoirs.

Measuring elastic parameters of transversely isotropic materials by cylindrical indentation

Based on the cylindrical indentation experiments, a novel model for characterizing the elastic mechanical property of transversely isotropic materials has been established. The cylindrical indentation of transversely isotropic materials was theoretically and dimensionally analyzed. Three-dimensional (3D) indentation experiments that encompass the wide range of transversely isotropic material parameters were simulated by finite element. The effect of each parameter (transversely isotropic Young’s modulus, EP , longitudinal Young’s modulus, EL , longitudinal shear modulus, GL , and loading orientation angle, α) on the normalized indentation modulus was investigated. Then, the dimensionless analytical relationship between indentation moduli and elastic parameters was obtained at three different indentation orientations . Several groups of transversely isotropic materials were selected as input parameters to carry out numerical indentation experiments for the error analysis. The sensitivity of the calculated elastic parameters to the experimental data was analyzed. Simultaneously, the technique was used in the particular case of a Zinc single-crystal material, and the accuracy of these derived formulas was verified. The good agreement shows that the proposed method is reliable and could be applied to characterize the elastic parameters of transversely isotropic materials.

Textural Features of Mouse Glioma Models Measured by Dynamic Contrast-Enhanced MR Images with 3D Isotropic Resolution.

This paper investigates the effect of anisotropic resolution on the image textural features of pharmacokinetic (PK) parameters of a murine glioma model using dynamic contrast-enhanced (DCE) MR images acquired with an isotropic resolution at 7T with pre-contrast T1 mapping. The PK parameter maps of whole tumors at isotropic resolution were generated using the two-compartment exchange model combined with the three-site-two-exchange model. The textural features of these isotropic images were compared with those of simulated, thick-slice, anisotropic images to assess the influence of anisotropic voxel resolution on the textural features of tumors. The isotropic images and parameter maps captured distributions of high pixel intensity that were absent in the corresponding anisotropic images with thick slices. A significant difference was observed in 33% of the histogram and textural features extracted from anisotropic images and parameter maps, compared to those extracted from corresponding isotropic images. Anisotropic images in different orthogonal orientations demonstrated 42.1% of the histogram and textural features to be significantly different from those of isotropic images. This study demonstrates that the anisotropy of voxel resolution needs to be carefully considered when comparing the textual features of tumor PK parameters and contrast-enhanced images.

Interbody Fusion Cage Design Driven by Topology Optimization

We used topology optimization technology to explore the new theory and method of interbody fusion cage design and realized an innovative design of interbody cages. The lumbar spine of a normal healthy volunteer was scanned to perform reverse modeling. Based on the scan data for the L1-L2 segments of the lumbar spine, a three dimensional model was reconstructed to obtain the complete simulation model of the L1-L2 segment. The boundary inversion method was used to obtain approximately isotropic material parameters that can effectively characterize the mechanical behavior of vertebrae, thereby reducing the computational complexity. The topology description function was used to model the clinically used traditional fusion cage to obtain Cage A. The moving morphable void-based topology optimization method was used for the integrated design of size, shape, and topology to obtain the optimized fusion cage, Cage B. The volume fraction of the bone graft window in Cage B was 74.02%, which was 60.67% higher than that (46.07%) in Cage A. Additionally, the structural strain energy in the design domain of Cage B was 1.48mJ, which was lower than that of Cage A (satisfying the constraints). The maximum stress in the design domain of Cage B was 5.336 Mpa, which was 35.6% lower than that (8.286 Mpa) of Cage A. In addition, the surface stress distribution of Cage B was more uniform than that of Cage A. This study proposed a new innovative design method for interbody fusion cages, which not only provides new insights into the innovative design of interbody fusion cages but may also guide the customized design of interbody fusion cages in different pathological environments.