Elastic Model Research Articles

Evaluation of Interlayer Reinforcement Effectiveness in Road Pavement Rehabilitation Using FEM Modeling and Fracture Mechanics Analysis

In this paper, the effectiveness of reinforcements for flexible pavements is evaluated through an analysis of reflective cracking. Different stiffness and thickness reinforcements are considered for the rehabilitation of an already cracked pavement. The effect of the reinforcement is assessed from two different perspectives: (i) the ability to reduce stresses in the rehabilitated pavement layers, and (ii) the capacity to mitigate the crack propagation from deeper layers. A finite element model (FEM) is adopted to study the stress and strain state of the pavement layers. The pavement model has been properly validated, transitioning from a simply supported beam scheme to an elastic multilayer model. In addition, to represent crack propagation, fracture evolution is analyzed using Linear Elastic Fracture Mechanics (LEFMs) and Paris’ law. The effect of different reinforcements on the pavement is then simulated. The results show that the reinforcement performance is strictly dependent on the interlayer thickness and stiffness. In particular, high stiffness reinforcements (geomembranes) show increasing effectiveness with stiffness, both in terms of reflective cracking and stress reduction. Conversely, low stiffness reinforcements (SAMIs) show a variable trend with the stiffness modulus. In fact, extremely low stiffness is effective in slowing down crack propagation but is detrimental to the wearing course’s stress condition. However, as the stiffness increases, the likelihood of cracking in the wearing course decreases, though only a small beneficial effect is registered for crack propagation in the base layer.

Prediction of internal stress in alumina laminates induced by shrinkage mismatch based on elastic model modification

AbstractCracks induced by internal stresses compromise the structural integrity of ceramic laminates. Such stresses can be classified into thermal stress derived from thermal expansion mismatch and shrinkage stress derived from shrinkage mismatch. Analytical models have been proposed for the former, whereas only numerical predictions have been explored for the latter. In this study, an equation is constructed to predict the shrinkage stress by modifying an elastic solution proposed in previous studies. We fabricated laminates with three‐layer sandwiched structures using only alumina specimens with high and low densities to control the shrinkage and avoid thermal mismatch. Surface cracks were initiated when the shrinkage stress exceeded the flexural strength of the surface layer. Although the original strength of the surface layer was 308.8 MPa, the laminates’ flexural strength was lower than that because of shrinkage constraint. Our results demonstrate that the shrinkage stress was successfully estimated analytically using a few material properties measured in an ordinary environment. This study will ensure the structural integrity of ceramic laminates in laminate designs.

Frequency analysis of open/closed polygonal channel aerostructures made of hybrid nanocomposite materials and supported by piecewise elastic foundation using GDQE technique

This research delves into the theoretical exploration of the generalized differential quadrature element (GDQE) method for analyzing the dynamic response and natural frequency of aerospace structures, specifically polygonal channels found in aircraft, satellites, and space vehicle components. These structures are critical in aerospace engineering, serving in various capacities such as airframe components and fluid conveyance systems. Emphasizing the practical significance of these structures, the study incorporates the influence of ground or support conditions, employing a two-parameter piecewise elastic foundation model. The investigated open or closed channels are characterized as laminated functionally graded hybrid nanocomposites, specifically denoted as FG-HNC, reinforced with Carbon nanotubes (CNTs) and Clay nanoparticles (CNP). Each composite layer is reinforced with randomly oriented and uniformly distributed tubes and particles. The homogenization of the hybrid composite domain is performed using the hierarchy Halpin-Tsai micromechanical rule. Utilizing the GDQE technique, the channels are discretized into plate elements, and motion equations for each plate element are calculated based on first-order shear deformation theory and Hamilton's principle. The resulting equations are then solved using the standard GDQ method, with subsequent application of appropriate continuity conditions at shared element boundaries. In this comprehensive study, the research scrutinizes the effects of structure dimensions, channel sides crank angles, composite characteristics, and boundary conditions on the free vibration behavior of the polygonal channels. By offering detailed insights into the vibrational characteristics of FG-HNC structures, this study contributes to the advancement of aerospace engineering design and analysis.

A stochastic production frontier model for evaluating the performance efficiency of artificial intelligence investment worldwide

As artificial intelligence (AI) begins to take center stage in technological innovations, it is essential to understand the business value of AI innovation efforts and investments. While some early work at the firm level exists, there is a shortage of literature that takes a larger country-level perspective. This study investigated the effect of AI innovation efforts on production efficiency across countries using stochastic production frontier approaches. In addition, our model also included the traditional economic inputs of capital and labor. We used both the Cobb–Douglas function and Constant Elastic Substitution model specifications. The significant findings of this study are as follows: Innovation efforts in AI measured by the number of AI-related patents and capital investment in AI have a substantial effect on economic output. The significance of AI investments indicates the need for a robust digital infrastructure as a prerequisite for harnessing AI capabilities. The complementary relationship between labor and AI-related patents implies that high-skilled labor is often necessary to incorporate AI inputs into production. However, as AI capabilities develop, they weaken the effect on labor input. The study also distinguishes between AI innovation (research and development activities indicated by AI patents) and the production efficiency of AI investments (return on every dollar invested), highlighting that more AI innovation does not always translate into better production efficiency. The findings indicate that while the United States leads innovation in AI, the UK has the best production efficiency. China ranked fourth in AI innovation and has the lowest production efficiency among the countries included in the study.

Contact detection between curved fibres: high order makes a difference

Computer Graphics has a long history in the design of effective algorithms for handling contact and friction between solid objects. For the sake of simplicity and versatility, most methods rely on low-order primitives such as line segments or triangles, both for the detection and the response stages. In this paper we carefully analyse, in the case of fibre systems, the impact of such choices on the retrieved contact forces. We highlight the presence of artifacts in the force response that are tightly related to the low-order geometry used for contact detection. Our analysis draws upon thorough comparisons between the high-order super-helix model and the low-order discrete elastic rod model. These reveal that when coupled to a low-order, segment-based detection scheme, both models yield spurious jumps in the contact force profile. Moreover, these artifacts are shown to be all the more visible as the geometry of fibres at contact is curved. In order to remove such artifacts we develop an accurate high-order detection scheme between two smooth curves, which relies on an efficient adaptive pruning strategy. We use this algorithm to detect contact between super-helices at high precision, allowing us to recover, in the range of wavy to highly curly fibres, much smoother force profiles during sliding motion than with a classical segment-based strategy. Furthermore, we show that our approach offers better scaling properties in terms of efficiency vs. precision compared to segment-based approaches, making it attractive for applications where accurate and reliable forces are desired. Finally, we demonstrate the robustness and accuracy of our fully high-order approach on a challenging hair combing scenario.

Laboratory Study on Wave Attenuation by Elastic Mangrove Model with Canopy

This study evaluates the effectiveness of artificial Kandelia obovata forests in wave attenuation through physical model experiments conducted in a wave flume. The experiments meticulously replicated real-world hydrodynamic conditions and mangrove movement responses using the principles of gravitational and motion similarity, with a scaled 1:10 model of Kandelia obovata. Our approach included comparative experiments against a 1:100 gradient concrete slope to isolate the effects of seabed friction and flume wall reflections. The wave height was measured using strategically placed wave gauges. The findings indicated that the artificial Kandelia obovata forests significantly attenuated waves, with a decrease in the total attenuation capacity as the water depth increased from 2.75 m to 3.28 m under both regular and irregular waves. The elastic mangrove model with a canopy effect led to a 15% increase in wave attenuation over cylindrical models. Predictive models using multivariate nonlinear regression and back propagation neural networks showed that the latter provided a superior accuracy in estimating wave transmission coefficients

Mechanical Properties and Constitutive Model for Artificially Structured Soils under Undrained Conditions

Triaxial tests are performed for remolded, artificially isotropic, and anisotropic structured samples under undrained conditions at confining pressures of 25, 100, and 200 kPa. Based on these test results, a binary-medium constitutive model is formulated based on homogenization theory and a breakage mechanism to describe the behaviors of structured soils. In this model, the binary-medium material is idealized as a representative volume element (RVE) composed of bonded elements, whose mechanical behaviors are expressed by the linearly elastic model, and frictional elements, whose mechanical behaviors are described by the double-yield surfaces constitutive model. The parameters of the bonded and frictional elements are determined from the test results of structured and remolded samples, respectively. The expressions for the breakage ratio and local stress coefficient matrix are introduced, and their parameters are provided. The computed results are compared with the test results, demonstrating that the model can reflect the main deformation features of structured soil relatively well, including the influence of anisotropy, gradual damage to particle bonding, and pore development.

Slip Rate for the Rose Canyon Fault through San Diego, California, Based on Analysis of GPS Data: Evidence for a Potential Rose Canyon–San Miguel-Vallecitos Fault Connection?

ABSTRACT The Rose Canyon fault is the southern extension of the larger Newport–Inglewood–Rose Canyon fault system, which represents a major structural boundary in the Inner Continental Borderland (ICB) offshore of southern California. Ten to fifteen percent of total plate boundary motion in southern California is thought to be accommodated by the faults of the ICB, but the exact distribution of slip is uncertain. With an onshore segment, the Rose Canyon fault offers an opportunity to measure the slip rate using traditional geodetic methods. In this study, we use Global Positioning System (GPS) surface velocities from a combined campaign and continuous GPS network to constrain elastic models of the Rose Canyon fault. We then compare the observed surface velocities with proposed conceptual models of regional fault connections that facilitate the transfer of slip into the Rose Canyon fault to assess how well the observations are explained by the models. The results of elastic half-space models suggest that the Rose Canyon fault may be slipping toward the higher end of geologic estimates, with the preferred model indicating a slip rate of 2.4 ± 0.5 mm/yr. Although limited in terms of near-fault benchmarks, we find an improved model fit using an asymmetrical elastic half-space model and a higher slip rate, suggesting a potential rheological contrast across the Rose Canyon fault, similar to observations from the northern Newport–Inglewood fault segments. Observed GPS surface velocities, background seismicity, and gravity anomalies south of San Diego Bay point toward a more easterly trace for the Rose Canyon fault, suggesting a possible connection with the San Miguel–Vallecitos fault system. Such a connection could increase the potential rupture lengths of future earthquakes and have important consequences for regional seismic hazards.

Identification and Design of Novel Potential Antimicrobial Peptides Targeting Mycobacterial Protein Kinase PknB

Antimicrobial peptides have gradually gained advantages over small molecule inhibitors for their multifunctional effects, synthesising accessibility and target specificity. The current study aims to determine an antimicrobial peptide to inhibit PknB, a serine/threonine protein kinase (STPK), by binding efficiently at the helically oriented hinge region. A library of 5626 antimicrobial peptides from publicly available repositories has been prepared and categorised based on the length. Molecular docking using ADCP helped to find the multiple conformations of the subjected peptides. For each peptide served as input the tool outputs 100 poses of the subjected peptide. To maintain an efficient binding for relatively a longer duration, only those peptides were chosen which were seen to bind constantly to the active site of the receptor protein over all the poses observed. Each peptide had different number of constituent amino acid residues; the peptides were classified based on the length into five groups. In each group the peptide length incremented upto four residues from the initial length form. Five peptides were selected for Molecular Dynamic simulation in Gromacs based on higher binding affinity. Post-dynamic analysis and the frame comparison inferred that neither the shorter nor the longer peptide but an intermediate length of 15 mer peptide bound well to the receptor. Residual substitution to the selected peptides was performed to enhance the targeted interaction. The new complexes considered were further analysed using the Elastic Network Model (ENM) for the functional site’s intrinsic dynamic movement to estimate the new peptide’s role. The study sheds light on prospects that besides the length of peptides, the combination of constituent residues equally plays a pivotal role in peptide-based inhibitor generation. The study envisages the challenges of fine-tuned peptide recovery and the scope of Machine Learning (ML) and Deep Learning (DL) algorithm development. As the study was primarily meant for generation of therapeutics for Tuberculosis (TB), the peptide proposed by this study demands meticulous invitro analysis prior to clinical applications.Graphical

A random elastoplastic framework of relationships between CBR and Young’s modulus for coarse-grained soils

The material quality indicator most commonly used for the quality of road materials is the California Bearing Ratio test (CBR). In addition, the CBR test provides a value commonly used to correlate with the resilient modulus (used in the design and analysis of pavement) due to its cost-effectiveness. This test measures soil resistance to penetration by a punch and compares it with the pressure measured in a standard material at the same penetration (2.5 mm or 5 mm). However, this test lacks physical explanations regarding mechanical behavior because the CBR value only compares soil penetration resistance with the pressure measured in a standard material. Another issue arises from the scattered results obtained from both equations and tests, highlighting the need for variability analysis of the CBR test to assess the effect of the different geotechnical variables on the CBR value. For this purpose, simulations using FEM (Finite Element Method) considering random soil parameters were performed for the CBR test. These FEMs included a linear elastic model and two failure criteria (Mohr–Coulomb and Drucker-Prager with a cap) and were prepared for granular soils. The evaluation shows that the increase or decrease in the CBR value is a function of the elastic modulus, yield stress, and friction angle. Moreover, the simulations expand the knowledge of the shearing mechanisms, generated stresses, displacement fields, and load sharing when the CBR test is made. From these results, a physical explanation of test results can be done. FEM simulations showed stress zones in conditions of elastic, compression, and shear behavior. These zones can explain the importance of elastic modulus, yielding stress, and friction angle in the CBR value. From numerical results, a new equation was proposed and compared with practical equations proposed by international standards and other sources to estimate the probability of underestimated values CBR according to the correlations used.

A numerical study on tensile strength of low-density Kagome networks made of brittle fibers

In this paper, we present a numerical study on the tensile strength of low-density Kagome networks made of brittle fibers. First, an elastic beam model is employed to analytically predict the effective elastic properties and tensile strength, as well as the critical condition for buckling of the fibers in Kagome networks. A series of finite element analyses are then conducted to simulate the elastic deformation and failure of Kagome networks under tension. The numerical results based on unit-cell models reveal four possible failure modes of the Kagome networks subject to uniaxial tension, summarized in a phase diagram in terms of the relative density and the fiber strength. The pre-buckling failure mode is restricted to cases with relatively high density and low fiber strength. A low-density Kagome network is likely to fail by one of the post-buckling modes, with an effective tensile strength much lower than the prediction by the elastic beam model. For Kagome networks consisting of a large number of unit cells, the effect of boundary conditions on the tensile strength is examined. Under periodic boundary conditions, the effective tensile strength is nearly identical to that predicted by the unit-cell model, independent of the model size. Under a roller boundary condition, with damage initiation near the free edges followed by a diffusive damage progression, the effective tensile strength is lower than that under periodic boundary conditions for the cases of relatively low fiber strengths. Under a clamped boundary condition, the effective tensile strength is higher than that under periodic boundary conditions for the cases of relatively high fiber strengths, where fiber buckling is largely suppressed by the clamped boundaries. Finally, the effect of a crack-like defect on the effective tensile strength is studied for Kagome networks under the clamped boundary condition. With a small defect, the effective strength is nearly independent of the defect size. In contrast, with a relatively long defect, the effective strength decreases almost linearly with the length of the crack-like defect. The effective toughness for damage initiation and steady-state damage progression in the Kagome networks is discussed from an energetic perspective.

Multi-Step Relaxation Characterization and Viscoelastic Modeling to Predict the Long-Term Behavior of Bitumen-Free Road Pavements Based on Polymeric Resin and Thixotropic Filler.

Asphalt pavements are fundamental to modern transportation infrastructure, requiring elasticity, firmness, and longevity. However, traditional asphalt, based on bitumen, faces several limitations. To improve pavement performance, polymer resins are being used to substitute bitumen and improve requirements. Therefore, a deep understanding of the material behavior is required. This study presents the analysis of the relaxation behavior of a poly(methyl methacrylate)-based pavement and the influence of mineral fillers. An approach using a linear elastic-viscoelastic material model was selected based on evidence and validated across the linear and nonlinear deformation range. The results reveal no influence of the mineral fillers on the relaxation behavior. The presented modification of the linear elastic and viscoelastic modeling reveals accurate results to predict long-term pavement performance. This approach offers a practical method for forecasting asphalt behavior. Further research is needed to incorporate deformation behavior into the model.

Asynchronous global–local non-invasive coupling for nonlinear monotone patches: Application to plasticity problems

This article presents the asynchronous global–local non-invasive coupling in the case of nonlinear monotone patches as encountered when inserting elastoplastic components in a global linear elastic model. The convergence of the method is theoretically established in a general framework using the paracontractions technique and illustrated in academic examples with a weak scalability study considering the case of balanced and unbalanced patches.

Simulate the elastic wavefields in media with an irregular surface topography based on staggered grid finite difference

Abstract Wave equation forward modeling is a useful method to study the propagation regulation of seismic wavefields. Finite difference (FD) is one of the most extensively employed numerical approaches for computing wavefields in earthquake and exploration seismology. However, the FD approach relying on regular grids often struggles to calculate wavefields in regions featuring surface topographies. The elastic wave equation can more accurately describe the propagation of seismic wavefields in elastic media compared to the acoustic wave equation. We introduce a new FD scheme to calculate the elastic wavefields in an isotropic model with a surface topography. The novel approach can use a conventional staggered grid FD (SGFD) approach based on regular grids. A new elastic model with a horizontal surface is first obtained from the nearby surface's elastic properties and the undulating terrain elevation. We subsequently employ a topography-related strategy to eliminate the effects of surface topographies on the seismic wavefields in models with irregular surface topographies. The merits of our proposed scheme lie in its ability to stable numerically compute wavefields in models with irregular surface topographies without altering the conventional SGFD relying on regular grids. To validate the effectiveness and practicality of our method, we utilize elastic models featuring complex surface topographies. Numerical experiments demonstrate that our approach efficiently calculates elastic wavefields in isotropic media with irregular topographies based on conventional SGFD.

Nonlinear vibration characteristics of thermo-viscoelastic coupling of moving PET films with temperature-dependent elastic modulus

In order to improve the transport stability of roll-to-roll produced polyethylene terephthalate films (PET films) in high temperature environments, this paper investigates the nonlinear vibrational properties of moving PET films under a uniform temperature field by considering the temperature dependence of the elastic modulus. Firstly, constant tensile tests were conducted to test the elastic modulus values of PET films at different hot air temperatures, and the Wachtman model was improved to establish a temperature-dependent elastic modulus model for PET films. Secondly, based on the Kelvin-Voigt model, the nonlinear vibrational equilibrium differential equations of the system were established by applying the Bubnov-Galerkin method of discretization according to D’Alembert’s principle. Finally, numerical simulations based on the 4th-order Runge-Kutta method were carried out to analyze the effects of films width, external excitation frequency, external excitation amplitude, transfer velocity, ambient temperature, damping coefficient and viscoelasticity coefficient on the nonlinear vibration of the system. This provides a theoretical basis for the commissioning of stabilized transfer parameters for roll-to-roll production of PET films.

From elastic shallow shells to beams with elastic hinges by Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence

In this paper, we study the Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document}-convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with “smooth” solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam.

MERCI: Mixed curvature-based elements for computing equilibria of thin elastic ribbons

Thin elastic ribbons represent a class of intermediary objects lying in-between thin elastic plates and thin elastic rods. Although the two latter families of thin structures have received much interest from the Computer Graphics community over the last decades, ribbons have seldom been considered and modelled numerically so far, in spite of a growing number of applications in Computer Design. In this paper, starting from the reduced developable ribbon models [Sadowsky 1929; Wunderlich 1962] recently popularised in Soft Matter Physics, we propose a both accurate and efficient algorithm for computing the statics of thin elastic ribbons. Inspired by the super-clothoid model for thin elastic rods, our method relies on compact ribbon elements whose normal curvature varies linearly with respect to arc length s , while their geodesic torsion is quadratic in s . In contrast however, for the sake of efficiency, our algorithm avoids building a fully reduced kinematic chain and instead treats each element independently, gluing them only at the final solving stage through well-chosen bilateral constraints. Thanks to this mixed variational strategy, which yields a banded Hessian, our algorithm recovers the linear complexity of low-order models while preserving the quadratic convergence of curvature-based models. As a result, our approach is scalable to a large number of elements, and suitable for various boundary conditions and unilateral contact constraints, making it possible to handle challenging scenarios such as confined buckling experiments or Möbius bands with contact. Remarkably, our mixed algorithm proves an order of magnitude faster compared to Discrete Elastic Ribbon models of the literature while achieving, in a few seconds only, high accuracy levels that remain out of reach for such low-order models. Additionally, our numerical model can incorporate various ribbon energies, including the RibExt model for quasi-developable ribbons recently introduced in Physics [Audoly and Neukirch 2021], which allows to transition smoothly between a rectangular Kirchhoff rod and a (developable) Sadowsky ribbon. Our numerical scheme is carefully validated against demanding experiments of the Physics literature, which demonstrates its accuracy, efficiency, robustness, and versatility. Our Merci code is publicly available at https://gitlab.inria.fr/elan-public-code/merci for the sake of reproducibility and future benchmarking.

Large-Scale Proteomics in Early Pregnancy and Hypertensive Disorders of Pregnancy

There is no consensus regarding the best method for prediction of hypertensive disorders of pregnancy (HDP), including gestational hypertension and preeclampsia. To determine predictive ability in early pregnancy of large-scale proteomics for prediction of HDP. This was a nested case-control study, conducted in 2022 to 2023, using clinical data and plasma samples collected between 2010 and 2013 during the first trimester, with follow-up until pregnancy outcome. This multicenter observational study took place at 8 academic medical centers in the US. Nulliparous individuals during first-trimester clinical visits were included. Participants with HDP were selected as cases; controls were selected from those who delivered at or after 37 weeks without any HDP, preterm birth, or small-for-gestational-age infant. Age, self-reported race and ethnicity, body mass index, diabetes, health insurance, and fetal sex were available covariates. Proteomics using an aptamer-based assay that included 6481 unique human proteins was performed on stored plasma. Covariates were used in predictive models. Prediction models were developed using the elastic net, and analyses were performed on a randomly partitioned training dataset comprising 80% of study participants, with the remaining 20% used as an independent testing dataset. Primary measure of predictive performance was area under the receiver operating characteristic curve (AUC). This study included 753 HDP cases and 1097 controls with a mean (SD) age of 26.9 (5.5) years. Maternal race and ethnicity were 51 Asian (2.8%), 275 non-Hispanic Black (14.9%), 275 Hispanic (14.9%), 1161 non-Hispanic White (62.8% ), and 88 recorded as other (4.8%), which included those who did not identify according to these designations. The elastic net model, allowing for forced inclusion of prespecified covariates, was used to adjust protein-based models for clinical and demographic variables. Under this approach, no proteins were selected to augment the clinical and demographic covariates. The predictive performance of the resulting model was modest, with a training set AUC of 0.64 (95% CI, 0.61-0.67) and a test set AUC of 0.62 (95% CI, 0.56-0.68). Further adjustment for study site yielded only minimal changes in AUCs. In this case-control study with detailed clinical data and stored plasma samples available in the first trimester, an aptamer-based proteomics panel did not meaningfully add to predictive utility over and above clinical and demographic factors that are routinely available.

A modified linear-elastic model for calibration of resonant column devices accommodating drive system compliance

Measurements of small-strain shear modulus of soils and rocks using the resonant column apparatus are highly dependent on accurate physical characterisation of the apparatus's drive components. This is typically achieved by way of a calibration exercise, yet it is widely reported that existing interpretation methods yield physical properties that vary with frequency, complicating subsequent interpretation of test data. Previous research has indicated that much of this apparent frequency dependency occurs due to compliance of the drive system. In this study the linear elastic model of the resonant column apparatus is adapted to include a new drive stiffness parameter, supported by finite-element analysis of the drive system. A novel calibration method is presented based on this drive compliance model. Thirteen calibration bars and three added masses are used to conduct an extensive calibration exercise for both a Hardin- and Stokoe-type resonant column apparatus. The novel calibration method is compared with three existing methods in the literature. Limitations of the four methods are identified and discussed. The drive compliance model and its associated calibration method is shown to be a robust means of characterising the apparatus behaviour while successfully eliminating frequency dependency of the calibration parameters. The model is valid where total system damping is small and is particularly valuable when testing stiff specimens where common apparatus assumptions may not apply.

On crack simulation by mixed‐dimensional coupling in GFEM with global‐local enrichments

AbstractA strategy that combines the global‐local version of the generalized finite element method (GFEM) with a mixed‐dimensional coupling iterative method is proposed to simulate two‐dimensional crack propagation in structures globally represented by Timoshenko‐frame models. The region of interest called the local problem, where the crack propagates, is represented by a 2D elasticity model, where a fine mesh of plane stress/strain elements and special enrichment functions are used to describe this phenomenon accurately. A model of Timoshenko‐frame elements simulates the overall behavior of the structure. A coarse mesh of plane stress/strain elements provides a bridge between these two representation scales. The mixed‐dimensional coupling method imposes displacement compatibility and stress equilibrium at the interface between the two different element types by an iterative procedure based on the principle of virtual work. After establishing the constraint equations for the interface, the 2D elasticity model is related to the small‐scale model by the global‐local enrichment strategy of GFEM. In such a strategy, the numerical solutions of the local problem subjected to boundary conditions derived from the global‐scale problem enrich the approximation of this same global problem in an iterative procedure. Each step of the crack propagation requires a new sequence of this iterative global‐local procedure. On the other hand, the constraint equation for the interface is defined only once. The crack representation in a confined region by the global‐local strategy avoids a remeshing that would require new constraint equations. Two numerical problems illustrate the proposed strategy and assess the influence of the analysis parameters.