Elastic Model Research Articles

Elastic properties identification of a bio-based material in tertiary packaging: Tools and methods development

This study focuses on the use of bio-based materials for structural purposes in the packaging field, which requires the identification of their mechanical properties at a representative scale. The mechanical properties of bio-based materials are more variable than those of traditional composite materials. In a standard characterization approach using elemental coupons under uniaxial loading, the variability depends on the chosen representative elementary volume (REV), free edges, boundary conditions, etc. for elastic properties that are not identified for representative working conditions; this could lead to the ineligibility of these bio-based materials as structural materials. This paper contributes to the debate on how to study the response of bio-based materials within a structure, here a packaging structure as a logistic unit (LU) subjected to a compressive load simulating storage and stacking conditions. In the set of tools and methods for the design of packaging materials made of bio-based materials, an elastic nonlinear geometric finite element model (FEM) and an experimental approach are presented. The FEM allows the numerical identification of zones of interest within the LU. Inevitably, the FEM classically requires input data which are elastic properties of the equivalent homogeneous material. The design of the FEM is based on a calculation-test approach using an existing reference LU and it can be summarized in two main steps. The first step concerns the development of a FEM able to restore the experimental conditions of vertical compression imposed by transport standards for packaging. The second step is based on updating the input properties of the FEM by reverse identification, to achieve the representative working condition properties, using experimental results obtained on the existing reference LU. For the reverse identification a multi-scale investigation is mandatory. For this purpose, the linear elastic part of the load/vertical displacement curves (at the LU stiffness scale) and the displacement and strain fields measured (at the local LU scale) by 3D digital image correlation (3D DIC) are evaluated. Then, FEM property updating is carried out by reducing the deviation of displacement/strain fields between FEM and experimentally measured results (3D DIC). Finally, we explain how FEM and 3D DIC help in decision-making by allowing the recognition of zones of interest in a phase of design of new LUs with the concept of Multi-Instrumented Technological Evaluator (MITE).

Genomic Profiling of Antimicrobial Resistance Genes in Clinical Salmonella Isolates from Cattle in the Texas Panhandle, USA.

Rising antimicrobial resistance (AMR) in Salmonella serotypes host-adapted to cattle is of increasing concern to the beef and dairy industry. The bulk of the existing literature focuses on AMR post-slaughter. In comparison, the understanding of AMR in Salmonella among pre-harvest cattle is still limited, particularly in Texas, which ranks top five in beef and dairy exports in the United States; inherently, the health of Texas cattle has nationwide implications for the health of the United States beef and dairy industry. In this study, long-read whole genome sequencing and bioinformatic methods were utilized to analyze antimicrobial resistance genes (ARGs) in 98 isolates from beef and dairy cattle in the Texas Panhandle. Fisher exact tests and elastic net models accounting for population structure were used to infer associations between genomic ARG profiles and antimicrobial phenotypic profiles and metadata. Gene mapping was also performed to assess the role of mobile genetic elements in harboring ARGs. Antimicrobial resistance genes were found to be statistically different between the type of cattle operation and Salmonella serotypes. Beef operations were statistically significantly associated with more ARGs compared to dairy operations. Salmonella Heidelberg, followed by Salmonella Dublin isolates, were associated with the most ARGs. Additionally, specific classes of ARGs were only present within mobile genetic elements.

Ultrasound Probe Pressure Affects Aortic Wall Stiffness: A Patient-Specific Computational Study in Abdominal Aortic Aneurysms.

Ultrasound imaging is key in the management of patients with an abdominal aortic aneurysm (AAA). It was recently shown that the cyclic diameter variations between diastole and systole, which can be quantified with US imaging, increase significantly with the strength of the applied probe pressure on the patient's abdomen. The goal of this study is to investigate this effect more thoroughly. With finite-element modeling, pulsatile blood pressure and probe pressure are simulated in three patient-specific geometries. Two distinct models for the aortic wall were simulated: a nonlinear hyperelastic and a linear elastic model. In addition, varying stiffness was considered for the surrounding tissues. The effect of light, moderate, and firm probe pressure was quantified on the stresses and strains in the aortic wall, and on two in vivo stiffness measures. In addition, the Elasticity Loss Index was proposed to quantify the change in stiffness due to probe pressure. Firm probe pressure decreased the measured aortic stiffness, and material stiffness was affected only when the wall was modeled as nonlinear, suggesting a shift in the stress-strain curve. In addition, stiffer surrounding tissues and a more elongated aneurysm sac decreased the responsiveness to the probe pressure. The effect of probe pressure on the AAA wall stiffness was clarified. In particular, the AAA wall nonlinear behavior was found to be of primary importance in determining the probe pressure response. Thus, further work will intend to make use of this novel finding in a clinical context.

Analytical model of friction at low shear rates for soft materials in 3D printing.

The biological properties of silicone elastomers such as polydimethylsiloxane (PDMS) have widespread use in biomedicine for soft tissue implants, contact lenses, soft robots, and many other small medical devices, due to its exceptional biocompatibility. Additive manufacturing of soft materials still has significant challenges even with major advancements that have occurred in development of these technologies for customized medical devices and tissue engineering. The aim of this study was to develop a mathematical model of tangential stress in relation to shear stress, shear rate, 3D printing pressure and velocity, for non-Newtonian gels and fluids that are used as materials for 3D printing. This study used FENE (finitely extensible nonlinear elastic model) model, for non-Newtonian gels and fluids to define the dependences between tangential stress, velocity, and pressure, considering viscosity, shear stress and shear rates as governing factors in soft materials friction and adhesion. Experimental samples were fabricated as showcases, by SLA and FDM 3D printing technologies: elastic polymer samples with properties resembling elastic properties of PDMS and thermoplastic polyurethane (TPU) samples. Experimental 3D printing parameters were used in the developed analytical solution to analyse the relationships between governing influential factors (tangential stress, printing pressure, printing speed, shear rate and friction coefficient). Maple software was used for numerical modelling. Analytical model applied on a printed elastic polymer, at low shear rates, exhibited numerical values of tangential stress of 0.208-0.216 N m - 2 at printing velocities of 0.9 to 1.2 mm s - 1, while the coefficient of friction was as low as 0.09-0.16. These values were in accordance with experimental data in literature. Printing pressure did not significantly influence tangential stress, whereas it was slightly influenced by shear rate changes. Friction coefficient linearly increased with tangential stress. Simple analytical model of friction for elastic polymer in SLA 3D printing showed good correspondence with experimental literature data for low shear rates, thus indicating possibility to use it for prediction of printing parameters towards desired dimensional accuracy of printed objects. Further development of this analytical model should enable other shear rate regimes, as well as additional soft materials and printing parameters.

Prediction and Application of Drilling-Induced Fracture Occurrences under Different Stress Regimes

Identifying and categorizing drilling-induced fractures is pivotal for understanding the mechanisms underlying wellbore instability, drilling fluid loss, and assessing reservoirs using imaging logging data. This study employs a linear elastic stress model around the wellbore, coupled with a tensile failure criterion, to establish a predictive framework for the orientation of drilling-induced fractures. It investigates how engineering parameters like wellbore trajectory and bottomhole pressure influence the distribution of principal stresses around the wellbore, as well as the angle and orientation of drilling-induced fractures relative to the wellbore axis, across various faulting scenarios. The results indicate that drilling-induced fractures exhibit structured arrangements and consistent patterns, often appearing at approximately 180° symmetric intervals and descending in similar orientations. This provides a theoretical basis for their systematic identification and classification. Under different stress conditions, these fractures can manifest as feather-like shapes, “J”-shaped, or transitional states between feather-like and “J”-shaped orientations, as well as “V”-shaped or “M”-shaped orientations. Accurate detection and classification of these fractures are essential for interpreting effective fractures, conducting thorough reservoir evaluations, and predicting appropriate drilling fluid densities to mitigate the wellbore failure risk. Moreover, this knowledge aids in effectively determining the magnitude and direction of in situ stress inversion.

Development and experimental verification of an advanced 3D elastoplastic progressive damage model for composite materials

This study develops a sophisticated three-dimensional elastoplastic progressive damage finite element analysis (FEA) model for stiffened composite materials under axial compression. The model integrates the Hashin and Ye criteria to capture the inception of damage within the composite and introduces a cohesive zone model (CZM) to simulate debonding between stiffeners and panels. Furthermore, damage evolution based on energy release rate and plastic flow rules grounded in Hill’s criteria are employed to thoroughly explore the progressive failure behavior of stiffened composite materials. Implemented within Abaqus/Explicit through user-defined ‘VUMAT’ subroutines, the model ensures computational accuracy and reliability. Comparative evaluations against standard linear elastic progressive damage models demonstrate a statistically significant improvement of at least 5% in predicting ultimate load capacities. Additionally, this model accurately captures different failure modes, providing a nuanced understanding of stiffened composite material failure under compressive loads.

Nonlinear Viscoelastic Modeling of Finger Arteries: Toward Smartphone-Based Blood Pressure Monitoring via the Oscillometric Finger Pressing Method.

Oscillometric finger pressing is a smartphone-based blood pressure (BP) monitoring method. Finger photoplethysmography (PPG) oscillations and pressure are measured during a steady increase in finger pressure, and an algorithm computes systolic BP (SP) and diastolic BP (DP) from the measurements. The objective was to assess the impact of finger artery viscoelasticity on the BP computation. Nonlinear viscoelastic models relating transmural pressure (finger BP - applied pressure) to PPG oscillations during finger pressing were developed. The output of each model to a measured transmural pressure input was fitted to measured PPG oscillations from 15 participants. A parametric sensitivity analysis was performed via model simulations to elucidate the viscoelastic effect on the derivative-based BP computation algorithm. A Wiener viscoelastic model comprising a first-order transfer function followed by a static sigmoidal function fitted the measured PPG oscillations better than an elastic model containing only the static function (median (IQR) error of 30.5% (25.6%-34.0%) vs 50.9% (46.7%-53.7%); p<0.01). In Wiener model simulations, the derivative algorithm underestimated SP, especially with high pulse pressure and low transfer function cutoff frequency (i.e., greater viscoelasticity). The mean of the normalized PPG waveform at the maximum oscillation beat was found to correlate with the cutoff frequency (r = -0.8) and could thus possibly be used to compensate for viscoelasticity. Finger artery viscoelasticity negatively impacts oscillometric BP computation algorithms but can potentially be compensated for using available measurements. These findings may help in converting smartphones into truly cuffless BP monitors for improving hypertension awareness and control.

Multipoint Variable parameter compliant control of redundant manipulator based on the equivalent twin model of flexible contact dynamics

To elucidate the dynamic coupling mechanism involved in multipoint/arbitrary point contact during human–robot interactions with redundant manipulators, we introduce a compliant control strategy that adapts to variable parameters. This strategy is based on the flexible contact dynamic equivalent twin system for human–robot interactions. Using the Virtual Elastic Element Representation model for arbitrary point contact dynamics and leveraging the skeleton principle for contact force conversion, we construct a flexible contact dynamic equivalent twin system tailored for redundant manipulators with multipoint/arbitrary point contact capabilities. Within this system, we implement real-time adjustments to the impedance stiffness coefficient in conjunction with the virtual end velocity of the manipulator. We optimize the joint angular velocity of the manipulator while considering the motion allocation of redundant degrees of freedom. This optimization enables multipoint contact variable parameter compliance control for safe human–robot interactions. To validate our approach, we analyze the multipoint contact dynamic model of the redundant manipulator's interaction with humans and assess the feasibility of the variable parameter compliance control method using robot operating system simulations. Ultimately, we verify the effectiveness and practicality of our proposed compliance control method through simulation and experimental results.

Image-domain least-squares imaging in an elastic vertically transversely isotropic medium: Multiparameter point-spread function deconvolution

By solving a linear inverse problem, least-squares migration (LSM) can provide higher-precision images of complex subsurface structures than traditional adjoint-operator-based migration. LSM can be conducted in the data domain and the image domain (IDLSM). IDLSM in acoustic media has been extensively studied, commonly using single-parameter point-spread function (PSF) deconvolution. For high-accuracy imaging of complex media, we develop an image-domain elastic least-squares imaging method using multiparameter PSF deconvolution for vertically transversely isotropic (VTI) media. The multiparameter PSFs, including P-P, P-S, S-P, and S-S components, are calculated on a sparse grid using elastic VTI wave equation Born modeling and migration. The traditional migration result is then decomposed into individual local results, each corresponding to the size of a single PSF, through unit partitioning. Finally, a set of filters is derived from four elastic VTI PSF components to approximate the Hessian inverse, which are subsequently assembled to reconstruct an entire deconvolved image. The numerical experiments confirm that our method can significantly decrease multiparameter crosstalk artifacts and improve spatial resolution and amplitude fidelity.

Association of metabolic signatures of air pollution with MASLD: Observational and Mendelian randomization study

Background & AimsTo identify metabolic signatures associated with exposure to ambient air pollution and to explore their associations with risk of metabolic dysfunction-associated steatotic liver disease (MASLD). MethodsWe utilized data from the UK Biobank Cohort. Annual mean concentrations of PM2.5, PM10, NO2 and NOx were assessed for each participant using bilinear interpolation. The Elastic Net regression model was used to identify metabolites associated with four air pollutants and to construct metabolic signatures, respectively. Associations between air pollutants, metabolic signatures and MASLD were analyzed using Cox models. Mendelian randomization (MR) analysis was used to examine potential causality. Mediation analysis was employed to examine the role of metabolic signatures in the association between air pollutants and MASLD. ResultsA total of 244,842 participants from the UK Biobank were included in this analysis. We identified 87, 65, 76, and 71 metabolites as metabolic signatures of PM2.5, PM10, NO2, and NOx, respectively. Metabolic signatures were associated with risk of MASLD, with hazard ratios (HRs) and 95% confidence intervals (95% CIs) were 1.10 (1.06, 1.14), 1.06 (1.02, 1.10), 1.24 (1.20, 1.29) and 1.14 (1.10, 1.19). The four pollutants were associated with increased risk of MASLD, with HRs (95% CIs) of 1.03 (1.01, 1.05), 1.02 (1.01, 1.04), 1.01 (1.01, 1.02) and 1.01 (1.00, 1.01). MR analysis indicated an association between PM2.5, NO2 and NOx-related metabolic signatures and MASLD. Metabolic signatures mediated the association of PM2.5, PM10, NO2 and NOx with MASLD. ConclusionThere may be association between PM2.5, PM10, NO2 and NOx-related metabolic signatures and MASLD, and metabolic signatures mediate the increase of PM2.5, PM10, NO2 and NOx in the risk of MASLD. Impact and implicationsAir pollution is a significant public health issue and an important risk factor for metabolic dysfunction-associated steatotic liver disease (MASLD), however, the mechanism by which air pollution affects MASLD remains unclear. Our study used integrated serological metabolic data of 251 metabolites from a large-scale cohort study to demonstrate that metabolic signatures play a crucial role in the elevated risk of MASLD caused by air pollution. These results are relevant to patients and policymakers because they suggest that air pollution-related metabolic signatures are not only potentially associated with MASLD but also involved in mediating the process by which PM2.5, PM10, NO2, and NOx increase the risk of MASLD. Focusing on changes in air pollution-related metabolic signatures may offer a new perspective for preventing air pollution-induced MASLD and serve as protective measures to address this emerging public health challenge.

Design and validation of a DMA-inspired device for in-vivo measurement of human skin mechanics: a finite element analysis approach

Abstract This study introduces a novel method for measuring the mechanical properties of human skin in-vivo, inspired by dynamic mechanical analysis (DMA). We designed and applied a DMA-like device to living human skin and validated its functionality through finite element analysis (FEA) on an ideally elastic skin model. The device features multiple testing modes, including horizontal movement in both same and opposite directions with optional pre-stretching. Stress-strain behaviours obtained from FEA align with initial setup parameters, serving as powerful tools for further research into the mechanical properties of skin. This method is expected to have potential significance in biomechanical theory, clinical, and healthcare applications.

392. MACHINE LEARNING TO PREDICT LYMPH NODE METASTASIS IN T1 ESOPHAGEAL SQUAMOUS CELL CARCINOMA: A MULTICENTER STUDY

Abstract Background Lymph node metastases (LNM) is a relatively uncommon but possible complication of T1 esophageal squamous cell carcinoma (ESCC). Existing models do poorly when it comes to quantifying this risk. As a branch of artificial intelligence, machine learning (ML) algorithms have developed and become more prominent. Up to now, no individualized ML prediction model aimed at predicting LNM in T1 esophageal squamous cell carcinoma patients is available. This study aimed to develop a machine learning model for LNM in patients with T1 esophageal squamous cell carcinoma. Methods Patients with T1 squamous cell carcinoma treated with surgery between January 2010 and September 2021 from 3 institutions were included. Machine-learning models were developed using data on patients’ age and sex, depth of tumor invasion, tumor size, tumor location, macroscopic tumor type, lymphatic and vascular invasion, and histologic grade. Elastic net regression (ELR), random forest (RF), extreme gradient boosting (XGB), and a combined (ensemble) model of these was generated. Use Area Under Curve (AUC) to evaluate the predictive ability of models. The contribution of each factor was calculated. To meet clinical needs, we designed the model as a user-friendly website. Results 926 and 341 patients were included in the derivation and validation cohorts. The lymph node metastasis rate was 14.8%. The models all exhibited potent discriminating power. The elastic net regression model performed best with externally validated AUC of 0.803 (AUC 0.773 for RF, 0.791 for XGB, 0.799 for ensemble) whereas the NCCN guidelines identified patients with LNM with an AUC of 0.576 and logistic model with an AUC of 0. 670. The most important features were lymphatic and vascular invasion as well as depth of tumor invasion. Conclusions The model created utilizing machine learning approaches had excellent performance estimating the likelihood of LNM in T1 ESCC, which can help patients achieve personalized treatment options.

An improved viscoelastic k- ε -v2-f turbulence model for intermediate and high drag reduction regimes

In this work, an improved anisotropic k-ε-v2-f model based on the finite extensible nonlinear elastic model with the Peterlin approximation for viscoelastic channel flows is proposed. This model is tested using direct numerical simulation (DNS) data for friction Reynolds numbers (Reτ) in the range of 120–1000, friction Wiesenberg numbers (Wiτ) in the range of 25–116, viscosity ratios (β) in the range of 0.6–0.9, and maximum polymer extensibility values (L2) in the range of 900–14 400. The flow characteristics of viscoelastic fluids with various parameters obtained from the new model agree well with existing DNS results. By adding closures for the flow, shear, and transverse components, the incomplete prediction of nonlinear terms from interactions between the fluctuating components of the conformation and velocity gradient tensors is improved. Compared with DNS results, these closures can fully obtain each component and significantly improve the accuracy of the flow direction component in the intermediate and high drag reduction regimes. Furthermore, the model in this paper retains the advantages of an anisotropic model, does not require a damping function, is simple to construct, and is easily extended to a variety of bounded flows.

Discrete element method model calibration and validation for the spreading step of the powder bed fusion process to predict the quality of the layer surface

A Discrete Element Method model, including interparticle cohesive forces, was calibrated and validated to develop a tool to predict the powder layer’s quality in the powder bed fusion process. An elastic contact model was used to describe cohesive interparticle interactions. The surface energy of the model particles was estimated by assuming that the pull-off force should provide the strength of the material evaluated at low consolidation with shear test experiments. The particle rolling friction was calibrated considering the bulk density of the layer produced by the spreading tool. The model was validated with the experiments by comparing the wavelet power spectra obtained with the simulations with those of the experimental layers illuminated by grazing light. The calibration proposed in this study demonstrated superior performance compared to our previous methods, which relied on measuring the angle of repose and unconfined yield strength.

Finite element algorithm for rigid pavement resting on Pasternak elastic foundation model under aircraft loading

Finite element algorithm for rigid pavement resting on Pasternak elastic foundation model under aircraft loading

Cubic B-spline based elastic and viscoelastic wave propagation method

The requirement for high computational efficiency in inversion imaging poses challenges to further enhancing the accuracy of imaging large elastic and viscoelastic models. Considering that forward modeling serves as a prerequisite for inversion imaging, it is essential to introduce a wave propagation simulation method that can enhance simulation accuracy without significantly compromising computational speed. In our paper, cubic B-spline is introduced into the forward modeling of the wave equation. The B-spline collocation method offers a linear complexity for computation and exhibits fourth-order convergence in terms of computational errors. We also find that it can perfectly adapt to the boundary conditions of the perfectly matched layer in the forward modeling solution of the wave simulation. Several typical numerical examples, including 2-D acoustic wave equation, 2-D elastic wave propagation, and 2-D viscoelastic propagation in homogeneous media, are provided to validate its convergence, accuracy, and computational efficiency.

On effective surface elastic moduli for microstructured strongly anisotropic coatings

The determination of surface elastic moduli is discussed in the context of a recently proposed strongly anisotropic surface elasticity model. The aim of the model was to describe deformations of solids with thin elastic coatings associated with so-called hyperbolic metasurfaces. These metasurfaces can exhibit a quite unusual behaviour and concurrently a very promising wave propagation behaviour. In the model of strongly anisotropic surface elasticity, strain energy as a function of the first and second deformation gradients has been introduced in addition to the constitutive relations in the bulk. In order to obtain values of surface elastic moduli, we compare dispersion relations for anti-plane surface waves obtained using the two-dimensional (2D) model and three-dimensional (3D) straightforward calculations for microstructured coatings of finite thickness. We show that with derived effective surface moduli, the 2D model can correctly describe the wave propagation.

Predicting the non-linear behaviour of cross laminated timber shearwalls with cut-out openings

The behaviour and failure mode expected in Cross Laminated Timber (CLT) shearwalls when either window or door openings are incorporated into the shearwalls may be considerably different than that of shearwalls without openings. Despite clear theoretical and experimental evidence of the possible occurrence of significant increase in the deformation contribution of the CLT panels and induce high stress concentrations around openings, limited studies have been conducted on the effect of crack propagation in CLT shearwalls with cut openings. The current study presents two modelling techniques to account for the crack propagation around openings, through concentrated plastic hinge (PHM) and continuous post-elastic (CPEM) models. The proposed models are validated using available experimental results obtained from six full-scale shearwalls in the literature while input parameters, such as the mechanical properties of the CLT panels, are obtained, in part, from component-level experimental investigation on CLT beams conducted by the authors as part of the current study. The impact and advantages of accurately predicting the non-linear behaviour of the CLT panels are investigated through a numerical analysis on a case-study representing a multi-storey shearwall with multiple openings. The results showed the inability of elastic models to predict the inelastic behaviour in the CLT shearwall after the crack opening, and this the study recommends the inclusion of stress redistribution near crack openings and subsequent inelastic behaviour in the analysis.

Calculation of 3D Shape of a Hyperelastic Body for Nonlinear Elasticity Models Using the Newton Method

This article discusses methods for calculating the deformations of objects with hyperelastic materials within the framework of the nonlinear elasticity theory. This topic is relevant due to the use of new technological materials in industry, and as a result, the emerging task of preliminary numerical calculations for operational reliability, research and modeling of deformation behavior. The first part provides a brief overview of the main provisions and formulas of the nonlinear elasticity theory. Then the spatial discretization of 3-dimensional objects and the calculation of the deformation gradient using the finite element method are considered. The article provides an algorithm for solving this problem, such as minimizing the functional of stored energy, and also considers the class of permissible deformations. Afterwards, a detailed description is given, along with pseudocode, of the method of implementing and calculating the minimization by Newton’s method. The last part demonstrates an example of the calculations performed, based on the developed software that allows for numerical experiments and computer modeling of deformations of hyperelastic bodies, and one of the capabilities of which is to perform these calculations using Newton’s method.

Statistical analysis of adhesive rod-tube joints under tensile stress for structural applications

Adhesive bonding has been replacing traditional joining methods such as welding, bolting, and riveting in the design of mechanical structures in the automotive, aerospace and aeronautic industries. This joining method has several advantages over traditional methods such as ease of manufacture, lower costs, ease of joining different materials, higher fatigue resistance, and high corrosion resistance. Although tubular adhesive joints have varying applications, such as in truss structures and vehicles, machine axles, and piping, different joint configurations exist, such as rod-tube joints (RTJ), which are not conveniently addressed in the literature. This work compares the tensile performance of adhesively bonded RTJ between aluminium alloy components (AW6082-T651), considering the variation of the main geometric parameters: overlap length (LO), tube thickness (tS), rod diameter (d), adhesive fillet angle (f), and type of adhesive. The Taguchi’s method was employed in the elaboration of the applied design of experiments (DoE). To compare the RTJ behaviour, a numerical analysis was carried out through finite element analysis (FEA) and cohesive zone modelling (CZM). Peel (σy) and shear (τxy) stresses in the adhesive layer were initially obtained by applying purely elastic models. CZM modelling made possible to obtain the damage evolution in the adhesive layer, the maximum load (Pm) and dissipated energy (U) at Pm of the adhesive joints. As a result of applying the Taguchi method, the adhesive joint that showed the best overall performance used the adhesive Araldite® AV138, LO = 40 mm, d = 20, and tS = 3 mm.