Finite Element Predictions Research Articles

Phase field theory for pressure-dependent strength in brittle solids with dissipative kinetics

A phase field theory of fracture mechanics is formulated to address dependence of material strength on stress state, noting that brittle solids are usually more fracture resistant when mean stress is compressive. Fracture is addressed via a dissipative kinetic law which instills rate dependence and viscous resistance to propagation. A dependence of kinetic viscosity on triaxiality for locally compressive stress states is proposed. Solutions are derived to one-dimensional problems for an isotropic material, linear or nonlinear elastic, under different loading protocols: uniaxial stress extension, uniaxial stress compression, and uniaxial strain compression. Analytical results enable determination of parameters and verification of finite element predictions. Three-dimensional simulations of polycrystalline microstructures are enacted under similar loading protocols. Results provide insight into effects of crystalline microstructure and anisotropy for different stress states. With increasing confinement, the ratio of macroscopic pressure to shear stress increases, and influences of microstructure and anisotropy on average stress and ductility are reduced.

Evaluation of loading-path-dependent constitutive models for springback prediction in martensitic steel forming

In this study, the performance of conventional and advanced constitutive models to the prediction of springback for ultra-high strength steel was assessed. The elasto-plastic behavior of a martensitic steel sheet sample was characterized to assess the conventional stress-strain behavior in uniaxial tension. More advanced tests such as uniaxial compression and tension-compression experiments were conducted to assess the strength-differential (SD) effect and hardening fluctuations during non-linear loading paths (NLLP effect). Three constitutive plasticity models, namely, the conventional isotropic hardening, Yoshida-Uemori (YU) two surface kinematic hardening and pure distortional hardening (HAH20) models were calibrated using an optimization procedure. Then, these models were employed for finite element predictions of springback after forming. The isotropic hardening model does not consider both SD and NLLP effects and the YU model captures only the influence of the NLLP effect. On the other hand, the HAH20 model describes both effects simultaneously. The performance of these models with respect to springback prediction was evaluated using three forming applications: wiper bending, C-rail drawing and Roof-Side-Rail crush forming. This work indicates that the HAH20 model is the best candidate for the prediction of forming and springback for such martensitic steel because of its ability to consider both SD and NLLP effects. However, the conventional isotropic hardening model led to results in good agreement with those obtained using the HAH20 model in specific cases. The reason, discussed in detail in this article, is likely due to the compensation of the permanent softening due to load reversal by the higher flow stress due to the SD effect.

Comparison between a predicted and an experimentally measured residual stress field generated by side-punching of API X65 steel

A residual stress field was generated by a circular, flat-ended, rigid punch indenting a thick test specimen extracted from X65 grade-controlled-rolled pipeline steel. Laboratory X-ray diffraction was used to measure residual stress field the near-surface, whereas the contour method and neutron diffraction were used to quantify the through-thickness residual stress field. A numerical method was proposed to account for gauge volume variation which allowed a direct comparison of the Finite Element prediction with the experimental measurements. A good agreement between the measurements and prediction was observed, showing that the through-thickness compressive residual stress reaches the highest magnitude in the centre of the specimen. The validated results can be used with confidence for residual stress-crack interaction studies in single-edge notched bend SEN(B) and single-edge notched tension SEN(T) fracture specimens which are common in the oil and gas industry due to the inherited close level of constraint experienced in a pipe.

Nonlinear FE Prediction of Shear Strength of RC T-Beams with Flange in Compression Zone

This research predicts the shear strength of reinforced concrete T-beams with flanges under compression stresses using nonlinear finite element (FE) analysis. A FE model is developed and verified against specially designed experiments (beams with varying flange width and depth). Results of the FE models were found to be in excellent agreement with their corresponding experimental results. The average load capacity and deflections (FE/experiments) ratios were 1.03 and 0.87, respectively. We then conducted an extensive parametric study to investigate the structural performance of flanged beams under the effect of two concentrated point loads. This parametric study examined four parameters: flange dimensions, longitudinal reinforcement in flange, concrete compressive strength, and shear span to depth ratio. Our findings indicated that the presence of compressed flanges in T-beams increases the shear strength by up to 260% of the shear strength of the web alone. The shear strength of flanged beams increases with the increase in flange dimensions, where the effect of flange thickness is more pronounced than that of flange width. Moreover, the presence of longitudinal reinforcement in the flange enhanced the beam's shear strength by up to 40%, compared to similar beams without flange reinforcement. Additionally, the shear strength increased up to three-fold for various beam conditions when the shear span to depth ratio was reduced from 2.0 to 0.5. These findings provide valuable insights for designing and constructing reinforced concrete T-beams with flanges under compression stresses.

Machine learning used for simulation of MitraClip intervention: A proof-of-concept study.

Introduction: Severe mitral regurgitation (MR) is a mitral valve disease that can lead to lifethreatening complications. MitraClip (MC) therapy is a percutaneous solution for patients who cannot tolerate surgical solutions. In MC therapy, a clip is implanted in the heart to reduce MR. To achieve optimal MC therapy, the cardiologist needs to foresee the outcomes of different scenarios for MC implantation, including the location of the MC. Although finite element (FE) modeling can simulate the outcomes of different MC scenarios, it is not suitable for clinical usage because it requires several hours to complete. Methods: In this paper, we used machine learning (ML) to predict the outcomes of MC therapy in less than 1s. Two ML algorithms were used: XGBoost, which is a decision tree model, and a feed-forward deep learning (DL) model. The MC location, the geometrical attributes of the models and baseline stress and MR were the features of the ML models, and the predictions were performed for MR and maximum von Mises stress in the leaflets. The parameters of the ML models were determined to achieve the minimum errors obtained by applying the ML models on the validation set. Results: The results for the test set (not used during training) showed relative agreement between ML predictions and ground truth FE predictions. The accuracy of the XGBoost models were better than DL models. Mean absolute percentage error (MAPE) for the XGBoost predictions were 0.115 and 0.231, and the MAPE for DL predictions were 0.154 and 0.310, for MR and stress, respectively. Discussion: The ML models reduced the FE runtime from 6 hours (on average) to less than 1s. The accuracy of ML models can be increased by increasing the dataset size. The results of this study have important implications for improving the outcomes of MC therapy by providing information about the outcomes of MC implantation in real-time.

Response of multi-cell steel–concrete–steel sandwich panels impacted by a hemi-spherical head: Experimental and numerical studies

In this study, a novel multi-cell steel–concrete–steel (MCSCS) sandwich panel was proposed for enhancing impact resistance of the traditional steel–concrete–steel​ (SCS) sandwich panel. The MCSCS sandwich panel employed stiffeners and headed studs to improve the bonding behavior between faceplates and concrete core as well as enhance its composite action and impact resistance. Impact tests were conducted on seven MCSCS panels via employing a drop weight loading system, and the influences of impact direction, spacing of headed stud and steel plate thickness on responses of MCSCS panels were investigated. Furthermore, the Finite Element (FE) model of the MCSCS panel was established, and the FE predictions were shown to be reasonable as compared to test results. Two types of failure modes of MCSCS panels under impact load were obtained via analyzing the test and FE results. In addition, based on the verified FE model, the influences of stiffeners, impact location and curvature of hammer head on impact responses of MCSCS panels were revealed via parametric studies. The results of FE simulations indicated that the impact location and curvature of hammer head had evident effect on the energy absorption and impact response of the MCSCS panel. Moreover, owing to the employment of stiffeners, the impact resistance of the MCSCS panel was evidently enhanced as compared to the traditional SCS panel.

3D Numerical Assessment of Rammed Aggregate Pier Performance under Dynamic Loading in Liquefiable Soils

Ground improvement (GI) techniques have shown promise in effective liquefaction mitigation, but the physical mechanisms governing their three-dimensional (3D) response during dynamic loading are not yet fully understood. To evaluate the 3D performance of one GI technique, the rammed aggregate pier (RAP), in-situ site characterization, full-scale field test data, and calibrated baseline constitutive soil model parameters are combined to model the 3D fully coupled hydromechanical response of natural (unreinforced) and improved (reinforced) soil profiles. To the authors’ knowledge, this contribution represents the first 3D model of a columnar-reinforced soil profile being calibrated using full-scale field testing. The field observations from the comprehensive ground improvement testing (GIT) program in New Zealand and insights from two-dimensional (2D) finite-difference analyses using constitutive model parameters calibrated against the field measurements were used. The developed 3D models were subjected to dynamic loads simulating the excitation generated by a vibroseis truck at one of the in-situ test sites of the GIT program, as well as unidirectional and bidirectional earthquake ground motions from the Canterbury Earthquake Sequence events. The 3D simulations showed that the improved soil profiles experienced reduced excess pore pressures and reduced dynamically induced shear strains compared to the natural, unreinforced soil models. The developed 3D finite-element predictions were compared and validated vis-à-vis the field observations of the GIT program. Compared to 2D analyses, 3D analyses provide a more accurate description of actual field conditions, and, for instance, it was observed that multidirectional shaking has a significant effect on liquefaction triggering, particularly for natural soil profiles. Finally, it was shown that soil densification around the installed pier elements and the lateral earth pressure increase within the densified soil and are the primary ground improvement mechanisms contributing to the reduction of dynamically induced shear deformations and excess pore pressure generation during earthquake shaking. It was also found that the permeability and shear stiffness of the installed RAP piers did not have a significant influence on the pore pressure response and shear strains developed along the centerline of the improved area.

Experimental Validation and Numerical Analysis of a High-Performance Blast Energy-Absorbing System for Building Structures

The paper presents a full-scale blast testing experimental campaign conducted on an energyabsorbing connector comprising thin-walled inversion tubes as kernel elements mounted in a façade protective panel. LS-DYNA finite element predictions of the global and local deformation/inversion of the panel/connectors compared reasonably well with the experimental observations. After validation, the numerical model was used to analyze the response of a simple idealized reinforced concrete structure under three blast-loading scenarios: the first two scenarios produce, approximately, the same impulse but are significantly different in terms of load duration and overpressures, and represent a far-field and a near-field scenario (1600 kg TNT at 20 m (i) and 150 kg TNT at 5 m (ii), respectively); the third scenario is more demanding, and consists in a half standoff distance of the second (150 kg TNT at 2.5 m (iii)). These numerical simulations allow to assess the effect of standoff distance and blast loading on the effectiveness of the protective system. One may conclude that the introduction of EACs strongly limits the forces imparted to the protected structure, reducing significantly the corresponding energy absorption demand. Comparing the energy absorbed by the structure in different scenarios, with and without the protective system (8 × ϕ64 × 2 mm), one can see that these reductions can reach, respectively 67%, 72% and 68% in the far-field, near-field and very near-field explosions.

Applying a homogeneous pressure distribution to the upper vertebral endplate: Validation of a new loading system, pilot application to human vertebral bodies, and finite element predictions of DIC measured displacements and strains

Image-based personalized Finite Element Models (pFEM) could detect alterations in physiological deformation of human vertebral bodies, but their accuracy has been seldom reported. Meaningful validation experiments should allow vertebral endplate deformability and ensure well-controlled boundary conditions. This study aimed to (i) validate a new loading system to apply a homogeneous pressure on the vertebral endplate during vertebral body compression regardless of endplate deformation; (ii) perform a pilot study on human vertebral bodies measuring surface displacements and strains with Digital Image Correlation (DIC); (iii) determine the accuracy of pFEM of the vertebral bodies.Homogeneous pressure application was achieved by pressurizing a fluid silicone encased in a rubber silicone film acting on the cranial endplate. The loading system was validated by comparing DIC-measured longitudinal strains and lower-end contact pressures, measured on three homogeneous pseudovertebrae of constant transversal section at 2.0 kN, against theoretically calculated values. Longitudinal strains and contact pressures were rather homogeneous, and their mean values close to theoretical calculations (5% underestimation).DIC measurements of surface longitudinal and circumferential displacements and strains were obtained on three human vertebral bodies at 2.0 kN. Complete displacement and strain maps were achieved for anterolateral aspects with random errors ≤0.2 μm and ≤30 μstrain, respectively. Venous plexus and double curvatures limited the completeness and accuracy of DIC data in posterior aspects.pFEM of vertebral bodies, including cortical bone mapping, were built from computed tomography images. In anterolateral aspects, pFEM accuracy of the three vertebrae was: (i) comparable to literature in terms of longitudinal displacements (R2>0.8); (ii) extended to circumferential displacements (pooled data: R2>0.9) and longitudinal strains (zero median error, 95% error: <27%). Circumferential strains were overestimated (median error: 39%).The new methods presented may permit to study how physiological and pathologic conditions influence the ability of vertebral endplates/bodies to sustain loads.

Analytic Solution to Longitudinal Deformation of Suspension Bridges under Live Loads

Live load of moving vehicles has a very important effect on the fatigue life of suspension bridges, which causes not only vertical deformation but also longitudinal deformation. In this study, a general analytical formulation for analyzing the quasistatic longitudinal displacement of suspension bridges under vertical live loads is developed, and the underlying deformation mechanism is revealed. First, the analytical vertical and longitudinal deformation equations for the single main cable subjected to live loads are formulated considering the geometric nonlinearity. Then, the relation of longitudinal displacements between the stiffening girder and the main cable for a single-span suspension bridge is established through analyzing the geometric configuration of deformed deck-suspender segment and imposing the null longitudinal force condition. The relation is further modified to incorporate the effect of central buckles (CBs). Compared with the finite-element (FE) prediction, the proposed analytical solution is quite accurate for both concentrated and distributed loads. It is found that the coupling of vertical and longitudinal displacement of main cables and the longitudinal constraint between the cables and girder, are responsible for the longitudinal displacement of the girder. The effects of sag-to-span ratio, CB, and inclined suspenders are studied. The longitudinal displacement of the girder can be reduced by about 20% when the sag-to-span ratio is varied from 1/9 to 1/11, and the CB with proper stiffness is more effective in reducing the longitudinal displacements. The proposed formulation can be conveniently applied for parameter optimization in the preliminary design stage so as to avoid tedious repetitive FE analysis.

Finite Element Model Tuning Using Analytical Sensitivity Values

This paper presents an efficient approach for tuning finite element models to match the measured ground vibration test and proof test data. Frequencies, mode shapes, total weight, location of the center of gravity, and static deformation computed from the finite element model are matched to the measured data. The model tuning procedure used in this work is based on solving an optimization problem in which the errors for the considered metrics, between the finite element prediction and the measured data, are minimized. Analytical sensitivity values of performance indices are computed using the NASTRAN-generated sensitivity values together with the in-house computer programs, which allow for faster computational time and the use of gradient-based optimizers. The method is applied to the Aerostructures Test Wing 4 model. The study shows that the military standard and the NASA standard for comparing analytical and experimental modal data are all satisfied. The final finite element model correlates well with the test data. The flutter speed decreases by 8.91% after model tuning compared with the original Aerostructures Test Wing 4 design.

An Efficient Calculation Method for Stress and Strain of Concrete Pump Truck Boom Considering Wind Load Variation

Digital twin is the development trend of concrete pump trucks to realize digitalization and intellectualization. The realization of digital twin requires high calculation efficiency and accuracy of the model. As the concrete pump truck works under the wind load, the wind speed and direction on site change frequently and intensely. However, existing methods, such as the finite element method, have the problems of low computational efficiency, high time complexity, and the update frequency being far lower than the frequency of wind change on site. We propose an efficient calculation model for the stress and strain of the pump truck boom based on the back propagation (BP) neural network. The novelty of this work is that when calculating the stress and strain of the boom, the change of the boom posture and the change of the site wind conditions are considered, and the calculation efficiency can be significantly improved. Compared with the finite element simulation, the fitting and prediction accuracy of the stress and strain are more than 99.7%, which can meet the requirements for real-time calculation of the stress and strain of the boom under different attitudes and wind loads in digital twins.

Fatigue of octet-truss lattices manufactured by Laser Powder Bed Fusion

The octet-truss lattice is a three-dimensional lattice with high strength and low density. Practical use of these lattices requires a knowledge of their resistance to fatigue crack growth. Lattice specimens manufactured by laser powder bed fusion technique were prepared with different orientations to explore the orientation effects on lattice fatigue behaviour. X-ray tomography was used to measure the surface roughness of the lattice struts, and also used to validate the accuracy of the crack length measurement by compliance method. The experimental results show that the fatigue crack growth rate and crack growth path depend on the orientation of the lattice. A finite element prediction of the fatigue life of the lattice was carried out, based on measurements of the fatigue life of single struts cut from the lattice. The finite element predictions were in good agreement with the experimental results. A procedure for predicting the crack growth path was proposed. These findings can help designers optimize the orientation of lattice structures in structural applications.

The effect of cross-section geometry on the lateral–torsional behavior of thin-walled beams: Analytical and numerical studies

In this paper, the elastic lateral–torsional behavior of simple beams is discussed by presenting a novel analytical solution and performing numerical studies. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, significantly different when the second-order nonlinear behavior of beams with initial imperfections is analyzed. To understand and explain the observed differences, a novel analytical model is worked out for the geometrically nonlinear analysis of beams with initial geometric imperfections. The advancement in the presented analytical solution is the explicit consideration of the changing geometry as the load increases. The most important steps of the derivations are summarized, and the resulting formulae are briefly discussed. The derivations are done for general cross-sections, however, the bending is assumed to act in one of the principal planes. Numerical studies are also presented, focusing on mono-symmetric cross-sections. As part of the numerical studies, first, the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae can capture the most essential elements of the behavior observed in the shell finite element calculations, justifying that the cross-section shape might have a significant effect on the nonlinear lateral–torsional behavior of beams. Then the effect of the lateral–torsional buckling is predicted by calculating buckling reduction factors, using the results of the geometrically nonlinear finite element calculations. The capacity prediction results, again, justify that the cross-section shape, as well as the sign of the assumed geometric imperfection, might have a non-negligible effect on the buckling reduction factors, and on the capacity of the member.

A developed hybrid experimental–analytical method for thermal stress analysis of a deep U-notched plate

A general framework of hybridizing experimentally-recorded load-induced thermal information by means of thermoelastic stress analysis (TSA) of a loaded structure with the Michell solution of Airy stress function in isotropic linear elasticity is proposed for in-plane stresses determination. The capability of the proposed hybrid method in separating the TSA signals into individual stresses is demonstrated by stress-analyzing a deep U-notched aluminum plate without neither knowing the entire geometry and distant loading/boundary conditions nor using supplementary experimental information. Even though no experimental data were processed at, and adjacent to, the edges of the U-notched plate, the individual stresses are determined throughout the surface of the plate. Prior processing actual experimental TSA data, the accuracy and the stability of the proposed hybrid method through adding artificial noise scatters in the processed simulated data with the number of retained terms in the generalized Airy stress expressions are firstly investigated. The effects of the superimposed noise scatters as well as the number of employed data in the evaluated stresses are also assessed. Finally, the reliability of the determined hybrid-experimental stresses is supported through a comparison with finite-element predictions and strain gauge measurements. The ease of implementation, the accuracy and the precision of the evaluated stress, and the versatility to the type of employed data make the proposed hybrid method more attractive and superior than other hybrid methods.

Finite Element Analysis of Restraint Intensities and Welding Residual Stresses in the Ti80 T-Joints

The restraint intensity of Ti80 T-joints was investigated using finite element analyses. The influence of slit height, vertical plate thickness and base plate thickness was studied, respectively. Results show that the slit height and vertical plate thickness have a significant impact, while the effect of base plate thickness is negligible. A prediction model of restraint intensity was constructed through binary linear regression; the error was estimated at about 10%. Then, finite element simulations were carried out to study the welding residual stresses of specimens with different restraint intensities. The results show that residual stresses on the backing weld surface are higher in the middle and lower at both ends, while the weld root shows opposite results. In general, stresses at the weld root are greater than those on the weld surface. The mean value of the residual stress at the weld root increases with the increase in restraint intensity but not uniformly, i.e., it is slow at first and then it increases rapidly. A prediction model of the residual stress was produced through cubic fitting, and the errors between the finite element simulations and predictions were about 8%. Using the prediction model, the residual stress of actual Ti80 alloy workpieces can be estimated before welding, and a corresponding strategy for avoiding cracks can be generated.

Plasticity, ductile fracture and ballistic impact behavior of Ti-6Al-4V Alloy

The strength and fracture behavior of a metal are crucial to its response in impact events. In the present paper, a hybrid experimental-numerical study was conducted to characterize the plasticity and ductile fracture behavior of Ti-6Al-4V alloy. To this end, ten types of specimens were utilized to cover a range of stress states from uniaxial tension to high stress triaxiality, shear, plane strain as well as elevated temperatures and strain rates. Especially, a slightly modified in-plane shear specimen suggested by Roth and Mohr was proposed and adopted to prevent premature fracture initiation from the free boundaries at a tension stress state. Aside from a Split Hopkinson Pressure Bar (SHPB) system, a high-speed servo-hydraulic testing machine was applied to conduct high-rate tests. A Modified Johnson-Cook (MJC) plasticity model and an extended Xue–Wierzbicki (XW) fracture criterion with strain rate and temperature effects were used and calibrated using a combined experimental-numerical approach. It was found that the fracture strain of the metal is sensitive to both the stress triaxiality and the deviatoric state parameter, and reduced ductility is reached at increasing stress triaxialities and a plane strain as well as shear stress states. The yield strength increases with increasing strain rate and decreasing temperature. An enhanced ductility is achieved at elevated temperatures and lower strain rates, except for at the highest strain rate of 750 /s, at which a higher ductility is observed compared with that at slightly lower strain rates. Ballistic impact tests on 4 mm thick Ti-6Al-4V alloy targets were conducted using 5.95 mm diameter blunt rigid projectiles in an impact velocity range of 167.9 – 321.6 m/s. Parallel finite element simulations were performed for the ballistic tests and the validity of the calibrated material models was confirmed by comparing the predicted ballistic resistance and failure pattern of the target with the experimental ones. In addition, it was found that a finite element prediction on the ballistic resistance of the Ti-6Al-4V alloy targets struck by blunt projectiles is highly mesh size sensitive and a converged solution was obtained by using a mesh size of 20 μm.

Active control of noise in plate-cavity coupled systems using the pole placement method

Structure-acoustic coupled systems have received great attention in engineering, and a typical representative is a plate coupled with a cavity. The sound in the cavity is excited by the vibration of the plate and when there is strong coupling between the acoustic modes of the cavity and the vibrational modes of the plate, the sound pressure can be enhanced dramatically. In this paper, active control based on the pole placement method is used for the first time to reduce the noise in a plate-cavity coupled system. The principle of the pole assignment is that the poles of a system represent the system’s dynamical behaviour, and their assignment allows one to modify the response of the system using sensors and actuators. In this work, the usage of pole assignment to modify the dynamics of the plate is theoretically derived, and the resulting sound in the cavity is analytically calculated by solving a coupled matrix equation. To access the performance of the pole placement method in reducing the noise in the coupled system, three example cases are considered. The first is a local control case which uses a single actuator to control the first two modes of the plate in order to attenuate the resulting sound in the cavity. The second case is imposing global control by using two actuators to modify the first four modes of the plate, weakening the strong interaction between the pate and the cavity by shifting their natural frequencies away from each other. The third is applying uncontrollability conditions to retain particular modes when the control method is applied. The analytical results show that the pole placement method can be effective to control both the vibration and the vibro-acoustics in the plate-cavity coupled system. The finite element (FE) method is used to validate the analytical models. The FE predictions show good agreement with the analytical results. The pole placement method is shown to be effective in controlling the noise in this plate-cavity coupled system, and there is the potential to extend the method to more complex structure-acoustic coupled systems.

Analysis and enhancement of the new Eurocode 5 formulations for the lateral elastic deformation of LTF and CLT walls

This paper analyses the analytical formulations for the lateral elastic deformation of Light Timber Framed (LTF) and Cross-Laminated Timber (CLT) shear walls according to the new Eurocode 5 (EC5) proposal. Finite Element (FE) models and the Standard predictions are compared by emphasizing the role of each deformation contribution. A total of 1830 comparisons between analytical and numerical estimations are carried out by exploiting the Application Programming Interface of SAP2000 to modify the FE model parameters automatically. The parametric analyses proved that the numerical and analytical predictions are pretty consistent. Furthermore, in both LTF and CLT shear walls, the estimates for in-plane shear and rigid body sliding are in excellent agreement. Conversely, the analytical formulas for kinematic rocking are generally conservative for LTF and monolithic CLT shear walls, with an approximate 18%–19% discrepancy. The analytical expressions of the upcoming EC5 perfectly match the numerical model for segmented CLT shear walls under lateral forces and no vertical load. However, the presence of the vertical load determines a significant bias. Additionally, the predictions for bending deformations are not in good agreement. Therefore, the paper discusses possible enhancements for the equations proposed in the next generation of Eurocodes for the rocking deformation of segmented CLT walls to better conform with FE predictions.

Dimensionless analysis of the elastoplastic constitutive properties of single/multilayered films under nanoindentation

<p indent="0mm">Among the features of substrate-film structures, based on the load-displacement curves obtained from the nanoindentation tests, the intrinsic parameters of film material (elastic modulus, hardening exponent, and yield strength) are considered as the influential parameters in the load-displacement curves in terms of the applied load and work done in the loading phase. Based on the influential parameters combined in a dimensionless manner, the dimensionless function formulations are presented in association with the finite element simulation results, leading to a novel methodology proposed to solve the constitutive parameters appropriate for single-layered elastoplastic film materials. The advantage of the proposed dimensionless function in reproducing the finite element prediction results is verified by comparing it with the constitutive parameters predicted by machine learning algorithms based on the vast indentation data. In addition, by proposing the concept of “composite constitutive parameters”, the constitutive parameters of unknown single-layered films are established using a layer-by-layer strategy based on finite element simulations, followed by the subsequent determination of the constitutive parameters of multilayered films. The current work on the mechanical properties of multilayered films holds significant potential in improving the reliability and lifetime of the systems and devices based on thin film technology.