Finite Element Predictions Research Articles

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.

Evaluation of the composite action of cold-formed steel built-up battened columns composed of two sigma-shaped sections

Cold-formed steel (CFS) built-up battened columns are employed to obtain a sufficient load-bearing capacity when individual profiles cannot withstand the specified stresses. This sufficient load-bearing capacity can be obtained when the individual profiles present a composite action. This paper presents the optimal layout for CFS built-up battened columns to achieve a high level of composite action between two Σ-shaped CFS profiles. A calibrated finite element modeling technique was used to evaluate the effect of the number of fasteners per batten panel and the distance between the batten panels on the axial capacity of CFS built-up battened columns. The optimal number of fastener rows and the distance between the batten panels were determined using 100 models, in which a high level of composite action was achieved between CFS profiles. Then the maximum axial load-bearing capacity of additional 600 finite element models using the optimal layout was compared with the analytical predictions in the European standard EN1993-1-1. The results recommended four rows of fasteners per batten panel. The results suggested an optimal distance of 30imin between batten panels. The results showed a close agreement between finite element and analytical predictions from EN1993-1-1, following the procedure specified in clause 6.3.1, adopting the modified slenderness ratio from the American Specification AISI S100-16. Reliability analysis was also performed to evaluate the analytical methods by targeting a reliability index of 2.5. The results showed that the analytical prediction following the EN1993-1-1, clause 6.3.1, incorporated with the recommended slenderness ratio from the AISI S100-16, is a reliable analytical procedure for CFS battened columns.

Ultrathin arch-like labyrinthine acoustic metasurface for low-frequency sound absorption

In this study, a novel compact design for an acoustic metasurface containing coplanar arch-like channels (ALC) is proposed. The ALC is squeezed within a compact disk-shaped volume with a small thickness of 1/94th wavelength for absorbing undesired sound energy at low frequencies in limited-volume circumstances. An impedance-based analytical model is proposed and used for determining the absorption characteristics of arch-like channels with high accuracy. Compared with a uniform cross-section, varied channel widths can effectively lower the operating frequency. Furthermore, using multiple branches with different width arrangements can create a multi-peak absorption profile and effectively broaden the absorption bandwidth. The 3D printing technique is employed to fabricate test samples. The analytical and finite element predictions are verified by comparing those results with experimental measurements. The proposed structure has great potential for applications in noise abatement.

Direct stress computations in arbitrarily shaped thin shells and elliptic bulge tests

Most of engineering and biological thin shell structures are characterized by non-axisymmetric and statically indeterminate configurations, which often require the knowledge of the constitutive material model to determine the stress state. In this work, a forward elastostatic method is introduced for the direct stress measurements in elastic homogeneous thin shells of arbitrary shape. The stress distribution is proven to be independent of the material properties for incompressible solids, while in compressible materials it depends only on the Poisson’s ratio, which is shown to have a negligible influence on the stress state. Hence, the proposed technique enables the direct assessment of the stress field in statically indeterminate thin shells without a known material model. The shell formulation is implemented using the finite difference method to independently measure the stresses during finite inflation of planar elliptical membranes and from the deformed shapes obtained through digital image correlation during bulge tests on a hyperelastic material, showing very good agreement with finite-element predictions and the applicability of the method to nonlinear elastic materials. Therefore, the procedure can be coupled with imaging techniques for the direct assessment of stresses in thin shell structures and in the identification of material parameters through non-axisymmetric bulge tests.

Advancing contact of a 2D elastic curved beam indented by a rigid pin with clearance

A two-dimensional analytical solution is presented for stresses and displacements in an elastic curved beam forming an incomplete ring in frictionless and unbonded contact with a rigid pin loaded by a point force and in the presence of clearance. The circular beam is modeled as an incomplete elastic thick ring, constrained at both ends and in a plane stress state. The stress and displacement fields within the beam are derived from a biharmonic Airy stress function, according to the Michell solution in polar coordinates. The mixed boundary value problem is reduced to a set of dual series equations and then to a non-homogeneous linear system of infinite equations, which is then solved by truncation. The non-linear relations between the applied load and the contact angle or the pressure distribution are obtained by using an inverse method. The analytical results are compared with finite element predictions for a pin-lug connection and a reasonable agreement is observed for several typical geometries. The peaks of contact pressure and von Mises equivalent stress and their location within the curved beam are evidenced.

A computational framework for micromechanical modelling of WC-Co composites

In this study, the mechanical behavior under monotonic loads of tungsten carbide‑cobalt (WC-Co) composites is investigated extensively by analyzing (1) nanoindentation tests on WC particles and Co matrix, (2) nanowires made of WC-Co composites tested in tension and (3) micropillars made of WC-Co composites tested in compression. To this end, a novel computational framework consisting of two different microplane constitutive models developed for WC and Co phases are proposed. For the Co matrix, the microplane J2-plasticity, called the model MPJ2, and for the WC particles a modified version of the microplane model M7, called the model M7WC, are employed. Furthermore, finite element meshes in 3D obtained from experimental tomography reconstructions of WC-Co composites are employed to rule out any spurious geometric features that is likely to be encountered in artificially generated meshes. After calibrating the aforementioned models, it is shown that the finite element predictions not only confirm the extensive experimental observations but also shed further light into the mechanical behavior of these composites.

Analytical GNI Analysis for Lateral-torsional Behavior of Thin-walled Beams with Doubly-symmetric I-Sections

In this paper elastic lateral-torsional behavior of simple beams is discussed. The motivation of the presented research is the observation that classic analytical prediction and finite element prediction are, typically, considerably different, when the second-order nonlinear behavior of beams with initial imperfections is analyzed. In order to understand and explain the observed differences, a novel analytical solution is presented for the geometrically nonlinear analysis of beams with initial geometric imperfection. The presented analytical solution is derived for doubly-symmetric cross-sections, but with the novelty that it takes into consideration the changing geometry as the load is increasing. The most important steps of the derivations are summarized, and the resulted formulae are briefly discussed. Numerical studies are performed, too: the results of the new analytical formulae are compared to those from shell finite element analysis. The results suggest that the new formulae are able to capture the most important elements of the behavior. By the analytical and numerical results, it is proved that classic analytical solutions for the geometrically nonlinear analysis of beams with geometric imperfections are necessarily different from the numerical results obtained by incremental-iterative procedures.

Developing a modelling approach for sound propagation through turbulent boundary layer and applying to train pantograph

Sound propagation through turbulent boundary layer (TBL) is of great significance in transports where a TBL is attached to their external surfaces, for instance, air planes and high speed trains. Precise predictions of sound propagation through TBLs to their external surfaces can be extremely useful for their corresponding interior noise control. It is well known that a TBL is classified as an inhomogeneous flow medium and existing approaches are not capable to well predict its influence on sound propagation. Insight of sound propagation through TBLs is required but relevant research on this topic is limited in the literature. In this work, a modelling approach is developed to predict the influence of TBLs on sound propagation. In the proposed approach, the ray tracing method is employed to predict the evolution of sound waves when they are passing through a TBL, with which the equivalent phase speed of sound can be obtained and used to calculate the the Doppler factor so that the traditional methods can be extended to predict sound distribution in inhomogeneous flow media. The validation of this modelling approach is performed by using two cases. The first case is to predict the convective effect of sound propagation in a uniform mean flow and the predicted results are compared with analytical solutions. The second case is sound propagation through a TBL and the predictions obtained from this proposed approach are compared with numerical simulations obtained from the finite element (FE) method. In both cases, the convective effect obtained from this proposed approach is close to the analytical solution or the FE prediction. After that, the proposed approach is used to predict the sound propagation from a high speed train pantograph to the external surfaces of the train with considering the influence of the TBL. The corresponding results are verified by using FE simulations. This work shows that the proposed approach is effective and efficient, and also, it enhances the understanding of sound propagation in inhomogeneous flow media.

Evaluation of Different Tools of Precision Finishing for Sun Gear with Inner-Outer Tooth Shapes.

Aiming at the technical difficulty of poor teeth accuracy of the extruded sun gears, an innovative precision finishing approach was developed as the subsequent process of producing high-quality sun gears, and three finishing tools were designed, namely mandrel with gap, mandrel without gap and interference mandrel. A finite element prediction method was proposed by using the post-processing toolbox of DEFORM software to study the distribution laws of outer and inner teeth deviations of the reshaped sun gear. Moreover, the effects of various precision finishing tools on the formability of sun gear (such as tooth deformation, tool stress and tooth accuracy) were investigated. The results show that the tooth accuracy class of the reshaped outer teeth in profile and helix were seventh and eighth, respectively, and the total M-value error of the inner teeth was decreased to 72.3 μm and the reduction ratio was 73.8% by adopting the interference mandrel, which indicates that the finishing effect of the interference mandrel was better than that of mandrels for both with gap and without gap, and the forming accuracy of the finished teeth could be considerably improved. Therefore, the interference mandrel can be recommended as the optimum finishing tool in the manufacture of precision sun gears. The simulated results were in good agreement with experimental ones within a maximum error of 14.4%, which proves the practicability of the sizing approach and the dependability of the finite element prediction method.

Experimental investigation on bandgap properties of lead/silicone rubber phononic crystals

In this paper, we investigate the bandgap properties of the one-dimensional and two-dimensional lead/silicon rubber phononic crystals theoretically, numerically and experimentally. Based on the plane wave expansion method and the finite element method, bandgap properties of lead/silicone rubber phononic crystals with finite linear periodic structure and finite square periodic structure are calculated and discussed. Bandgap properties due to the filling fraction are also studied. In the experimental section, a finite linear periodic lead/silicone rubber phononic crystal structure and a finite square periodic lead/silicone rubber phononic crystal structure have been designed and experimentally investigated. The results demonstrate that the linear periodic structure can generate two bandgaps in the low-frequency range and the square periodic structure can reduce the vibration by 44 dB in the frequency range of 215 Hz to 310 Hz. The experimental results agree well with the theoretically finite element predictions.

The use of circumferential guided waves to monitor axial cracks in pipes

Guided wave testing is in routine use to detect corrosion, particularly in the oil and gas sector, but the detection of axial cracking is difficult using the axially propagating waves commonly used for corrosion detection. This paper presents a novel guided wave monitoring technique for the detection of axial cracking in piping. Circumferential SH0 waves, travelling around the circumference were used in a monitoring configuration to detect axial defects in a 6 inch schedule 80 steel pipe. Finite Element (FE) analysis showed that both the defect reflection and the decline in the transmitted SH0 wave can be used for defect detection. Baseline subtraction was utilised to produce residual signals that can be better analysed for small defect reflections. The Root-Mean-Square (RMS) of the residual signal after baseline subtraction was found to be the most satisfactory means of monitoring defect progression. An amplification effect was identified where the residual signal is compounded by continued interaction with the defect on each revolution of the incident wave. The FE predictions were validated by an experiment in which an Electrical Discharge Machining (EDM) notch was grown in four stages. Temperature compensation using Location Specific Temperature Compensation (LSTC) was applied to the experimental data, allowing residuals to be compared for a ∼10 °C temperature swing over a monitoring period of over 2 months. It was determined that a 10 mm long (∼23% of wavelength), 5 mm deep (∼45% of the wall thickness) defect at an axial offset from the line of the transducers of 1.5 wavelengths (65 mm) would be readily detectable with a very high Probability of Detection (POD) and virtually no chance of a false call. Therefore, this novel guided wave monitoring system for axial crack detection is likely to be attractive for applications in a range of industries for its sensitivity to axial cracking combined with large coverage from a single transducer location.

Prediction on aeroengine blade foreign object damage validated by air gun tests

Aeroengine in service was prone to ingest foreign objects, leading to foreign object damage (FOD) and failure accidents of the blades. In this paper, laboratory FOD tests were firstly conducted on TC4 and AM355 steel simulated airfoil specimens impacted by 3 mm diameter projectile at a speed of 350 m/s, and numerically reproduced using Johnson-Cook (J-C) model with failure criterion. A penetrating-type notch (P-notch) with severe material loss was observed, and a good agreement between experiments and finite element (FE) predictions could be found for both notch morphology and size. The influence of impact velocity on FOD and the FOD-induced residual stress were investigated by the proposed FE model. High tensile stress was observed along the notch edge, while the bottom of notch was mainly dominated by compressive stress. Finally, a FE model of aeroengine blade considering the initial centrifugal force was developed, and the influences of FOD to compressor blade on its modal properties were discussed. Compared to the normal blade, the damage induced a deviation in frequency within 1 %.

Predicting rupture locations of ascending aortic aneurysms using CT-based finite element models

Accurate rupture risk assessment of ascending aortic aneurysms is important for reducing aneurysm-related mortality. More recently, computational models have been shown to better predict rupture risk than diameter-based measurements. However, it remains unclear whether finite element (FE) models of the ascending aorta can predict rupture location, and over what timeframe those predictions are reliable. The aim of this study was to evaluate FE models of the ascending aorta generated from computed tomography (CT) scans in predicting rupture location. Pre- and post-rupture CT scans were obtained of 12 patients who underwent emergency surgical repair for ascending aorta rupture with varying time intervals between scans (20 days – 6 years). A rigid iterative closest point (ICP) registration was used to overlay post-rupture aortic geometries with pre-rupture FE models and directly compare predicted regions of high equivalent strain with actual rupture. The FE model predicted the rupture location in the 5 patients with the shortest time intervals between the pre- and post-rupture scans (20 days – 2 years, 3 months). However, rupture location was not predicted in the 4/5 patients with greater than 3 years between scans. Achieving a physiological equivalent strain distribution in the FE model was highly dependent on the resolution of the pre-rupture scan and whether contrast agent was present. The results suggest there may be a time interval beyond which FE predictions of rupture location may not be reliable. The results in this study may help clinical validation of FE models of ascending aortic aneurysms predicting rupture risk.

Creep buckling of long-term-serving super-heating pipes in boilers subjected to high temperature loading

This paper proposes a novel approach to scrutinize the creep buckling of the super-heating pipes in boilers subjected to external pressure in high temperature environment. It is well known that once buckling occurs, cylindrical shells will collapse instantly. As the load carrying capability of the cylindrical shell decreases sharply upon the occurrence of the buckling, the proposed analysis is based on the consideration that the creep will have a significant influence on the material properties only in the pre-buckling stage. According to the creep aging theory, the influence of the creep deformation on the mechanical response of the super-heating pipes is defined by introducing two parameters--the reduced Young's modulus and the reduced Poisson's ratio. The nonlinear constitutive relation for creep deformation of the super-heating pipes in high-temperature environment is established based on the deformation theory in mechanics of plasticity. Governing equations for creep buckling of super-heating pipes in boilers are derived by considering the extra change of curvature due to the initial curvature of the super-heating pipes. MATLAB programs are developed based on the analytical expression for super-heating pipes with simply supported boundary conditions at the two ends and are tested against the available experimental results and the finite element prediction from ABAQUS software. It is found that the components of the creep strain caused by the stress at high temperature far exceeds those of the elastic strain. As a results of that, the creep buckling load of the super-heating pipes is much lower than its elastic buckling load. From this study, an explicit expression to compute the creep buckling load is provided which facilitates engineer to easily predict the residual life of the super-heating pipes at different servo temperature and servo time.

Nonlinear coarse-graining models for 3D printed multi-material biomimetic composites

Bio-inspired composites are a great promise for mimicking the extraordinary and highly efficient properties of natural materials. Recent developments in voxel-by-voxel 3D printing have enabled extreme levels of control over the material deposition, yielding complex micro-architected materials. However, spatial complexity makes it a formidable challenge to find the optimal distribution of both hard and soft phases. To address this, a nonlinear coarse-graining approach is developed, where foam-based constitutive equations are used to predict the mechanics of biomimetic composites. The proposed approach is validated by comparing coarse-grained finite element predictions against full-field strain distributions measured using digital image correlation. To evaluate the degree of coarse-graining on model accuracy, pre-notched specimens decorated with a binarized version of a renowned painting were modeled. Subsequently, coarse-graining is used to predict the fracture behavior of bio-inspired composites incorporating complex designs, such as functional gradients and hierarchical organizations. Finally, as a showcase of the proposed approach, the inverse coarse-graining is combined with a theoretical model of bone tissue adaptation to optimize the microarchitecture of a 3D-printed femur. The predicted properties were in exceptionally good agreement with the corresponding experimental results. Therefore, the coarse-graining method allows the design of advanced architected materials with tunable and predictable properties.

Multimodal data augmentation for digital twining assisted by artificial intelligence in mechanics of materials

Digital twins in the mechanics of materials usually involve multimodal data in the sense that an instance of a mechanical component has both experimental and simulated data. These simulations aim not only to replicate experimental observations but also to extend the data. Whether spatially, temporally, or functionally, augmentation is needed for various possible uses of the components to improve the predictions of mechanical behavior. Related multimodal data are scarce, high-dimensional and a physics-based causality relation exists between observational and simulated data. We propose a data augmentation scheme coupled with data pruning, in order to limit memory requirements for high-dimensional augmented data. This augmentation is desirable for digital twining assisted by artificial intelligence when performing nonlinear model reduction. Here, data augmentation aims at preserving similarities in terms of the validity domain of reduced digital twins. In this article, we consider a specimen subjected to a mechanical test at high temperature, where the as-manufactured geometry may impact the lifetime of the component. Hence, an instance is represented by a digital twin that includes 3D X-Ray tomography data of the specimen, the related finite element mesh, and the finite element predictions of thermo-mechanical variables at several time steps. There is, thus, for each specimen, geometrical and mechanical information. Multimodal data, which couple different representation modalities together, are hard to collect, and annotating them requires a significant effort. Thus, the analysis of multimodal data generally suffers from the problem of data scarcity. The proposed data augmentation scheme aims at training a recommending system that recognizes a category of data available in a training set that has already been fully analyzed by using high-fidelity models. Such a recommending system enables the use of a ROM-net for fast lifetime assessment via local reduced-order models.

Comparative Study of Biased Flux PM Machines Having Different Stator Core Segments and Armature Winding Configurations

This article proposes a comparative study of biased flux permanent magnet (BFPM) machines having different stator core segments and armature winding configurations. The topologies of the four investigated machines and their operating principles are introduced first. Then, in the case of same envelope size and copper loss, all four BFPM machines are designed based on the single variable optimization method to obtain higher average torque, along with their comparison of electromagnetic characteristics such as phase back-electromotive force (back EMF), cogging torque, and torque capability. It is shown that by exploiting both flux focusing (FC) and dual armature (DA) design, the average torque of the BFPM machine has a 132% sharp increase. Furthermore, to reveal the real performance of the DA-FC-BFPM machine, its comparison with machines such as DA doubly salient permanent magnet (DA-DSPM) machine, DA flux reversal permanent magnet (DA-FRPM) machine, DA flux switching permanent magnet (DA-FSPM) machine, wound rotor synchronous (WRS) machine, and surface-mounted permanent magnet (SPM) machine is performed. Finally, a prototype machine is built and tested to verify the finite-element predictions.