Two-dimensional Finite Element Model Research Articles

Influence of extent of remedial ground densification on seismic site effects via 2-D site response analyses

Remedial ground densification techniques are widely employed in seismically active regions to mitigate geotechnical hazards and reduce the potential for damage to structures. These techniques can substantially modify the local soil conditions and the seismic site response characteristics of the profile. This study provides a quantitative insight into the local site amplification in remedially densified soils. Parametric site response analyses are performed using various subsoil conditions and extents of ground densification. The free-field site responses obtained with and without ground densification are compared using two-dimensional (2-D) finite element models. The results show that the frequency content of ground motions propagating in densified sites is modified, with a shift of soil response harmonics towards higher frequencies. When a densified crust is implemented with unimproved soft soil layers underneath, the PSAs at the ground surface are generally reduced, at frequencies between 5 and 10 Hz. However, the levels of de-amplification decrease as the depth of ground densification increases. In particular, the densification of the full depth of liquefiable soil layers leads to higher PSAs at the ground surface. The results presented provide a better understanding of the geometry and density of the improved zones that can lead to the amplification of ground surface motions in the frequency range of interest for building response, prior to investigating more complex problems that include soil-structure interaction.

Longitudinal seismic response of integral abutment bridges

A finite-element (FE) investigation into the response of integral abutment bridges (IABs) to seismic loading in the longitudinal direction was conducted. An example multi-span reinforced concrete solid-slab bridge was designed and analysed using an elasto-plastic two-dimensional FE model. The bridge abutment was taken as supported on steel H-piles. The proposed FE model was found to have the capability of simulating both the bridge construction and the backfilling process using a multi-step numerical process. The bridge was examined considering various lengths and different backfill materials, and was subjected to earthquake loading. The analyses showed that the seismic response of IABs is notably affected by the bridge length. Longer bridges may be subject to higher pressures on the abutments and internal forces in the bridge structure. The stiffness and strength parameters of the backfill material may also markedly influence dynamic pressures on the abutments and internal forces in the structure. Backfill materials with greater stiffness and strength parameters may cause significant reductions in the seismic flexural stresses in both the abutments and the deck. Coupling seismic and thermal loads could be suggested for the design of IABs.

Study of constitutive relation of rail decarburized layer

Rail decarburized layer has significant impact on the wear and rolling contact fatigue in the wheel-rail interaction. Due to the lack of constitutive relation of rail decarburized layer, it is impossible to analyse accurately the influence of rail decarburized layer on wheel-rail contact. To obtain the constitutive relation of this layer of decarburized non-uniform material, nano-indentation experiments were carried out at different vertical positions in the decarburization layer on a rail specimen with decarburization thickness of 0.55 mm. Young’s modulus and hardness were determined using Oliver and Pharr method. Axisymmetric two-dimensional finite element models were established in ABAQUS to simulate the nano-indentation loading process and the power law elastic–plastic stress–strain relationships were obtained for material at different vertical positions in the rail decarburized layer. A set of dimensionless functions were proposed for Young’s modulus, hardness, yield stress and strain hardening exponent at arbitrary depth in a rail decarburized layer or in a decarburized layer treated by rail pre-grinding. The results show that the Young’s modulus and hardness decrease from the rail bulk to the surface of the decarburized layer. The Young’s modulus and hardness near the surface are 11% and 35% lower than those in the rail bulk, respectively. However, the yield stress exhibits an increasing trend from rail bulk to the decarburized surface, where yield stress is 20% higher than the rail bulk. Analysis shows that the main reason that causes the reduction of hardness at the decarburized layer surface is the reduction of Young’s modulus but not the yield stress.

Numerical simulation of damage characteristics of jointed rock under blasting load

In nature, rock masses are often accompanied by joints and weak interlayers. Due to the existence of joints, rock masses are characterized by anisotropy. When the rock mass is excavated by the blasting method, the joints and situ stresses have a great influence on the propagation of the explosion stress wave and the propagation of cracks. In this paper, a two-dimensional finite element model is used to calculate the damage and cracking of jointed rocks under blasting load. Results have shown that the angle between borehole and joint can affect the development of rock crack, and the propagation of stress wave can be suppressed. In addition, it has been verified that initial stress field and its magnitudes of major principal stresses affect the development of the crack zone around the borehole.

Numerical investigations of the clinching process and the failure prediction of clinched joints for dissimilar sheets

The clinching process is more and more used in automotive design and manufacturing. Traditional quality inspection of joints needs a lot of destructive tests, which is time-consuming and material-consuming. In this paper, the clinching process and joints failure of dissimilar materials, 6061 aluminium alloy and HC340/590DP dual-phase steel, are studied. A two-dimensional finite element model is established. Experiments were carried out to verify the numerical model. Through the axial tensile test, the quality of clinched joints for upper steel-lower aluminium alloy and upper aluminium alloy-lower steel were measured, respectively, and the strength and safety of the joints met the requirements of design indexes. The conventional prediction model of maximum tensile force and its modified model was researched. Combined with numerical simulation results, the fracture load, the separation load, and the failure mode of two clinched joints were predicted, respectively. Furthermore, the results are in good agreement with the experimental results. The results show that the modified prediction model of maximum tensile force has a good prediction result, and the error rate is less than 10%. The modified prediction model of maximum tensile force can effectively predict the tensile failure test results, which provides a basis for the quality evaluation and strength prediction optimization of dissimilar materials clinched joints.

Numerical Investigation of Ground-Borne Vibration Mitigation by Infilled Trenches in a Poroelastic Half-Space Considering the Moving Water Table

Abstract The moving water table would vary soil layering and may significantly affect the isolation efficiency of wave barriers. A two-dimensional finite-element model is then developed using COMSO...

On the influence of eccentricity on Thick Adherend Shear Tests

Two main mechanical tests are commonly used to measure the critical shear stress of an adhesive, the Single Lap Shear (SLS) test and the Thick Adherend Shear Test (TAST). In these tests, the assessment is performed with mode mixity. In this work, a two-dimensional Finite Element Model of an asymmetric TAST is set-up and a few mechanical tests are performed on titanium/epoxy specimens. The model takes into account a shift of the adhesive joint on the loading axis. The impact of a shifted loading is estimated on two specimen geometries though a sensitivity analysis. Then, a method is suggested to assess the state of stress that caused the specimen failure. The results show that the failure location and the mode mixity can be tuned by the shift. Furthermore, it is shown that a standard TAST geometry is remarkably sensitive to a shifted loading. As a consequence, this parameter should be set with a submillimeter accuracy or a modified version of classical shear tests should be used. The reported results are consistent with one another and the method used provides a clear link between the critical stresses of the model and the mechanical response of the specimen until failure.

Modelling of mid-rise concrete shear walls reinforced with superelastic shape memory alloys: Nonlinear analysis

The response of hybrid Shape Memory Alloy (SMA)-steel reinforced concrete shear walls containing Nickel-Titanium superelastic SMA as alternative reinforcement in the plastic hinge region was investigated using nonlinear finite element modelling. The hybrid wall system promotes self-centering and significant reduction of permanent deformations. Two types of conventional steel-reinforced concrete shear walls were designed for a prototype 10-storey office building according to the current Canadian concrete design standard, assuming two distinct seismic design scenarios. A moderately ductile shear wall was designed for a moderate seismic zone in eastern Canada, whereas a ductile shear wall was designed for a high seismic zone in western Canada. Equivalent, hybrid SMA-steel reinforced concrete shear walls were defined following the design of the two conventional shear walls, in terms of geometry and reinforcement layout. Full-scale, two-dimensional finite element models were developed to assess the pushover and hysteretic responses of the walls. Similarities in wall cross-section and yield force capacity of the steel and SMA reinforcement permitted a comparison between the walls, including strength, stiffness, self-centering, and energy dissipation capacities. The results indicate similar lateral strength and displacement capacities, and superior restoring capacity of the SMA-reinforced walls in comparison to the steel-reinforced walls. Furthermore, a preliminary study was conducted to investigate the effect of the SMA-bar length in the ductile wall due to concentration of damage near the base of the wall. Lengths corresponding to approximately 50% and 20% of the original SMA length were considered. Based on the analyses, a satisfactory response could be achieved with shorter SMA reinforcing bars, which reduces the quantity of SMA reinforcement without significant loss in self-centering capacity.

Refractive changes of a new asymmetric intracorneal ring segment with variable thickness and base width: A 2D finite-element model.

PurposeTo evaluate the local geometric effects of a unilateral intrastromal ring segment with a combined variation of ring thickness and base width in a finite element simulation, and to compare it against the isolated effect of thickness or base width variation alone.MethodsA two-dimensional finite-element model of a transversely isotropic cornea was created assuming either axisymmetric stress or plane strain condition. The model geometry was composed of a three-layered corneal tissue (epithelium, anterior and posterior stroma) fixed at the limbus. The implantation of a triangular-shape asymmetric ring segment with varying ring thickness (150 to 300 μm) and base width (600 to 800 μm) was simulated. Also, changes induced by thickness or base width alone were studied and compared their combined effect in the asymmetric ring segment. Geometrical deformation of the simulated cornea and sagittal curvature were the main parameters of study.ResultsIncreasing ring thickness and base width along the arc of the asymmetric ring segment produced a more pronounced flattening in this part of the ring. The asymmetric design did find a good balance between maximizing corneal flattening at one end and minimizing it at the other end, compared to the isolated effect of ring thickness and width. Ring thickness was the most robust parameter in flattening both, the central and peripheral cornea.ConclusionThe finite-element model permitted a theoretical study of corneal deformation undergoing implantation of realistic and hypothetical ring geometries. Intracorneal asymmetric ring segments with varying thickness and base width can be a good alternative in corneas with asymmetric keratoconus phenotypes.

Experimental and numerical investigations of aluminium-timber composite beams with bolted connections

This paper presents an investigation of aluminium-timber composite (ATC) beams subjected to bending. In the proposed ATC beam, a timber slab was connected to an aluminium beam using bolts. ATC beams are a relatively new civil engineering solution and they are still being developed. The authors conducted push-out tests of the bolted connections and bending tests of the ATC beams. The slip moduli k0.4 and k0.6, and the load-carrying capacity of the connection were determined experimentally. Furthermore, the short-term behaviour, load carrying-capacity, mode of failure, load-deflection and load-slip response of the ATC beams with bolted connections were investigated. What is more, the authors used a calculation procedure for steel-concrete composite elements to calculate the load-carrying capacity of the ATC beams. The results from the analytical estimations were compared with the results from the laboratory tests. In addition, two non-linear finite element models of the tested composite beam were developed and verified against the experimental results. In the three-dimensional finite element model, laminated veneer lumber was described as an elastic-perfectly plastic material, and, as a consequence, this model did not need many input parameters. In the two-dimensional finite element model, laminated veneer lumber was described as an orthotropic material and its failure was captured using the Hashin damage model. It was an advanced model which needed many input parameters. The numerical results were similar to the experimental results.

Finite element analysis of indentation contact of double piezoelectric spheres

As a result of the limited research works on the contact between piezoelectric materials, this research seeks to delve into this area, by using the finite element method. A two-dimensional finite element model of nanoindentation response of piezoelectric materials is established via this method. The axisymmetric contact behavior of the two transversely isotropic piezoelectric spheres under the condition of friction-free sliding is analyzed, and the relationship between indentation displacement, electric potential and contact force is obtained, which are linear and quadratic respectively. The results show that the variation trend of the stress field and electric field at the contact boundary presents a non-monotonic relationship with an increase in the distance from the indenter to the center of the loading axis. In addition, the results of finite element numerical simulation are in good agreement with the numerical verification results. For semi-infinite materials, the model can be used for accurate contact analysis, which guides verifying the extraction technology of contact characteristics of finite piezoelectric materials. The results obtained in this paper are helpful to understand the microscopic contact mechanics of piezoelectric materials.

Theoretical band-gap bounds and coupling sensitivity for a waveguide with periodically attached resonating branches

Elastic metamaterials may exhibit band gaps at wavelengths far exceeding feature sizes. This is attributed to local resonances of embedded or attached substructures. In configurations with attached substructures, such as a pillared plate, waves propagating in the base medium–e.g., the plate portion–experience attenuation at band-gap frequencies. Considering a simplified lumped-parameter model for a waveguide with attached resonating branches, we present a theoretical treatment for a periodic unit cell comprising a base mass-spring chain with a multi-degree-of-freedom, mono-coupled branch. Bloch’s theorem is applied, combined with a sub-structuring approach where the resonating branch is modeled separately and condensed into its effective dynamic stiffness. Thus, the treatment is generally applicable to an arbitrary branch regardless of its size and properties. We provide an analysis–supported by guiding graphical illustrations–that yields an identification of fundamental bounds for the band-gap edges as dictated by the dynamical characteristics of the resonating branch. Analytical sensitivity functions are also derived for the dependence of these bounds on the degree of coupling between the base and the branch. The sensitivity analysis reveals further novel findings including the role of the frequency derivative of the branch dynamic stiffness in providing a direct relation between the band-gap edge locations and variation in the coupling parameters—the mass and stiffness ratios between the base chain and the branch root. In additional analysis, sub-Bragg bounds of an exact model comprising a one-dimensional continuous base–modeled as a rod–and a discrete resonating branch are derived and shown to be tighter than those of the all-discrete model. Finally, the applicability of the derived bounds and sensitivity functions are shown to be valid for a corresponding full two-dimensional finite-element model of a pillared waveguide admitting out-of-plane shear waves.

Coating delamination analysis of diamond/Ti and diamond/Ti-6Al-4V systems using cohesive damage and extended finite element modeling

Diamond coatings are known to improve the wear resistance properties of substrate materials. This paper aims at analyzing damage behavior of brittle diamond coating deposited on two different ductile substrates, namely pure-Ti and Ti-6Al-4V alloy, subjected to uniaxial tensile loading. In-situ tensile tests were conducted on diamond/Ti and diamond/Ti-6Al-4V coated samples to identify the stress-strain response and the damage behavior of the coating. Surface imaging was performed using scanning electron microscope (SEM). The cross sections were made with the focused ion beam (FIB) gun installed in SEM to observe the coating failure modes. Energy dispersive x-ray and x-ray diffraction analyses were carried out to determine composition. The SEM analysis revealed micro-crystalline morphology of the coating and FIB cross-sections showed diamond coating top-layer, TiC interlayer and substrate at the bottom. The XRD and EDX findings confirmed the regions observed in FIB cross-section via chemical analysis. The in situ tensile tests revealed that the coating had undergone failure through crack initiation, fragmentation and delamination. The bucking of the coating under transverse compressive strain of the substrate was also observed. The Ti-6Al-4V alloy caused early cracking and delamination of the coating owing to its higher yield strength and higher rate of stress transfer to the coating. Two-dimensional finite element models were developed to simulate various damage modes, such as cracking, buckling and delamination. Extended finite element method and cohesive damage modeling were exploited to observe cracking and buckling, respectively. Numerical results revealed that the coating was more prone to failure when Ti-6Al-4V, a high yielding less ductile, substrate was used instead of a low yielding highly ductile Ti substrate. Moreover, buckling was found to be the major reason of delamination than bulk cracking. The coating is, therefore, likely to delaminate more severely under the compressive (buckling) than the tensile (bulk cracking) mode of deformation.

Numerical investigation of the earplug contribution to the low-frequency objective occlusion effect induced by bone-conducted stimulation.

The use of earplugs is commonly associated with an increased perception of the bone-conducted part of one's own physiological noise. This phenomenon is referred to as occlusion effect and is most prominent at low frequencies. Several factors influence the occlusion effect, such as the ear anatomy; the bone-conducted stimulation; and the type of occlusion device and its fit, insertion depth, and material properties. The latter factor is of great interest to potentially reduce the occlusion effect of passive earplugs. This paper investigates the mechanism(s) of contribution of earplugs to the objective occlusion effect. A two-dimensional axi-symmetric finite element model of the outer ear is used and investigated in an electro-acoustic framework. Simulation results are shown to compare reasonably well with measurement data, which qualifies the model to study the influence of earplugs on the occlusion effect. Two mechanisms are highlighted: (i) a Poisson effect induced by the normal component of the earcanal wall vibration and (ii) a longitudinal motion caused by the tangential component of the earcanal wall vibration. By varying the geometry of the surrounding tissues, the spatial distribution of the earcanal wall vibration is shown to influence the contribution of the earplug to the occlusion effect.

Potential of surrogate modelling in compressor casing design focussing on rapid tip clearance assessments

ABSTRACTLosses induced by tip clearance limit decisive improvements in the system efficiency and aerodynamic operational stability of aero-engine axial compressors. The tendency towards even lower blade heights to compensate for higher fluid densities aggravates their influence. Generally, it is emphasised that the tip clearance should be minimised but remain large enough to prevent collisions between the blade tip and the casing throughout the entire mission. The present work concentrates on the development of a preliminary aero-engine axial compressor casing design methodology involving meta-modelling techniques. Previous research work at the Institute for Turbomachinery and Flight Propulsion resulted in a Two-Dimensional (2D) axisymmetric finite element model for a generic multi-stage high-pressure axial compressor casing. Subsequent sensitivity studies led to the identification of significant parameters that are important for fine-tuning the tip clearance via specific flange design. This work is devoted to an exploration of the potential of surrogate modelling in preliminary compressor casing design with respect to rapid tip clearance assessments and its corresponding precision in comparison with finite element results. Reputed as data-driven mathematical approximation models and conceived for inexpensive numerical simulation result reproduction, surrogate models show even greater capacity when linked with extensive design space exploration and optimisation algorithms.Compared with high-fidelity finite element simulations, the reductions obtained in computational time when using surrogate models amount to 99.9%. Validated via statistical methods and dependent on the size of the training database, the precision of surrogate models can reach down to the range of manufacturing tolerances. Subsequent inclusion of such surrogate models in a parametric optimisation process for tip clearance minimisation rapidly returned adaptions of the geometric design variables.

Improvement of structural efficiency in metals by the control of topological arrangements in ultrafine and coarse grains

Improvement of structural efficiency in various materials is critically important for sustainable society development and the efficient use of natural resources. Recently, a lot of attention in science and engineering has been attracted to heterogeneous-structure materials because of high structural efficiency. However, strategies for the efficient design of heterogenous structures are still in their infancy therefore demanding extensive exploration. In this work, two-dimensional finite-element models for pure nickel with bimodal distributions of grain sizes having ‘harmonic’ and ‘random’ spatial topological arrangements of coarse and ultrafine-grain areas are developed. The bimodal random-structure material shows heterogeneities in stress–strain distributions at all scale levels developing immediately upon loading, which leads to developing concentrations of strain and premature global plastic instability. The bimodal harmonic-structure material demonstrates strength and ductility significantly exceeding those in the bimodal random-structure as well as expectations from a rule of mixtures. The strain hardening rates also significantly exceed those in homogeneous materials while being primarily controlled by coarse-grain phase at the early, by ultrafine-grain at the later and by their compatible straining at the intermediate stages of loading. The study emphasises the importance of topological ultrafine-/coarse-grain distributions, and the continuity of the ultrafine-grain skeleton in particular.

Elliptic vibration assisted cutting of metal matrix composite reinforced by silicon carbide: an investigation of machining mechanisms and surface integrity

This paper aims to investigate the deformation mechanisms and surface integrity of SiCp/Al composites machined by elliptic vibration assisted cutting (EVAC). Self-designed EVAC device was applied to generate the elliptical trajectory on tool tip, which is driven by three piezoelectric actuators along different directions with phase difference. A two-dimensional (2D) microstructure-based finite element (FE) model of SiCp/Al composites was also established to research the deformation mechanisms and surface integrity in the process of EVAC, including material removal mechanisms, cutting force, surface roughness and microstructure. Systematic orthogonal cutting experiments shown that the relative position of tool-particles are changed by the time-varying cutting thickness in EVAC, leading to more obvious particle fracture during SiC particles removal process. Particle fracture appears in the area of particle clusters affected by chip lifting of tool. The intermittent cutting effect not only reduces the average cutting force, but also eliminates the scratch on machined surface caused by SiC particles entering the flank face–workpiece interface, improving the machined surface quality. Limited by the volume of material removal, 2D FE model has a high prediction accuracy for the micro-removal process of composite materials. The application of elliptical vibration is able to create the special functional surfaces. In order to increase the hydrophobicity of machined surface, larger feed rate and smaller cutting depth should be selected as far as possible.

Contribution of Lamb wave modes in the formation of higher order modes cluster (HOMC) guided waves

In recent years, Higher Order Modes Cluster (HOMC) guided waves have been considered for ultrasonic testing of plates and pipes. HOMC guided waves consist of higher order Lamb wave modes that travel together as a single nondispersive wave packet. The objective of this paper is to investigate the effect of frequency-thickness value on the contribution of Lamb wave modes in an HOMC guided wave. This is an important issue that has not been thoroughly investigated before. The contribution of each Lamb wave mode in an HOMC guided wave is studied by using a two-dimensional finite element model. The level of contribution of various Lamb wave modes to the wave cluster is verified by using a 2D FFT analysis. The results show that by increasing the frequency-thickness value, the order of contributing modes in the HOMC wave packet increases. The number of modes that comprise a cluster also increases up to a specific frequency-thickness value and then it starts to decrease. Plotting of the cross-sectional displacement patterns along the HOMC guided wave paths confirms the shifting of dominant modes from lower to higher order modes with increase of frequency-thickness value. Experimental measurements conducted on a mild steel plate are used to verify the finite element simulations. The experimental results are found to be in good agreement with simulations and confirm the changes observed in the level of contribution of Lamb wave modes in a wave cluster by changing the frequency-thickness value.

Low-effort determination of heat capacity and thermal conductivity for cylindrical 18650 and 21700 lithium-ion cells

High-fidelity simulations of lithium-ion cells describing fast charging or safety-critical events often rely on precise thermal parameters. Usually, the determination of cell parameters such as heat capacity or thermal conductivity is time consuming and cost intensive. To streamline this process, a simple yet precise measurement method for determining the specific heat capacity of lithium-ion cells is now extended by an approach that also captures their thermal conductivity. The method presented here was developed using two cylindrical cell formats, each containing a lithium–nickel–manganese–cobalt-oxide (NMC) cathode and a silicon-graphite anode. The extension is based on a two-dimensional finite element (FEM) model, whose geometry is parameterized by computed tomography (CT) scans. To ensure the simplicity of the experimental evaluation, the FEM model is approximated by a rational function. The new measurement method is applied at three different temperatures and states of charge (SOC). The results show that while the specific heat capacity of the jelly roll increases with temperature by 0.2%/K for both cell formats, it is only minimally influenced by the SOC. In contrast, the through-plane thermal conductivity of the electrode-separator-composite decreases by -0.5%/K and is enhanced by up to 9% by increasing the SOC in a window ranging from 10% to 71%.

Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior

Abstract In the present investigation, a two-dimensional (2D) finite element (FE) model of closed-cell AlSi12Mg1Cu1 alloy foam (AAFs) of 0.35 relative density of different cell shapes, i.e., square, hexagonal, octagonal, and circular shaped cell established with the help of ABAQUS simulation software. Experimentation is also done for 0.35 relative density metal foam to report its compressive behavior. The plateau stress σ p l $\left(\right.{\sigma }_{pl}$ ) and energy absorption capacity (E ab) of AAFs (ρ rd = 0.35) properties are calculated from the plotted stress–strain graph and a significant effect of cell shape on compressive performance observed. By SEM characterization, it was noted that the experimental specimen also had near circular cells. The strength and energy absorption values are calculated for square-shape, circular-shaped, octagonal-shaped, and hexagonal-shaped cells in descending order from maximum to minimum. A convergence study is also carried out concerning the number of elements to obtain the most accurate FE results.