Explicit Finite Element Method Research Articles

Численное исследование задачи низкоскоростного столкновения стального шара с ледяной плитой

In this paper, the dynamic deformation process during the low-speed collision was investigated. The full 3D dynamic contact problem was simulated in the Abaqus software, based on the explicit finite-element method on structured meshes. Two basic mechanical models (linear isotropic elastic and elastoplastic) are considered. The obtained results showed the possibility of the experimental data, available in the open literature for different striker velocities, reproduction. The better understanding of the ice deformation process can be useful for different applied problems, like the ice impact on the aircraft wings estimation and the ice-water contact reflected waves filtration during the seismic survey in the Arctic region.

Micromechanical modeling for longitudinal tensile property of unidirectional CFRP considering dispersion of fiber properties

Longitudinal tensile failure prediction has always been the focus of research on unidirectional (UD) Carbon Fiber Reinforced Polymer (CFRP). In this paper, the longitudinal tensile tests of unidirectional T800 grade carbon fiber reinforced epoxy resin composite were carried out first. The experimental stress–strain curves show that there are obvious progressive damages before the final failures of the specimens. However, this phenomenon is usually neglected in most of the existing investigations and tests to only obtain elastic modulus and ultimate strength. Thus, a Representative Volume Element (RVE) model based on micromechanics was established using finite element method, considering the randomness of fiber spatial distribution and fiber strength. The tensile strength of fiber monofilaments was assumed to follow a statistical two-parameter Weibull distribution. The failure process of UD composite under longitudinal tensile load was simulated by explicit finite element method. The stress–strain curves obtained by simulation are in good agreement with the experimental results. Finally, the influence of different boundary conditions on the calculation of the RVE was studied. It is found that the final failure strengths of the RVE with uniform displacement boundary conditions are similar to the case of periodic boundary conditions, while the former has higher computational efficiency.

Investigation of frictional rolling contact behavior in a switch panel considering traction load

The dynamic effects involved in wheel-rail interactions can be increased by the traction force potentially causing rapid degradation of turnout rails. A precise stress/strain analysis is essential for wheel-rail frictional rolling contact and the related degradation. Therefore, an explicit finite element method is established considering dynamic effects related to the contact. Furthermore, the frictional rolling contact solutions and related degradation with different traction coefficient in turnout are investigated. The results indicate that the effect of asymmetric excitation caused by traction force and geometric irregularities will lead to yaw motion of wheelset. The width of running band on the switch rail is increased as the top surface width of the switch rail increases. In addition, the contact patch on the switch rail will gradually shift forward compared to that on the stock rail, leading to excessive shear stress and increase of microslip. Meanwhile, the adhesion-slip distribution, uneven wear and severe plastic deformation during transition are recognized.

Direct spatio-temporal stress field determination combining full-field deformation measurements and explicit finite element method: Concept verification

High strain rate loading of materials with spatially heterogeneous properties produces non-homogeneous and transient stress-strain states. Such stress-strain states are atypical of classical split Hopkinson pressure bar (SHPB) analysis that assumes homogeneous deformation and dynamic force equilibrium. To determine spatio-temporal stress fields in heterogeneous materials, a novel concept combining digital image correlation (DIC) full-field deformation measurements and explicit dynamic finite element method (EFEM) is described in this paper. The concept utilizes measured boundary forces and DIC measurements including both displacements and accelerations as input. The measured input is used to calculate internal forces, and hence the stress fields, within each continuum finite element by solving the governing equations of motion using the framework of EFEM. The DIC+EFEM concept procedure is verified using simulated synthetic data considering one-dimensional stress wave propagation in a bar. The reconstructed axial stress fields match identically with the exact EFEM solution for both homogeneous and heterogeneous materials that are elastic or elastic-plastic. The influence of DIC measurement noise on the reconstructed stresses is also studied.

On the development of a high strain-rate tensile testing method for thin low-impedance materials

This work deals with the high strain-rate characterization of paper under uniaxial tension using a Split Hopkinson test bench. An aluminum bar system featuring a highly sensitive hollow transmission bar was used. Paper tests were performed in a strain-rate range between approximately 60 s−1 and 210 s−1. The experimental tests showed that the breaking strength appears to decrease with increasing strain-rate. To verify these results, a digital twin of both the paper specimen and the entire test rig was created in an explicit Finite Element method environment. The numerical model was then used to perform a parameter study with different types of transmission bars. It was shown that the system is quite sensitive to additional masses caused by the specimen fixtures, as well as to drastic reductions in the cross section of the transmission bar. As a result, the transmitted measuring signal can be distorted and may need to be corrected using the digital twin.

Folding, stowage, and deployment of composite thin-walled lenticular tubes

Composite thin-walled lenticular tube (CTLT) is a lightweight foldable and deployable structural material that enables large-scale deployable mechanisms for various space missions. A key step toward the structural design of CTLT is to understand its folding, stowage, and deployment behaviors. This work presents an integrated experimental and numerical investigation of the dynamic deployment behavior of CTLT that wraps around a central hub, with emphasis on the effect of long-term storage. A two-meter-long CTLT prototype was manufactured, and a gravity compensation system was designed and built for the on-ground dynamic deployment experiments. The deployment experiments were performed on the CTLT prototype both before and after it had been stowed for extended storage periods. The results indicate that after being stowed for 6 and 10.5 months the CTLT is deployed slower and the deployment time increases by 8.2% and 15.0%, respectively. Furthermore, a high-fidelity numerical model was constructed using the explicit dynamic finite element method, where the CTLT was modeled as a deformable part and the folding/deployment mechanisms were modeled as rigid bodies to perform the folding, stowage, and deployment simulations. The long-term storage effect was accounted for in the numerical analyses with the use of a viscoelastic fiber-reinforced composite material model, and a good agreement has been achieved between the experimental and numerical results.

Numerical Investigation of Elastic Layer Effects in Wheel–Rail Rolling Contact

In railway systems, layered structures could be induced in wheel–rail contact interfaces due to several causes, such as head hardening, work hardening, plastic deformation, and mechanical or thermal excursion-induced phase transformation. This study proposes an explicit finite element (FE) method for investigating elastic layer effects in wheel–rail rolling contact. The proposed method is first validated by comparing its solution with that of Kalker’s boundary element method (BEM) when the layer is not present, with a focus on the tractive rolling contact. To investigate general layer effects, the rail is assumed to consist of two layers, i.e., the top layer and the matrix material. The top layer is assumed to have different elastic moduli from the matrix material and then the top elastic layer effects on contact characteristics such as contact stress, contact patch, and subsurface stress are investigated. Different layer thicknesses are also considered. It is observed that a harder layer tends to introduce larger contact pressure and surface shear stress, but a smaller contact patch. A harder layer also produces larger subsurface stresses. A thicker layer may intensify these effects. The results suggest that in engineering applications, the analysis of wheel–rail rolling contact consequences such as wear and rolling contact fatigue (RCF) may need to consider the layered structures using appropriate methods.

Numerical study on crushing damage and energy absorption of multi-cell glass fibre-reinforced composite panel: Application to the crash absorber design of tsunami lifeboat

Abstract During an evacuation, the tsunami lifeboat should be able to withstand the possible external loads that might be occurred, such as collisions, violent crashes, and capsizing events. Special structural reinforcement and improvement, such as a crash absorber, are attached to prevent damage due to the impact load. Therefore, this article focuses on the crushing behaviour of the tsunami lifeboat crash absorber made of the multi-cell glass fibre-reinforced composite panel. The effect of the cross-section geometry design of the cell on the damage mechanism and energy absorption behaviour was investigated. The explicit dynamic finite element method was used to identify the multi-cell configuration’s crashworthiness performance. Experimental studies such as tensile and three-point bending tests were conducted to define the material properties and validation of the FE model. The simulation results showed that the explicit dynamic finite element method has effectively estimated the crash absorber crushing damage. The circular cross-section has shown the most significant crash absorption capability compared to the others, namely the honeycomb, the square, and the triangular cell. Furthermore, the 4CSM laminate type has revealed a lower energy absorption than the 4WRC45 and 4WRC laminates. Otherwise, the study exhibits that the cross-sectional geometry and the laminate type significantly influence the crash absorber performance for improving the tsunami lifeboat crashworthiness.

Numerical predictions of intralaminar and interlaminar damage in thin composite shells subjected to impact loads

This paper investigates the impact dynamics of thin semicylindrical woven composite laminate shells, with a particular focus on understanding the influence of thickness. Utilizing the finite element (FE) method, the study evaluates both intralaminar and interlaminar damage associated with the impact response. The findings show that the implementation of the explicit FE method, along with a continuum damage mechanics model, for the intralaminar damage, and a surface-based cohesive model, for the interlaminar damage, may be used to correctly predict the load histories, as well as the maximum impact force, maximum displacement, contact time and impact bending stiffness (IBS). The numerical predictions reproduce well the linear response of the maximum impact force and maximum displacement to the thickness variation, as well as the 2nd order polynomial curve of the IBS, with errors ranging from 2.7% to 15.9%. Moreover, the damage areas and the effect of thickness on the damage severity were accurately replicated. These results’ validation enables the prediction of the energy histories and the ensuing energy dissipation forms. According to the findings, the intralaminar damage is around 5 times more significant than the other energy dissipation forms. The accuracy of the simulation creates the possibility for more impact investigations using a similar numerical approach, reducing the expenditures of experimental testing.

Energy dissipation mechanism and ballistic characteristic optimization in foam sandwich panels against spherical projectile impact

This study systematically examines the energy dissipation mechanisms and ballistic characteristics of foam sandwich panels (FSP) under high-velocity impact using the explicit non-linear finite element method. Based on the geometric topology of the FSP system, three FSP configurations with the same areal density are derived, namely multi-layer, gradient core and asymmetric face sheet, and three key structural parameters are identified: core thickness (tc), face sheet thickness (tf) and overlap face/core number (no). The ballistic performance of the FSP system is comprehensively evaluated in terms of the ballistic limit velocity (BLV), deformation modes, energy dissipation mechanism, and specific penetration energy (SPE). The results show that the FSP system exhibits a significant configuration dependence, whose ballistic performance ranking is: asymmetric face sheet > gradient core > multi-layer. The mass distribution of the top and bottom face sheets plays a critical role in the ballistic resistance of the FSP system. Both BLV and SPE increase with tf, while the raising tc or no leads to an increase in BLV but a decrease in SPE. Further, a face-core synchronous enhancement mechanism is discovered by the energy dissipation analysis, based on which the ballistic optimization procedure is also conducted and a design chart is established. This study shed light on the anti-penetration mechanism of the FSP system and might provide a theoretical basis for its engineering application.

Design and verification of continuous forming process of ultra-long thin-walled Lenticular Deployable Composite Boom

Ultra-long thin-walled deployable composite structures with high-strain ability are of considerable interest and increasingly used in large-size deployable spacecraft structures due to their high folding-storage ratio function. This paper seeks to investigate continuous curing technology of an ultra-long thin-walled Lenticular Deployable Composite Boom (LDCB) made of high strain carbon-fiber-reinforced-plastics. The equipment for continuous curing of thin-walled boom is designed. The continuous forming process including flattening, traction and coiling are simulated by explicit finite element method for determining the length of the transition zone of the equipment, the gap of the flattening roll, and the radius of the reeling roller.

Spherical cavity expansion method dependent on strain, strain rate, and temperature

This paper presents a spherical cavity expansion method based on the self-similar field considering dynamic hardening, which includes plastic strain, plastic strain rate, and temperature for an infinite compressible medium under J2 plasticity. This study proposes an approach based on the gradients of plastic strain and temperature under self-similarity transformation to deal with dynamic hardening models such as the Johnson-Cook (JC) and the modified Johnson-Cook (mJC) models. A theoretical model shows that the effective and radial stresses are reduced near the cavity surface and increased away from the cavity under the mutual influence of hardening and thermal softening. The JC hardening model is used to analyze the behavior of the cavity expansion for AISI 4340 steel. The proposed theoretical model was validated by comparing the result of the explicit finite element method (FEM). This study discusses the behavior of the expanding cavity problem for thermal softening and strain rate sensitivities. In addition, rigid penetration problems are simulated to analyze the application of the presented method. FEM and the proposed cavity expansion method were compared with the penetration depth of AA6061-T651 target using the mJC hardening model for a hemispherical-nosed penetrator. A comparison is made for the performance of the penetration depth with an ogive-nose projectile for AA7075-T651 and AA6061-T651 materials using the mJC hardening model. This study concludes that the proposed method can be applied without modifying the hardening models to spherical cavity expansion problems that involve dynamic hardening models dependent on strain, strain rate, and temperature under adiabatic heat.

Optimization of a temporary road traffic steel barrier using explicit finite element method and laboratory testing

Over a million people die in road crashes and tens of millions result injured or disabled each year, globally. Hence, there is a constant concern for improving the safety of the roads to protect road users, and those at the most risk, the road workers. Construction, maintenance, and utility work are constantly needed to ensure safety and functionality of roads and highways. Temporary road traffic barriers are used to separate passing traffic from the workspace and protect the workspace from an errant vehicle intrusion. Steel barriers are light, and their major advantage is rapid installation. These barriers are not anchored to the ground, and their behavior relies on the base-pavement friction, mass inertia, and stiffness of the system. The paper describes a methodology that was successfully applied for the development of a temporary road traffic steel barrier in compliance with the European specification EN 1317. The study included a simplified theoretical analysis of 178 barriers, static laboratory tests of three types of barrier connectors, development of explicit finite element models (EFEMs) of four selected barrier designs, and a full-scale crash test of the final barrier design. It is shown that static laboratory tests of complex connector systems can help to improve the design process and reduce the cost. The analysis and use of EFEMs was enough so that just a single full-scale crash test was sufficient for certification of the barrier design for use in Europe. The final barrier is compliant with the EN 1317–2 requirements for T1/W1 (TB21) containment level, which was confirmed by a full-scale crash test.

Investigation of transient wheel-rail interaction and interface contact behaviour in movable-point crossing panel

The high-speed turnout is a key part of railway track infrastructure. A process of wheel-load transition and single-wheel/multi-track contact take place in the turnout area, causing significant wheel-rail interaction. Most high-speed turnouts include movable-point crossings. To investigate the wheel-rail transient rolling contact behaviour in movable-point crossings, a 3D finite element (FE) model of a wheelset rolling over a crossing was introduced. The actual geometrical profile of the wheel and the rails in turnouts, the nonlinear materials, the actual relative motion between the point/wing rail, and the moving postures of the wheelset were considered. The simulated mode shape was compared with the experimental mode shape to verify the wheel-rail coupling model. Precise frictional rolling contact solutions and dynamic response, including wheel-rail force, contact stress, equivalent stress, equivalent plastic strain, and stick-slip distribution of the contact patches, were all studied. After this, the parametric analysis of dynamic wheel-rail contact behaviour was carried out. The simulated results indicate that the proposed explicit finite element method can characterise wheel-rail coupled dynamic interaction and mesoscopic rolling contact behaviour well, and improve the understanding of wheel-rail contact behaviour in the movable-point crossing panel of the high-speed turnouts.

Multiscale analysis of wheel-rail rolling contact wear and damage mechanisms using molecular dynamics and explicit finite elements

As traffic density and axle loads increase, the macroscopic wheel-rail contact can lead to severe rail wear. This paper constructs a multi-scale analysis framework from macroscopic force characteristics to microscopic wear mechanisms based on explicit finite element methods and molecular dynamics models. The study shows that the mutual proximity and annihilation of reverse dislocations in the rail material under the action of wheel-rail forces is an important cause of grain boundary fragmentation, while the proliferation of dislocations on the Subsurface leads to work hardening of the rail. The analytical framework proposed in this paper achieves a multiscale correlation between wheel-rail macroscopic contact and material microscopic response, and the conclusions obtained reveal the microscopic wear mechanism of rail materials.

Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part II. Numerical simulations

An experimental study was carried out to examine the impact-induced loads and structural responses of a three-dimensional non-prismatic aluminium wedge. The findings of the experimental study were presented in the first part of this publication, entitled “Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part I. Experimental study.” This paper describes the second part of the study, which deals with numerical simulations of slamming loads acting on the wedge and its dynamic responses. Two different two-way coupling methods are assessed and compared to simulate the water entry problem. Initially, an explicit nonlinear finite element method with a Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver is employed to evaluate the elastic response of the structure following a free-fall water impact. Subsequently, the hydroelastic slamming problem is modelled using a two-way coupled technique with a k-ε turbulence model and implicit unsteady solver for both the fluid and structural domains (Star-CCM+/ABAQUS). The effect of viscosity on slamming loads and responses was examined, and numerical results are compared with experimental data. To investigate the effect of rigidity on structural response and bottom deflection, the wedge was designed with bottom plates of varying thickness. The computed results from the two numerical models and the experimental data are in good agreement. The study concluded that the bottom plates deformation affects hydrodynamic loads during slamming. It is also observed that impact-induced loads depend on the water impact velocity and the flexibility of the bottom plates. This suggests that the slamming pressure increases with an increase in impact velocity and decreases when the structures become more flexible. According to this study, both numerical models are suitable for accurate and efficient computations of hydroelastic slamming; however, the MMALE method results in larger numerical fluctuations.

Torsional Vibrations in the Resonance of High-Speed Rotor Bearings Reduced by Dynamic Properties of Carbon Fiber Polymer Composites.

The present study deals with the harmful torsional resonance vibrations of textile rotor bearings, the amplitudes of which are reduced mainly by the use of high-capacity damping materials, characterized by an internal hierarchical structure and macroshape, added into the machine mechanical system. The additional materials are polymer matrix composites reinforced either by carbon nanofibers or carbon chopped microfibers and either aramid or carbon continuous fibers. The macroshape is based on a honeycomb with internal cavities. Torsional vibrations arise in mechanical systems as a result of fluctuations in the low-level pressing load of the flat belt driving the rotor-bearing pin and the changing of kinematic conditions within it, which, in the resonance area, leads to cage slip and unwanted impulsive torsional vibrations. Moreover, this occurs during high-frequency performance at around 2100 Hz, i.e., 126,000 min-1. The condition, before the redesign, was characterized by significantly reduced textile rotor-bearing life due to significant impulse torsional vibrations in the resonance area. The study showed a significant reduction in average and maximum torsional amplitudes in the resonance area by 33% and 43%, respectively. Furthermore, the paper provides visualization of the propagation of a stress wave at the microscale obtained by the explicit finite element method to show the dispersion of the wave and the fibers as one of the sources of high damping.

An explicit finite element approach for simulations of transient meshing contact of gear pairs and the resulting wear

A 3D time-domain modelling approach is developed with the explicit finite element method to simulate transient meshing contact of gear pairs and the resulting wear. Taking a helical gear pair used in a locomotive as an example, the dynamic contact states of gear teeth are predicted for different speeds in consideration of actual geometries (including those of damaged teeth), time dependent torques, and structural and continuum vibrations of the gear system. The friction between mating teeth is taken into account by a non-Newtonian EHL friction model. A tiny time step of 4.5 × 10−8 s determined by conditional stability of the explicit time integration ensures the capture of transient effects. Based on detailed contact solutions during meshing, the dynamic wear on teeth is further calculated using an Archard wear model to predict tooth profile evolvement. Taking initial involute profiles and a speed of 120 km/h, the model is first validated for dynamic contact solutions. More results show that structural vibrations and worn profiles influence the dynamic meshing contact significantly, tooth wear increases as lubrication fails, and tooth pitting's influence is localized. This approach provides key load boundaries for detailed studies on mating gears, and may be employed for studies on tooth damages and as a reference for lumped parameter dynamic models of gear pairs.

An explicit phase field material point method for modeling dynamic fracture problems

AbstractA novel explicit phase field material point method (ex‐PFMPM) is proposed for modeling dynamic fracture problems. The rate‐dependent phase field governing equation is discretized by a set of particles, and the phase field is updated by the explicit forward‐difference time integration. Furthermore, the stability of the ex‐PFMPM is studied. A novel explicit critical time step formula is obtained based on the system eigenvalues in one dimension and then extended to two and three dimensions. The critical time step formula takes the effect of particle position and neighboring cell interaction into consideration, and can also be used in an explicit phase field finite element method. Several numerical examples, including a dynamic crack branching, a plate with pre‐existing crack under velocity boundary conditions and a three point bending problem are studied to verify the proposed ex‐PFMPM. The use of the history field in the explicit method is studied, which shows that it will lead to fake phase field update and overestimation of the fracture energy in the unloading case. All of the numerical results show that the proposed ex‐PFMPM has the capacity of modeling the crack initiation and propagation problems with both accuracy and efficiency.

Binaural Auralization of Room Acoustics with a Highly Scalable Wave-Based Acoustics Simulation

This paper presents a proposal of an efficient binaural room-acoustics auralization method, an essential goal of room-acoustics modeling. The method uses a massively parallel wave-based room-acoustics solver based on a dispersion-optimized explicit time-domain finite element method (TD-FEM). The binaural room-acoustics auralization uses a hybrid technique of first-order Ambisonics (FOA) and head-related transfer functions. Ambisonics encoding uses room impulse responses computed by a parallel wave-based room-acoustics solver that can model sound absorbers with complex-valued surface impedance. Details are given of the novel procedure for computing expansion coefficients of spherical harmonics composing the FOA signal. This report is the first presenting a parallel wave-based solver able to simulate room impulse responses with practical computational times using an HPC cloud environment. A meeting room problem and a classroom problem are used, respectively, having 35 million degrees of freedom (DOF) and 100 million DOF, to test the parallel performance of up to 6144 CPU cores. Then, the potential of the proposed binaural room-acoustics auralization method is demonstrated via an auditorium acoustics simulation of up to 5 kHz having 750,000,000 DOFs. Room-acoustics auralization is performed with two acoustics treatment scenarios and room-acoustics evaluations that use an FOA signal, binaural room impulse response, and four room acoustical parameters. The auditorium acoustics simulation showed that the proposed method enables binaural room-acoustics auralization within 13,000 s using 6144 cores.