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Automotive coatings are a multi-layered polymer composite structure whose impact resistance is closely related to the appearance and safety of a vehicle. Since experimental methods are of high cost and poor repeatability, in our work, a finite element model is developed for the single-impact failure of automotive coatings. In this model, a multi-mechanism damage model and a large deformation cohesive zone model are employed to account for the polymer-ply and interlaminar failures of the coating, and some rate-dependent material models are adopted to capture the effect of impact velocity. The simulated results indicate that the proposed model can reproduce the failure patterns of automotive coatings well. In addition, the impact failure mechanisms of the coating are revealed. Numerical findings show that both brittle and ductile failures are found in the coating and there are three stages for the propagation of the delamination crack. Finally, we numerically investigate the effects of primer mechanical properties, i.e., Young’s modulus, yield strength, and re-hardening modulus, on the impact resistance of automotive coatings. Our work is helpful to the design of coating, which can improve the impact resistance of automotive coatings.

The real sand is usually idealized by using upscaled particles, due to the large number of particles of tire-sand interaction. This study aims to determine a unique and complete set of DEM-FEM model parameters to improve numerical accuracy of tire-sand interaction after particles idealization. To achieve this aim, a novel method based on experimental design is proposed to calibrate the DEM-FEM model parameters by a series of single-factor numerical calibration tests. Initially, the interaction properties such as equivalent friction coefficients of particle-particle, particle-soil bin and particle-tire are determined successively by comparing experimental test with numerical simulation using the angle of repose as a bulk response. The material parameters of particles are then obtained by modified iteratively to match the stress-strain behavior of the granular assembly in triaxial test. After that, the calibrated parameter set is used to investigate the interaction mechanisms between the off-road tire and the granular terrain. Finally, the simulation results are qualitatively in agreement with the soil bin experiments, which verifies the effectiveness of the calibrated parameter set for the tractive performance analysis of tire-sand interaction.

The interaction between off-road tires and granular terrain has a great influence on the tractive performance of off-road vehicles. However, the finite element method or the discrete element method cannot effectively study the interaction between off-road tires and granular terrain. The three-dimensional combined finite element and discrete element method is applied to handle this problem. In this study, a calibrated finite element method–discrete element method model is established, in which the finite element model of off-road tire is validated by stiffness tests, while the discrete element model of gravel particles is validated by triaxial compression tests. The calibrated finite element method–discrete element method model can describe the structural mechanics of the off-road tire and the macroscopic mechanical properties of the gravel road. Tractive performance simulations of the off-road tire on gravel road under different slip conditions are performed with the commercial software LS-DYNA. The simulation results are basically corresponded with the soil-bin test results in terms of granular terrain deformation and tractive performance parameters versus the slip rates. Finally, the effects of tread pattern, wheel load, and tire inflation pressure on tractive performance of off-road tire on granular terrain are investigated. It indicates that the calibrated finite element method–discrete element method can be an effective tool for studying the tire–granular terrain interaction and predicting the tractive performance of off-road tire on granular terrain.

This work aims to determine a complete set of input parameters of the DEM-FEM coupling model, which ensures us obtain more realistic simulation results of the tire-terrain interactions. Firstly, we investigate the macroscopic responses of the gravel sample, the stress-strain curves and deformations, which is finished by the triaxial tests at different confining pressures of 25 kPa, 50 kPa and 100 kPa. Then, the microscopic input parameters of the numerical simulations are obtained by iteratively adjusting the coupling model parameters, which are employed to meet the macroscopic responses of the triaxial tests. Finally, the traction behavior researches of an off-road tire on gravel terrain are carried out by the DEM-FEM coupling model with the calibrated microscopic input parameters mentioned above. The predicted traction performance parameters such as the vertical reaction force, tractive force and tire sinkage are qualitatively in agreements with the corresponding experimental results. The effectiveness of the calibration method using numerical triaxial tests is validated in traction behavior of tire-terrain interactions.

The combined discrete-finite element method is often used for dynamic interaction simulations, in which contact detection is the most time-consuming but critical constituent. Therefore, it is significant to develop an accurate and efficient contact detection algorithm. In this study, an efficient contact detection algorithm termed TSC (tire-sand contact) is developed for dealing with the interactions between spherical discrete elements and hexahedral finite elements. The global search of TSC is suitable for the contact detection of tire-sand interaction. In the global search phase, according to the contact characteristics of tire movement on granular terrain, the potential contact pairs are quickly determined by using the method of dynamically changing the slave nodes and master segments within a moving contact region. The local search is based on the principle of inside-outside algorithm, and the contact region is divided into three types, i.e. surface contact region, edge contact region and node contact region. In the local search phase, the invalid contact pairs and repeated contact pairs can be quickly excluded from the multiple potential contact pairs of one particle according to the relevant judgment conditions. And the Hertz-Mindlin contact model is used in corresponding contact force calculation. As a result, the quick contact search and accurate evaluation of contact force are accomplished. Finally, several numerical examples are presented to validate the accuracy and efficiency of the TSC algorithm in 3D contact analysis, which also demonstrates the advantages of the proposed algorithm in tire-sand interaction simulations.

In the interaction between rubber tire and granular terrain, the dynamic behavior of granular terrain is significantly affected not only by the shape of soil grains, but also by the deformation contact of tread rubber. Therefore, the effect of these two factors should be considered in tire–sand interactions. In this study, an improved contact model including the effect of sand grain shape and tread rubber deformation is developed for dealing with the interaction between rubber tire and sand terrain. In sand–sand contact model, the interaction between sand grains takes the form of surface contact instead of conventional point contact, where the contact calculation contains four interactions, i.e., normal force, tangential force, rolling resistance and twisting resistance. And in tread–sand contact model, the contact between tread rubber and sand grains is surface contact, which includes the rolling resistance and twisting resistance on the grains caused by rubber deformation during contact. As a result, the complete and realistic evaluation of contact forces is accomplished. Next, a comparison of sandpile simulation of coarse particles and experiment is carried out to verify the effectiveness of the sand–sand contact model. Finally, the novel contact model is applied to tire–sand interaction simulations and compared with the single-wheel experiments. The results indicate that the proposed contact model can be a powerful tool to simulate the interactions between rubber tire and sand terrain.

In recent decades, growing efforts have been devoted to coupling the Computational Fluid Dynamics (CFD) and the Discrete Element Method (DEM), i.e., CFD-DEM coupling methods, to account for particle–fluid interactions. However, it remains a challenging task for the well-known Immersed Boundary Method (IBM) belonging to the resolved CFD-DEM methods to improve the computational efficiency of large particles occupying several fluid cells and to simulate the interactions between irregularly shaped particles and fluids. In this paper, we present a novel unresolved CFD-DEM method to achieve the end. The main idea of the presented method is to split a large particle into multiple small spherical particles without overlapping using the Bonded-Particle Method (BPM), and simulate the particle–fluid interactions based on each small particle in the context of an unresolved CFD-DEM method. We validate the accuracy and efficiency of the novel method by comparing our numerical results of spherical particles in viscous fluids with those calculated using the IBM and existing experimental data. The presented method is further applied to the irregular large particle–fluid interaction problems, and the numerical results demonstrate the capacity of our method in simulating the motions of nonspherical large particles in the fluid.

Interfacial debonding is one of the major failure patterns in composite structures. In this work, a nodal-based extrinsic cohesive/contact model is proposed for the purpose of efficient and accurate debonding analyses. On one hand, unlike the commonly used intrinsic cohesive zone model, finite element nodes in the proposed model are adaptively duplicated when and where needed along with the advance of debonding, and thus to save computational cost. On the other hand, a fracture criterion, which is performed directly at nodes, is proposed to guarantee nodal forces to be continuous before and after nodal duplication. In doing so, the new model is capable of addressing the so-called time continuity problem existing in the conventional extrinsic model in an efficient way. In addition, a simple but efficient detection technique is developed to facilitate adaptive nodal duplication. The developed cohesive zone model is then coupled with a tributary node-to-segment contact algorithm to achieve a smooth transition from cohesive failure to contact sliding. Several numerical examples are performed to validate the efficiency and effectiveness of the proposed model.

Though windshield laminated glass is a simple sandwiched composite structure, it is of vital importance to investigate its damage and energy absorption behavior for the purpose of pedestrian safety protection. This paper proposes an intrinsic cohesive zone approach to achieve this end. A finite element windshield glazing model is established by inserting cohesive elements into the common surfaces between glass elements, and the interfaces between glass and PVB prior to simulations. The appeal of this model is that both of the two main failure patterns and their energy absorptions, i.e. glass fracture and glass-PVB debonding, of the windshield can be captured by means of the intrinsic cohesive zone approach. The effectiveness of the proposed model is validated by comparing the simulation results under center and corner impact with the corresponding experimental outcomes. Finally, the effects of adhesion parameters, PVB material parameters, and impact velocities and angles on the impact fracture behavior and energy absorption performance of the windshield are thoroughly investigated.

Thin-wall structures which are usually modeled by using shell finite elements have found widespread applications in various industries. It is of vital importance to evaluate the mechanical performance, including fracture behavior, of this kind of structures. In this work, an efficient extrinsic cohesive zone model is proposed for thin-shell fracture analyses. During simulations, cohesive elements are adaptively inserted into the common boundaries between shell elements when and where needed, which requires frequent manipulation of the topological data information. For the purpose of quick data retrieval, an efficient data structure is proposed by introducing a concept of edge status. The proposed data structure is compared with the widely used TopS in terms of storage and computational efficiency. Finally, the effectiveness of the proposed computational framework is validated by means of several representative numerical examples.

Recently, the discrete-finite element method (DEM-FEM) has proved to be an advanced technique for solid-particle interaction simulations. However, the low computational efficiency limits its applications to practical engineering problems. To achieve this end, this paper proposes a Graphics Processing Unit (GPU) based DEM-FEM, including contact detection, force calculation and information update, in the context of Compute Unified Device Architecture (CUDA) FORTRAN environment. Three numerical examples are performed to validate the efficiency, effectiveness and scalability of the developed method. On this basis, the GPU-based DEM-FEM is extended to a computing platform, and programmed into our in-house code PDFP-OVS for a typical solid-particle interaction problem, i.e. the running performance of a pneumatic tire on granular sand. Numerical result shows that a speedup of more than 15 can be achieved. The simulation results are found to be in good agreement with the experiment results in terms of the gross tractive effort, the drawbar pull and the running resistance, which validates the capacity of the platform in the travel performance analysis of the tire on granular sand.

A driving technical concern for the automobile industry is their assurance that developed windshield products meet Federal safety standards. Besides conducting innumerable glass breakage experiments, product developers also have the option of utilizing numerical approaches that can provide further insight into glass impact breakage, fracture, and fragmentation. The combined finite-discrete element method (FDEM) is one such tool and was used in this study to investigate 3D impact glass fracture processes. To enable this analysis, a generalized traction-separation model, which defines the constitutive relationship between the traction and separation in FDEM cohesive zone models, was introduced. The mechanical responses of a laminated glass and a glass plate under impact were then analyzed. For laminated glass, an impact fracture process was investigated and results were compared against corresponding experiments. Correspondingly, two glass plate impact fracture patterns, i.e., concentric fractures and radial fractures, were simulated. The results show that for both cases, FDEM simulated fracture processes and fracture patterns are in good agreement with the experimental observations. The work demonstrates that FDEM is an effective tool for modeling of fracture and fragmentation in glass.

As an important component of a vehicle, the automotive windshield glazing normally consists of two glass sheets bonded with one polyvinyl butyral (PVB) film. In the context of pedestrian-vehicle accidents, the impact cracking mechanism of the windshield is conductive to pedestrian safety protection and traffic accident reconstruction. The purpose of this paper is to validate the capacity of the intrinsic cohesive zone model (CZM) in impact fracture simulations of a windshield. A windshield finite element (FE) model is established, where cohesive elements are inserted into all the common faces between glass hexahedral finite elements. The fracture behavior of a windshield impacted by a standard adult headform impactor is simulated with the commercial explicit finite element code LS-DYNA. Numerical simulation results are validated by comparison with the corresponding experimental outcomes. For comparison, additional simulations have been performed by the widely used element deletion method (EDM) with a plasticity strain failure criterion. Simulation results show that the intrinsic CZM is more suitable to capture the impact failure characteristics of windshield. Finally, the effects of the glass cohesive strength, mechanical properties of PVB and interfacial adhesion on the impact fracture behavior of the windshield are investigated.

The forced air cooling system is of great significance in the battery thermal management system because of its simple structure and low cost. The influences of three factors (the air-inlet angle, the air-outlet angle and the width of the air flow channel between battery cells) on the heat dissipation of a Lithium-ion battery pack are researched by experiments and computational fluid dynamics (CFD) simulations. Then the three structure parameters are optimized by using single factor analysis and orthogonal test method. It is shown that the layout of the air flow channels has great impacts on the maximum temperature and the temperature difference. The best cooling performance is obtained under the condition of 2.5° air-inlet angle, 2.5° air-outlet angle and equal channels width. With the optimization method, the maximum temperature and the temperature difference are decreased by 12.82% and 29.72% respectively. Therefore, the presented approach in this paper is able to optimize the battery thermal management system for electric vehicles.

The three-dimensional finite-discrete element method (FEM/DEM) is applied to the simulation of tire-sand interactions, where the tire is discretized into hexahedron finite elements and sand is modeled by using the discrete element method. The feasibility and effectiveness of the method are proven by comparing the simulation results with the current reported results. Since long test roads are usually required for investigating tire running behaviors, which lead to large-scale simulation models and time consuming problems, the alternately moving road method is proposed to handle this problem. It can simulate tire running behaviors on an arbitrary length sand road with a constant road length value. The numerical model of a lug tire running on a bisectional road with fine and coarse sand is established to verify the feasibility of the method.

Automotive laminated glass is generally composed of two pieces of outer glass layers and one piece of polyvinyl butyral (PVB) interlayer. Its impact fracture behavior is very important to the safety of drivers, passengers and pedestrians. The objective of this work is to numerically investigate the impact fracture behavior of laminated glass via an intrinsic cohesive model (CM). To achieve this end, we propose a laminated glass model by inserting cohesive elements on all common surfaces of solid finite elements (FEs) in glass layers prior to simulations and describing the nonlinear characteristic of PVB by using the generalized Mooney-Rivlin (MR) model. Besides, the difference between this MR model and another one commonly used MR model is investigated. Then, the impact fracture process of a laminated glass plate is simulated, and the proposed approach is verified by comparing the numerical results with the corresponding experimental observations. Afterwards, parametric studies are performed to investigate the influence of the cohesive penalty stiffness and the strength of glass. Finally, the effects of the stiffness of the PVB film, the support conditions and the thicknesses of glass layers on the impact force history, the cracking and the kinetic energy loss of the impactor are investigated. Keywords: Laminated glass, Impact fracture, Cohesive model, PVB, Mooney-Rivlin model

The requirements of cooling and weight reduction for lithium-ion battery packages in electric vehicles are increasingly important. In this paper, a liquid cooling heat dissipation structure is designed and optimized. First of all, the effects of tube diameter, spacing, thickness and layout of the cooling plate on the heat dissipation of the battery package are investigated by using computational fluid dynamics. Afterwards, based on the optimal results of the single factor analysis, an orthogonal table with four factors and three levels are constructed to perform a single-objective optimization, where the minimization of the maximum temperature is the optimization object. Meanwhile, an experiment is carried out to verify the accuracy of the simulation model. In order to further reduce the mass of the cooling plate, a multi-objective optimization is performed, where the minimization of the maximum temperature and the mass are the optimization objects. The maximum temperature is increased by 10.9% in the multi-objective optimization when compared with that in the single objective optimization. However, the mass of the cooling plate in the multi-objective optimization can drop by 82.4%.

The interaction simulations between particles and structures are often performed in the context of the combined discrete-finite element (DEM-FEM) method, where an efficient, robust and accurate contact algorithm for challenging contact problems is essential. A three-dimensional (3D) discrete and finite element contact algorithm, named ZGL here, has been proposed in our research group (Zang, M.Y. et al., 2011. A contact algorithm for 3D discrete and finite element contact problems based on penalty function method. Comput. Mech. 48, 541–550.). Despite being quite well-established, ZGL algorithm may lack efficiency, robustness and accuracy in certain situations, e.g., when special mesh pattern is applied. However, since such cases are readily to appear in practice engineering application, an algorithm named DZCell is developed to resolve these issues and thus significantly applicable to challenging contact problems. The proposed DZCell algorithm includes an improved global phase to directly find the potential segments rather than the nearest node for discrete elements as contact counterparts. Furthermore, both the memory cost and time consumption of this algorithm are linear, and the algorithm is readily to extend to parallel computing. Several numerical examples demonstrate the achievable improvements in terms of efficiency, robustness and accuracy for 3D contact analysis and validate the capability of the DZCell algorithm in the granular science and mechanical engineering.

As one of the important component of an automobile, the investigation of impact fracture characteristics of the automotive windshield glass contributes to the pedestrian safety protection, traffic accident reconstruction and the design of the windshield glass. Currently, the impact fracture mechanism of laminated glass is investigated by means of theoretical analyses, experimental investigations and numerical simulations. In view of the advantages of numerical simulations, in this work, we focus on the development of cohesive zone-based numerical algorithms for the application of interest here. The purpose of this work is to numerically investigate initiation and propagation of crack in the framework of cohesive zone modelling (CZM). Based on the cohesive theory, we develop two cohesive elements for brick and shell elements respectively. Different from the predefined approach adopted in the commercial codes, such as LS-DYNA, the cohesive elements are inserted adaptively during calculation. We improve node-to-surface and single surface contact algorithms to correspond to the adaptive generation of contact pairs, and propose edge-edge algorithm to describe crack closure. Two laminated glass models are proposed, among which brick elements are adopted to discretize glass in one model, and shell elements are adopted in the other. The main fracture patterns including radial and circular cracks are captured, the impact force history is obtained during calculation. The simulation results compare well with the corresponding experimental outcomes in terms of the fracture patterns and impact force, which demonstrates the capacity of the proposed method to simulate the impact fracture behaviors of laminated glass. Both the two cohesive elements, used in brick and shell element respectively, are certainly accurate and computational efficient for the simulation of material failure.

In this study, a discrete element method is employed to simulate the mixing process of solid particles in a horizontal ribbon mixer with a double U-shaped vessel. A mixing index, i.e. the so-called Lacey index, is adopted to evaluate the mixing quality of particles. The effects of the operational and geometrical parameters including initial loading, particle size, impeller rotational speed, and inner blades on the mixing quality of particles have been investigated. Results suggest that the initial loading and the impeller rotational speed have significant effects on the mixing quality of particles, while the other two parameters have relatively small effects. Moreover, the effect of each parameter on the mixing quality has been explained by utilizing the relative velocity components between the centroids of particles after collision, and this ribbon mixer provides much more intense relative movements of particles along the vertical direction than the axial and side–side directions. Finally, the mixing performance between the ribbon mixers with respective single and double U-shaped vessels is compared. Results show that the ribbon mixer with a double U-shaped vessel shows better mixing performance under top–bottom and front–back initial loadings, however, worse mixing performance under side–side initial loading.

The combined finite-discrete element method takes the advantages of both the finite element (FE) method and the discrete element (DE) method, but a coupling approach is required for effective combination of the two methods. In this paper, a novel coupling approach is proposed by means of ghost particles. The entire domain is decomposed into a FE- and a DE-subdomain, and ghost particles are constructed inside the interface FE domain to connect with the DE domain in a consistent interaction manner as the DE method. A novel one-step back strategy is proposed to overcome the incompatibility of degree of freedoms between FE nodes and DE particles from a numerical sense. The coupling approach is very simple to implement and its effectiveness is validated by numerical examples. Development of a novel coupling approach for the combined finite-discrete element method by means of ghost particles.A novel one-step back strategy is proposed to overcome the incompatibility of DoFs between FE nodes and DE particles.Demonstrated effectiveness of the proposed coupling approach.

In this paper, an effective approach to couple finite elements (FEs) with discrete elements (DEs) is presented. The proposed approach conforms to displacement compatibility condition at the interface between FEs and DEs, and this constraint is enforced by the Lagrange multiplier method. The coupling system is solved by the Gauss-Seidel iteration strategy and the incompatibility of degrees of freedom between FEs and DEs can be effectively addressed. Two numerical examples are employed for validation and the effectiveness of the proposed approach is also demonstrated via comparison with other numerical methods.

Automotive laminated glass is normally comprised of two soda-lime glass sheets bonded with one plastic interlayer, polyvinyl butyral (PVB). Glass-ply cracking is the principal damage pattern in PVB laminated glass under low-velocity impact. The purpose of this work is to numerically investigate the glass-ply cracking mechanism in the framework of cohesive zone modelling. Toward this end, the glass-ply cracking is modelled via an extrinsic cohesive model. Besides, a laminated glass model is proposed, in which brick elements are adopted and an intrinsic cohesive formulation is employed to model the adhesion between glass and PVB. The nonlinear characteristic of PVB is described by using a Mooney–Rivlin constitutive model. Then, the glass-ply cracking behaviours of a laminated glass beam under drop-weight impact are simulated. The proposed approach is qualitatively validated by comparing the simulation results with the experimental observations. In the simulation, the propagations of stress waves of the laminated glass beam during the crack process are illustrated, and the glass-ply cracking mechanism is revealed. Finally, the effects of the PVB film and the adhesion on glass-ply cracking are investigated.

A new contact search algorithm named virtual-surface contact algorithm is developed for dealing with the interaction between spherical discrete elements (DEs) and finite elements (FEs). The basic idea of the contact algorithm is forming a virtual surface above the FE surface. Therefore, the contact problem between DE and FE surface is treated as that between the DE mass center and the virtual surface. Then, the projection of the DE mass center on the virtual surface is determined using spatial area coordinates without solving nonlinear equations and the contact force is processed by using a penalty function method. So, the quick contact searching and accurate evaluation of penetration have been achieved. Finally, the accuracy of this algorithm is investigated via four numerical examples. HighlightsThe virtual-surface contact algorithm, which is based on inside-outside method and penalty function method, is developed. Innermost details regarding local search, contact force calculation and the algorithmic implementations are presented.In the proposed contact algorithm, the penetration between discrete element and finite element can be determined without solving nonlinear equations.The proposed contact algorithm has been implemented into in-house developed code. Four numerical examples are employed to validate the accuracy and robustness of the proposed contact algorithm.

Numerical methods have become useful tools for predicting vehicle mobility performance on granular terrain. However, due to the large number of soil particles and complex contact search in tire-granular terrain simulation, time-consuming calculation has become the most critical problem restricting the application of these methods. In this study, an efficient GPU-based DEM-FEM for simulation of the interactions between an off-road tire and granular terrain is implemented to improve computational efficiency. In this method, the main body of calculation is executed on GPU and programmed into an in-house developed code CDFP. The new GPU-based computing framework consists of 14 kernels, including efficient contact calculation between large-scale particles, novel contact calculation between particles and complex tread, contact calculation between particles and boundary wall, internal force calculation of finite elements, and information update. As a result, the efficient contact search and the complex interactions between an off-road tire and granular terrain are accomplished. Based on the self-developed single-wheel test device, an accurate simulation model consistent with the experiment is established. The validity of the proposed method is verified by comparing the simulation results with the experimental results. Finally, the discussion of computational efficiency shows that the proposed GPU-based DEM-FEM can be a powerful tool to simulate the interactions between an off-road tire and granular terrain.

In recent years, the cohesive zone model (CZM) coupled with linear solid elements has become increasingly popular for the impact fracture analysis of laminated glass. Meanwhile, the computational inefficiency problem accompanied by the method has also been highlighted, where the internal force calculation requires high computational cost. In view of this, this work presents a fracture model combining efficient solid-shell elements with an extrinsic CZM to improve computational efficiency. Instead of using solid elements, it is preferable to use solid-shell elements to discretize the thin-walled glass layers. Moreover, the employed pentahedron solid-shell element is more computationally efficient than linear solid elements. The extrinsic CZM, where the cohesive elements are adaptively inserted into the shared surfaces between the finite elements, is employed to represent the onset and growth of glass cracks. Numerical examples, including an out-plane bending test, an in-plane bending test, and a laminated glass plate drop-weight test are carried out in order to validate the effectiveness of the proposed method. Finally, the computational efficiency of the proposed method in the laminated glass fracture analysis is investigated by comparison with the solid element based extrinsic CZM.

Automotive laminated glass is normally sandwiched by two soda-lime glass layers and one polyvinyl butyral (PVB) layer. Though it is a simple composite structure, its mechanical performance including failure behaviour plays an important role in the context of pedestrian-vehicle accidents. This paper develops a numerical approach, including an extrinsic cohesive shell model and a tie-break algorithm, for impact failure analysis of automotive windshield glazing subjected to a dummy pedestrian headform. During impact, cohesive shell elements are adaptively inserted into the windshield finite element model to represent progressive glass cracking. An edge-to-edge approach is proposed to tackle the contacts between glass cracks. The interaction between glass and PVB is switched from tied connection to contact sliding after a defined fracture criterion is satisfied. The effectiveness of the developed numerical approach is validated by comparing the simulation and experimental results in terms of final fracture patterns and acceleration histories. Besides, numerical studies have been conducted to investigate the influences of impact velocity, impact angle, impact location, and boundary constraint condition on head injury criterion values.

The purpose of this work is to propose a computational framework for impact fracture of laminated glass. The novel computational framework is based on a newly proposed extrinsic cohesive shell model that is theoretically more accurate than the element deletion method and the intrinsic cohesive model to describe fracture in thin-shell glass layers. A laminated glass model is established, where the glass is discretized into shell elements and the PVB film is modelled by solid elements. The bonding between glass and PVB is described via a developed tied contact method. A single surface contact algorithm is developed for the interaction between impactor and glass. Cohesive shell elements are adaptively inserted into the common boundaries between shell elements along with the growth of glass cracks. An edge-edge contact approach is developed to properly describe the interaction between glass cracks. Several simple examples are performed to validate the effectiveness of the proposed contact algorithms. Finally, the developed numerical framework is applied to the impact fracture simulation of a laminated glass plate. The simulation results are found to be in good agreement with the experimental ones, which validates the capacity of the computational framework in impact fracture analysis of laminated glass.

In recent decades, intrinsic cohesive zone models (CZMs) have proved to be an effective approach to modeling progressive interfacial cracking of laminated composite structures. However, matching cohesive interface elements are usually required, which imposes constraints on finite element mesh discretization and reduces computational efficiency for interfacial cracking analysis in bi-material structures with a large modulus mismatch. To address this issue, we develop two intrinsic CZMs, i.e. node- and facet-based models, allowing interfacial cracking modeling with both matching and non-matching cohesive elements in a unified way. Prior to cracking simulations, node and facet cohesive pairs can be easily constructed by recourse to contact detection algorithms. During cracking, cohesive forces of such two models are evaluated in pointwise and integral ways, respectively. The developed models are then respectively coupled with tributary node-to-segment and mortar algorithms to account for a smooth transition from cohesive failure to unilateral contact. Several representative numerical examples are performed to validate the effectiveness of the proposed models, where the numerical performance is also compared and discussed.

This work is concerned with a three-dimensional modelling of impact fracture behaviours of laminated glass. A cohesive model that is able to account for path-dependent behaviours is extended to three dimensions to predict the onset and evolution of fracture. A compact and efficient adjacency-based topological data structure termed TopS is utilized to store and manipulate mesh information. In view of contact characteristics, a global contact search algorithm is developed, which includes a regular search and an adaptive search. The regular search is performed by recourse to a linear contact algorithm named LC-Grid. The adaptive search algorithm is proposed to efficiently update new contacts during fracture. Additionally, a local contact search algorithm is developed, which facilitates the judgements of node–face and edge–edge contacts with a unified inside–outside approach. Afterwards, the cohesive model is coupled with the frictional contact algorithm to account for the unilateral and frictional sliding effects of cohesive elements under mixed mode loading. Finally, the impact fracture behaviours of a laminated glass plate are simulated. The simulation results compare well with the experimental outcomes, which validates the capability of the proposed method in the impact fracture analysis of laminated glass.

The finite element (FE) model of a tire to simulate tire blowout is developed, the effectiveness of which is validated by the tire blowout test. Then, a simplified FE model of a vehicle that integrates the tire model is established. The vehicle responses to tire blowout are analyzed under the situation of no steering and braking behavior on the vehicle. Finally, some meaningful results, such as the trajectory, yaw velocity of the vehicle, and the forces acting on the tires, are obtained. This study provides the foundation to further investigate the handling stability and control strategy of a vehicle when a tire blowout occurs during normal vehicle operation.

When applying the combined finite-discrete element method for analysis of dynamic problems, contact is often encountered between the finite elements and discrete elements, and thus an effective contact treatment is essential. In this paper, an accurate and robust contact detection algorithm is proposed to resolve contact problems between spherical particles, which represent rigid discrete elements, and convex quadrilateral mesh facets, which represent finite element boundaries of structural components. Different contact scenarios between particles and mesh facets, or edges, or vertices have been taken into account. For each potential contact pair, the contact search is performed in an hierarchical way starting from mesh facets, possibly going to edges and even further to vertices. The invalid contact pairs can be removed by means of two reasonable priorities defined in terms of geometric primitives and facet identifications. This hierarchical contact searching scheme is effective, and its implementation is straightforward. Numerical examples demonstrated the accuracy and robustness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

A 3D simulation method was developed to investigate the tire–sand interactions, where the discrete element (DE) and finite element (FE) methods were coupled. An algorithm for the contact of FE and DE was introduced. The Hertz–Mindlin theory was applied to calculate the contact force among elements. A 3D numerical model was established based on the soil-bin experiment to validate the feasibility of the method in the analysis of the tire–sand interactions. The traveling process of the smooth tire on the sandy soil was simulated and the traction performance parameters of the tire under different slip values (0%, 10%, 20%, 30%, 40%, 50% and 60%) were obtained. The overall trend of the drawbar pull versus the slip ratio is qualitatively in agreement with current experimental results. The result also proved the feasibility of the 3D FE–DEM in the simulation of the tire–sand interactions. 2014 ISTVS. Published by Elsevier Ltd. All rights reserved.

The contact searching is computationally intensive and its memory requirement is highly demanding; therefore, it is significant to develop an efficient contact search algorithm with less memory required. In this paper, we propose an efficient global contact search algorithm with linear complexity in terms of computational cost and memory requirement for the finite element analysis of contact problems. This algorithm is named LC-Grid (Lei devised the algorithm and Chen implemented it). The contact space is decomposed; thereafter, all contact nodes and segments are firstly mapped onto layers, then onto rows and lastly onto cells. In each mapping level, the linked-list technique is used for the efficient storing and retrieval of contact nodes and segments. The contact detection is performed in each non-empty cell along non-empty rows in each non-empty layer, and moves to the next non-empty layer once a layer is completed. The use of migration strategy makes the algorithm insensitive to mesh size. The properties of this algorithm are investigated and numerically verified to be linearly proportional to the number of contact segments. Besides, the ideal ranges of two significant scale factors of cell size and buffer zone which strongly affect computational efficiency are determined via an illustrative example.