Contact-impact Problems Research Articles

An Improved Bulk Viscosity Method for Contact-Impact Problems

An Improved Bulk Viscosity Method for Contact-Impact Problems

Validation of compliant contact force models for low coefficient of restitution impact

Low coefficient of restitution impact occurs frequently in agricultural machinery systems. In recent decades, many compliant contact force models have been proposed. However, there are no experimental validation studies for low coefficient of restitution impact problems. Based on this, this study conducted impact experiments using the tobacco main vein and the rubber ball as impact bodies to verify the accuracy and applicability of the contact force models for low coefficient of restitution impact. Firstly, A drop tower test rig was built to measure the coefficient of restitution and the impact force at different pre-impact velocities. Then the measured value of the coefficient of restitution was brought into some typical contact force models to simulate the impact process. Finally, the simulation results were compared with the experimental results. The comparison results showed that the Flores et al. model, the Gharib-Hurmuzlu model, and the Yu et al. model could describe the impact process relatively better. This study can provide a reference for the description of the low coefficient of restitution contact-impact problems. • Experimentally validating the accuracy of compliant contact force models. • Prediction error of the peak impact force is less than 30%. • Using rubber ball and tobacco main vein as impact bodies. • The measured value of the coefficient of restitution is less than 0.6.

Influence of longitudinal structural connectivity on seismic performance of three-hinged precast arch culverts

The hinge type of precast concrete arch culvert was introduced to Japan from France in the 1990s in consideration of the saving of labor, shortening of the construction period, and high quality control of the concrete members. However, due to the 2011 off the Pacific Coast of Tohoku Earthquake (March 11, 2011), the three-hinged precast arch culverts that had been constructed in Japan at the beginning of the period when precast arch culverts were firstly introduced, suffered damage, which spoiled their serviceability. According to the extent of the damage and the type of culverts that were damaged, the longitudinal structural connectivity of the culverts was assumed to be one of the possible reasons for the reported damage mechanism. Therefore, the objective of this paper was to clarify how strongly the longitudinal structural connectivity influenced the longitudinal seismic behavior of the three-hinged arch culverts. To achieve this objective, an elasto-plastic finite element analysis was conducted with an analytical model that could capture the characteristics of the damaged culverts. Simultaneously, a penalty method with the bi-linear spring model was applied as a solution to the contact-impact problems of the precast segmental arch members. As a result, it was found that the weaker longitudinal structural connectivity in the damaged culverts allowed the torsional displacements of the arch members to induce critical damage to the arch members, namely, edge defects in the arch crown and concrete foundation. The numerical results proved the unignorable influence of the longitudinal structural connection on the possible damage to three-hinged arch culverts.

Bi-penalty stabilized technique with predictor–corrector time scheme for contact-impact problems of elastic bars

This paper presents a stabilization technique for the finite element modelling of contact-impact problems of elastic bars via a bi-penalty method for enforcing contact constraints while employing an explicit predictor–corrector time integration algorithms. The present proposed method combines three salient features in carrying out explicit transient analysis of contact-impact problems: the addition of a penalty term associated with a kinetic energy expression of gap constraints, in addition to the conventional internal energy penalty term of the gap constraints; an explicit integration method that alleviates spurious oscillations; and, a judicious selection of two penalty parameters such that the stable time steps of the resulting explicit method is least compromised. Numerical experiments have been carried out with three explicit methods: the standard central difference method, the stabilized predictor–corrector method (Wu, 2003 [50]) and a method for mitigating spurious oscillations (Park et al., 2012 [44]) as applied to simulate one-dimensional contact-impact problems of the Signorini problem and the impact of two elastic bars. Results indicate that the proposed method can maintain the contact-free stability limit of the central difference and yield improved accuracy compared with existing bi-penalty methods.

Continuous contact force model with an arbitrary damping term exponent: Model and discussion

More than twenty continuous contact force models have been presented for modeling contact-impact problems; however, there was no uniformity regarding the value of the damping term exponent in these models. A new type of continuous contact force model is proposed in this research, in which the value of the damping term exponent can be arbitrary. Then, the effect of the value of the damping term exponent on the model accuracy is investigated by comparing the simulation and experimental results. As it is almost impossible to obtain an analytical solution based on the system dynamic equation, according to the rule of energy equivalence, an approximate dynamic equation is developed by introducing an equivalent indentation and equivalent velocity. Based on the system dynamic equation and the approximate dynamic equation, a primary formula for the hysteresis damping factor of the model can be obtained. Through nondimensional analysis, new models for different values of the damping term exponent are established by modifying the primary formula. The comparison between the simulation results and published experimental data demonstrates the validities of the new models and reveals that the influence of the value of the damping term exponent on the model accuracy can be considered to be negligible.

Collision in the expansion joint effects on the seismic behavior of large-scale aqueduct

ABSTRACT Under earthquake, two beams of the aqueduct’s expansion joint may collide; thus, this will endanger the safety of the structure and even lead to girder falling accident. Quite a few studies of this issue use the simple one-dimensional model, but little takes the collision phenomenon under the action of multi-dimensional earthquake into account. According to the Contact-Impact Problems of large-scale aqueduct under earthquake action between the adjacent beam segments, a three-dimensional contact analysis model has been used to simulate the collision phenomenon. And the response of aqueduct structure collision one-dimensional seismic and multidimensional earthquake is compared; the results reveal that the three-dimensional frictional contact impact finite element model can simulate the real aqueduct structure under seismic pounding effect.

An improved compliant contact force model using a piecewise function for impact analysis in multibody dynamics

Contact-impact problems have attracted more and more attention in mechanical multibody systems. In the past period of time, a few compliant contact force models have been put forward. However, some compliant contact force models are only applicable to a specific range of coefficient of restitution impact problems. And, some compliant contact force models have large errors with the actual situation. In order to reduce the errors, an improved compliant contact force model is proposed in this paper, which is applicable to the whole range of coefficient of restitution impact problems. In this work, the permanent deformation is taken into account during the contact process. Meanwhile, the method of piecewise fitting is used to reduce the errors in numerical solutions. Therefore, the improved compliant contact force model uses a piecewise function for the whole range of coefficient of restitution. In order to illustrate the situation, six independent contact force models are numerically analyzed by using Matlab codes. The result shows that the improved compliant contact force model in this paper is applicable to both soft and hard impact and nearer to the actual situation.

Analytical Study of Babbitt/steel Composite Structural Bars in Oblique Contact-impact with a Solid Flat Surface

Abstract. The oblique contact-impact characteristic of the composite structural bar composed of Babbitt alloy and low-carbon steel (ZChSbSb11-6 ∕ AISI 1020) with a solid flat surface (AISI 1045) was studied theoretically and experimentally. The dynamic equation of the composite structural bar with vibration response during the contact-impact was established using the momentum theorem and assumed mode method, and the instantaneous contact forces during different impact phases were analyzed based on modified Jackson–Green model. Four sets of experiments (i.e. different proportion of Babbitt, ξ={1/8,1/2,3/4,7/8}) for the initial angle, θ=45∘, and different initial velocities were performed; and, the rebound linear and angular velocity of the contact point of composite structural bar after impact was calculated and compared with experimental results. Besides, the coefficient of restitution, the relation of contact force and contact deflection, and the permanent deformation were also compared for the composite structural bars with different proportions in combination, ξ. Three critical angles are found to determine whether the composite bar slides or not, but are prominently different for the composite bars with different ξ. In comparing with the experimental results, the numerical solutions of rebound linear and angular velocity had yield encourage results and, all relative errors were small, indicating that the simulations are in good agreement with the experimental results. Also, the oblique contact-impact behavior involving the coefficient of restitution, the relation of contact force and contact deflection, and the permanent deformation was explained in detail. It can be concluded that as the proportion of Babbitt ξ increases, the composite structural bar presents a characteristic of ease of deflection. And the contact-impact behavior of structural entity is closely related to the inherent properties of the elasto-plastic material, especially for the weak material of composite structures. The more easily the impacting object is deformed, the small the contact force during the contact-impact, which also indicates the yield strength of weak material is a very significant parameter in the event of collision. Such work could give conducive insights to contact-impact problems of the key parts or structures composed of composite materials in mechanical system.

Model smoothing method of contact-impact dynamics in flexible multibody systems

An original model smoothing method for contact-impact dynamics in flexible multibody system is proposed in this work. First, the model smoothing method is applied to improve the computational efficiency, in which the instant stresses of flexible bodies are replaced by the time-averaged stresses in a short time during the modeling stage, the resulting equations of motion do not contain high frequency components. In the following, the fundamental issues of continuous contact force models are discussed. A smoothing method of modeling linear complementarity problem (LCP) is proposed for the dynamic analysis of flexible multibody system. This approach takes into account the permanent contact and impact, which has the great merit that can be used straightforward without switching contact models. Numerical results show that the model smoothing method is a new effective approach for the numerical analysis of contact-impact problems in flexible multibody system.

Ductile fracture at high velocity impact of cylindrical tubes

Study of impact problems is of great interest in many engineering fields, such as automotive industry, aircraft industry, defense industry etc. Orbital debris impact on space station, crash-worthiness of automobiles etc. are few examples of impact problems. Impact problems are characterized by short duration, large plastic deformation, high strain rates, rapid dissipation of energy, thermal softening etc. Contact-impact problems like crash-worthiness of vehicles, impact testing etc often involve ductile fracture. Ductile fracture is a mode of failure in which voids either pre-existing within the material or nucleated during deformation grow until they link together or coalesce to form a continuous fracture path. The continuum damage mechanics model of Lemaitre is one of the most commonly used approaches to study ductile fracture. A number of studies on damage growth and fracture simulation, in static processes have been carried out using this approach. However, number of such studies on the prediction of fracture in impact problems are limited. In the present work, damage growth, and effect of high strain rate are studied for ductile fracture during high velocity impact of cylindrical tubes using commercial finite element software ABAQUS/Explicit.

A parallel finite element procedure for contact-impact problems using edge-based smooth triangular element and GPU

The edge-smooth finite element method (ES-FEM) can improve the computational accuracy of triangular shell elements and the mesh partition efficiency of complex models. In this paper, an approach is developed to perform explicit finite element simulations of contact-impact problems with a graphical processing unit (GPU) using a special edge-smooth triangular shell element based on ES-FEM. Of critical importance for this problem is achieving finer-grained parallelism to enable efficient data loading and to minimize communication between the device and host. Four kinds of parallel strategies are then developed to efficiently solve these ES-FEM based shell element formulas, and various optimization methods are adopted to ensure aligned memory access. Special focus is dedicated to developing an approach for the parallel construction of edge systems. A parallel hierarchy-territory contact-searching algorithm (HITA) and a parallel penalty function calculation method are embedded in this parallel explicit algorithm. Finally, the program flow is well designed, and a GPU-based simulation system is developed, using Nvidia’s CUDA. Several numerical examples are presented to illustrate the high quality of the results obtained with the proposed methods. In addition, the GPU-based parallel computation is shown to significantly reduce the computing time.

General framework for dynamic large deformation contact problems based on phantom-node X-FEM

This paper presents a general framework for modeling dynamic large deformation contact-impact problems based on the phantom-node extended finite element method. The large sliding penalty contact formulation is presented based on a master-slave approach which is implemented within the phantom-node X-FEM and an explicit central difference scheme is used to model the inertial effects. The method is compared with conventional contact X-FEM; advantages, limitations and implementational aspects are also addressed. Several numerical examples are presented to show the robustness and accuracy of the proposed method.

Methodology for Assessment of the Allowable Sea States During Installation of an Offshore Wind Turbine Transition Piece Structure Onto a Monopile Foundation

In this paper, a methodology suitable for assessing the allowable sea states for installation of a transition piece (TP) onto a monopile (MP) foundation with focus on the docking operation is proposed. The TP installation procedure together with numerical analyses is used to identify critical and restricting events and their corresponding limiting parameters. For critical installation phases, existing numerical solutions based on frequency and time domain (TD) analyses of stationary processes are combined to quickly assess characteristic values of dynamic responses of limiting parameters for any given sea state. These results are compared against (nonlinear and nonstationary) time domain simulations of the actual docking operations. It is found that a critical event is the structural damage of the TP's bracket supports due to the potential large impact forces or velocities, and a restricting installation event (not critical) is the unsuccessful mating operation due to large horizontal motions of the TP bottom. By comparing characteristic values of dynamic responses with their allowable limits, the allowable sea states are established. Contact–impact problems are addressed in terms of assumed allowable impact velocities of the colliding objects. A possible automatic motion compensation system and human actions are not modeled. This methodology can also be used in connection with other mating operations such as float-over and topside installation.

Toward Robotic Pseudodynamic Testing for Hybrid Simulations of Air-to-Air Refueling

Hybrid simulation couples experimental tests of novel components to validated numerical models of the remainder of a system and provides high-confidence predictions of their coupled dynamic behavior. Air-to-air refueling (AAR) is an example of the type of system that can benefit from this development approach. The work in this paper concerns the on-ground validation and preflight verification of probe–drogue contact–impact scenarios in AAR maneuvers using off-the-shelf multiaxis industrial robots as part of a hybrid test to interface the refueling hardware with numerical models of the flight environment. While industrial manipulators present a cost-effective solution, bandwidth and power limitations inevitably cause practical problems for real-time hybrid testing. These deficiencies typically manifest themselves as significant tracking inaccuracies or instabilities when sharp nonlinearities or discontinuities are encountered as part of a contact phase. Here, the novel robotic pseudodynamic testing (RPsDT) method is employed to circumvent the contact-response speed limitations of industrial robots. This paper presents and discusses the application of RPsDT to contact–impact problems, outlines the challenges and limitations of the technique in an easily reproducible validation experiment, and details the first RPsDT hybrid simulation of an AAR maneuver using scaled refueling hardware. It is concluded that RPsDT provides a useful tool for the investigation of a particular subclass of multibody contact–impact problems including AAR, where the response of the contacting structures does not possess significant rate-of-loading effects. Future work will comprise tests with full-scale AAR hardware.

Simulation of Large Deformation Elasto-plastic Impact Problems Using Two Different Objective Stress Measures

A comparative study of two different incremental objective stress measures - Jaumann stress rate measure and a new incremental objective stress - are compared for simulations of large deformation, dynamic, elasto-plastic, contact-impact problems. Elasto- plastic behaviour is modelled by an associated flow rule based on the von Mises yield criterion and power law type isotropic hardening. The material and geometric non-linearities are handled by using the updated Lagrangian method. A node-to-segment interface model is used for developing the contact stiffness matrix. Contact constraints are imposed using Lagrange multiplier method. Coulomb's friction law is used for calculating the friction forces. A finite element – finite difference scheme is used for spatial and temporal discretization respectively. Some dynamic large deformation contact-impact problems are numerically simulated. The response is computed and compared using both the Jaumann stress rate and the new incremental objective stress. It is shown that the response of the new incremental objective stress is comparable with the response of the Jaumann stress rate measure.

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper, an efficient formulation based on the Lagrangian method is presented to investigate the contact–impact problems of flexible multi-body systems. Generally, the penalty method and the Hertz contact law are the most commonly used methods in engineering applications. However, these methods are highly dependent on various non-physical parameters, which have great effects on the simulation results. Moreover, a tremendous number of degrees of freedom in the contact–impact problems will influence the numerical efficiency significantly. With the consideration of these two problems, a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in flexible multi-body system numerically. Meanwhile, the finite element meshing laws of the contact bodies will be studied preliminarily. A numerical example with experimental verification will certify the reliability of the presented formulation in contact–impact analysis. Furthermore, a series of numerical investigations explain how great the influence of the finite element meshing has on the simulation results. Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficiency. In this paper, an efficient formulation based on the Lagrangian method is presented to investigate the contact–impact problems of flexible multi-body systems. A transformation from finite element coordinates p to component mode synthesis generalized coordinates y can be performed. When a contact pair is activated, a set of constraint equations should be added to the system

Polygonal finite element methods for contact-impact problems on non-conformal meshes

In this paper, a polygonal finite element method is presented for large deformation frictionless dynamic contact-impact problems with non-conformal meshes. The geometry and interfaces of the problem are modeled independent of the background mesh based on the level set method to produce polygonal elements at the intersection of the interface with the regular FE mesh. Various polygonal shape functions are employed to investigate the capability of polygonal-FEM technique in modeling frictionless contact-impact problems. The contact constraints are imposed between polygonal elements produced along the contact surface through the node-to-surface contact algorithm. Several contact-impact problems are modeled using various polygonal interpolation functions, including the Wachspress interpolation functions, the metric coordinate shape functions, the natural neighbor based functions, and the mean value coordinate functions to demonstrate the efficiency of proposed technique in modeling contact-impact problems.

An enhanced energy conserving time stepping algorithm for frictionless particle contacts

AbstractAn Enhanced Energy Conserving Algorithm (EECA) formulation for time integration of frictionless contact–impact problems is presented. In it the energy, linear and angular momentum are conserved for every contact using an enhanced Penalty method. Previous formulations for these problems have shown that the total bodies' energy decreases for contact due to an artificial energy transfer between the penalty spring and the contacting bodies. Consequently, they are not able to reproduce a physical response after a single contact, introducing errors in trajectories and velocities.Through the conserving balance equations, EECA computes a physical response by inserting for every contact an additional amount of linear momentum and contact force. The structure of these equations defines the additional linear momentum to restore the energy and the enhanced Penalty method based on a spring and a dashpot. This method approximately enforces the first and second Kuhn–Tucker conditions.The new algorithm has been applied to several frictionless rigid problems using the Discrete Element Method. The first two problems consist of the simulation and analytical comparison of the Newton's Cradle and Carom problems (billiard pool problem). The last two are the hopper filling process and the breaking of a pool ball's triangular arrangement, both of which involve a medium number of contacts. Application of this formulation will be straightforward to elastic and general‐shaped bodies using the Finite Element Method. Copyright © 2010 John Wiley & Sons, Ltd.

NS-FEM/ES-FEM for contact problems in metal forming analysis

A new approach based on the node-based smoothed finite element method (NS-FEM) / edge-based smoothed finite element method (ES-FEM) is presented for the analysis of contact-impact problems with large deformations and for the simulation of metal forming processes. The formulations are based on 3-node triangular and linear interpolation functions. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In the presented methods, the strain field is smoothed by means of gradient smoothing technique over smoothing domains constructed associated with nodes for NS-FEM and element edges for ES-FEM. In the total Lagrangian formulation the strain smoothing is performed for the deformation gradient and Green strain. The smoothed deformation gradient, smoothed strain tensor, and the smoothed stress tensor are derived at the reference (or initial) configuration. ES-FEM is used to analyze deviatoric part and NS-FEM is selectively employed in the volumetric part of deformation in order to relax the incompressible constraints and remedy the volumetric locking. Solutions to upsetting, extrusion of metals with large material distortions are given to show the effectiveness and efficiency of the proposed method.

A linearly conforming radial point interpolation method (LC-RPIM) for contact problems in metal forming analysis

The total Lagrangian formulation and implementation of a linearly conforming radial point interpolation method (LC-RPIM) is presented for the analysis of contact-impact problems with large deformations and for the simulation of metal forming processes. In present method, the displacement field function is approximated using RPIM shape functions possessing Kronecker delta function property, which facilitates easy the enforcement of essential boundary conditions. The gradient smoothing operations are performed to the displacement gradient and the deformation gradient over smoothing domains associated with field nodes, and an integration scheme is used based on conforming nodal integration techniques. The geometrical nonlinearities and material nonlinearities for the dynamic solution are treated by using the total Lagrangian description and an elastic-plastic constitutive law. A simple general contact searching algorithm is used to treat the contact interface in the metal forming analysis and an algorithm is presented for the contact force. A typical numerical example is given to evaluate the effectiveness of present method compared with the FEM.