Protection effectiveness of an oblique plate against a long rod

Protection effectiveness of an oblique metallic plate against a long rod projectile has been evaluated through a three-dimensional dynamic finite element computer program. The parameters considered in the simulations are the impact velocity, oblique plate thickness, gap distance between oblique plate and witness block, and obliquity. It was found that protection performance of an oblique plate was maximized in case that the ratio of line-of-sight (LOS) plate thickness to projectile diameter is around 2.0. This result may be used as a guide for the design of obliquely spaced armour structures against long rod projectiles.     

A contact algorithm for 3D discrete and finite element contact problems based on penalty function method

A contact algorithm in the context of the combined discrete element (DE) and finite element (FE) method is proposed. The algorithm, which is based on the node-to-surface method used in finite element method, treats each spherical discrete element as a slave node and the surfaces of the finite element domain as the master surfaces. The contact force on the contact interface is processed by using a penalty function method. Afterward, a modification of the combined DE/FE method is proposed. Following that, the corresponding numerical code is implemented into the in-house developed code. To test the accuracy of the proposed algorithm, the impact between two identical bars and the vibration process of a laminated glass plate under impact of elastic sphere are simulated in elastic range. By comparing the results with the analytical solution and/or that calculated by using LS-DYNA, it is found that they agree with each other very well. The accuracy of the algorithm proposed in this paper is proved.     

Dynamic large deflection response of composite laminates subjected to impact

Impact responses of composite laminates with and without initial stresses are investigated using the finite element method. A nine-node isoparametric quadrilateral element based on the Mindlin plate theory and the von Karman large deflection assumptions is developed. An experimentally established contact law which accounts for the permanent indentation is incorporated into the finite element program to evaluate the impact force. In the time integration, the Newmark constant acceleration algorithm is used in conjunction with successive iterations within each time step. Numerical results, including the contact force histories, deflections and strains in the plate, are presented.     

A monolithic smoothing‐gap algorithm for contact‐impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact‐impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact‐impact. The smoothed signed distance functions are constructed by a moving least‐squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright © 2002 John Wiley & Sons, Ltd.     

A parallel finite element contact/impact algorithm for non-linear explicit transient analysis: Part I—The search algorithm and contact mechanics

A contact algorithm has been developed and implemented in a non-linear dynamic explicit finite element program to analyse the response of three-dimensional shell structures. The contact search algorithm accounts for initial contact, sliding, and release through the use of a parametric representation of the motion of points located on the surface of the structure combined with a contact surface representation which approximates the actual surface by means of triangular search planes. The mechanics of contact is handled by taking advantage of the fact that an explicit time integration scheme results in very small displacements during a time step. The amount of overlap of the discrete representation of the surfaces which occurs at contact is taken as a measure of the approach of the surfaces. Hence, experimental data which relates approach to normal contact pressure can be used to determine the contact pressure applied to the finite element model of the surface as contact evolves. The friction model also incorporates experimental data on the dependence of the coefficient of friction on both the relative sliding velocity and on the relative tangential displacement between surfaces in contact observed in friction tests. The parallel implementation of this contact algorithm and its performance on a 128-processor distributed-memory multiprocessor computer is discussed in Part II of this paper.     

Generalized mixed variational methods for Reissner plate and its applications

 Based on the mechanism of shear locking phenomenon and potential functional of Reissner plate bending problem, the generalized mixed variational principle for Reissner plate analysis is presented by parameterized Lagrange multiplier method. The proposed variational functional contains splitting factors which are able to adjust the shear potential energy and shear complementary energy components in it. The generalized mixed finite element formulation of bilinear quardrilateral element for Reissner plate bending analysis is established in terms of the new variational principle. The stiffness of the finite element model can be changed by the alteration of the splitting factors. Thus both the free of shear locking and higher accuracy are obtained by the choice of appropriate splitting factors. The most important is that this paper gives one self-adaptative way to choose the splitting factors for thin and moderately thick plates. This results in the comparative order of magnitude between the bending stiffness and shear stiffness for the arbitrary thickness. In the application of two-by-two exact Gaussian integration scheme to the proposed mixed element model, numerical examples show that free of locking is obtained even in the thin plate limit and high accuracy is given for moderately thick plate. Received: 15 January 2002 / Accepted: 10 September 2002 This work is partially supported by the National Nature Science Fund in China under Award No. 53978376     

Modelling of failure mode transition in ballistic penetration with a continuum model describing microcracking and flow of pulverized media

An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2002; 55(4):499–501. A new continuum model to describe damage, fragmentation and large deformation of pulverized brittle materials is presented. The multiple‐plane‐microcracking (MPM) model, developed by Espinosa, has been modified to track microcracking on 13 orientations under high pressure, high strain rate and high deformation. This model provides the elastic and inelastic response of the material before massive crack coalescence. When pulverization occurs, the constitutive response is modelled by means of a visco‐plastic model for granular material, which is a generalization to three dimensions of the double‐sliding theory augmented by a consolidation mechanism. The initialization of the granular model is governed by a yield surface at the onset of massive crack coalescence. This is accomplished by examining a representative volume element, modelled using the MPM model, in compression‐shear. The main advantage of this approach is to keep a continuum model at all stages of the deformation process and thus avoid the difficulties of crack representation in a discrete finite element code. This model has been implemented in LS‐DYNA and used to examine interface defeat of long rod penetrators by a confined ceramic plate. The numerical simulations are compared to experiments in order to identify failure modes. The model parameters were obtained independently by simulating plate and rod impact experiments. The proposed model captures most of the physical observations as well as failure mode transition, from interface defeat to full penetration, with increasing impact velocity. Copyright © 2002 John Wiley & Sons, Ltd.     

有限元模拟在研究弹丸冲击钢板过程中的应用

综述了有限元模拟在研究弹丸冲击钢板过程中的应用,对几何模型的建立、材料模型及参数的确定、网格的划分和接触法则的定义进行描述和推荐。指出影响抗弹性能的主要因素如弹丸和钢板的材质、弹丸的速度和几何形状、钢板倾斜和复合结构等,均可进行有限元模拟研究。对钢板和弹丸的破坏形貌、应力应变分布、钢板的弹道极限、弹丸速度和加速度随时间的变化、钢板和弹丸的内能变化等有限元模拟结果进行了分析,最后对有限元模拟的局限性进行了说明。     

Simulation of high speed impact into ceramic composite systems using cohesive-law fracture model

A numerical study for the analysis of oblique metal/ceramic/metal three layer composite systems against a long-rod has been performed. The study was done using a three-dimensional dynamic program NET3D, which uses the finite element Lagrangian method with explicit time integration. To model the discrete nature for fracture and damage of brittle materials, we implemented cohesive-law fracture model with a node separation algorithm for the tensile failure and Mohr–Coulomb model for the compressive loading. A tetrahedral element implemented in the code provides more potential fracture surfaces than a hexahedral element. As a verification of the scheme, an oblique impact into the composite system was conducted and the calculated penetration depth and propagating crack paths were found to be in good agreement with experiment. Next a series of three-dimensional numerical simulations have been conduced to examine the ballistic performance of three layer composite systems. The residual velocity and residual length of the rod were computed for different plate thickness ratios of equal areal density. The impact velocities considered are 1.5, 1.8 and 2.2 km/s. The oblique angle of the plate is 0° and 45°. The optimum thickness ratios of ceramic to metal are very similar to those obtained from the previous experiment.     

A contact detection algorithm for multi‐sphere particles by means of two‐level‐grid‐searching in DEM simulations

In discrete element method simulations, multi‐sphere particle is extensively employed for modeling the geometry shape of non‐spherical particle. A contact detection algorithm for multi‐sphere particles has been developed through two‐level‐grid‐searching. In the first‐level‐grid‐searching, each multi‐sphere particle is represented by a bounding sphere, and global space is partitioned into identical square or cubic cells of size D, the diameter of the greatest bounding sphere. The bounding spheres are mapped into the cells in global space. The candidate particles can be picked out by searching the bounding spheres in the neighbor cells of the bounding sphere for the target particle. In the second‐level‐grid‐searching, a square or cubic local space of size (D + d) is partitioned into identical cells of size d, the diameter of the greatest element sphere. If two bounding spheres of two multi‐sphere particles are overlapped, the contacts occurring between the element spheres in the target multi‐sphere particle and in the candidate multi‐sphere particle are checked. Theoretical analysis and numerical tests on the memory requirement and contact detection time of this algorithm have been performed to verify the efficiency of this algorithm. The results showed that this algorithm can effectively deal with the contact problem for multi‐sphere particles. Copyright © 2015 John Wiley & Sons, Ltd.     

Penetration of limestone targets by ogive-nosed VAR 4340 steel projectiles at oblique angles: experiments and simulations

In this paper, we document the results of a combined experimental, analytical, and computational research program that investigates the penetration of steel projectiles into limestone targets at oblique angles. We first conducted a series of depth-of-penetration experiments using 20.0 g, 7.11-mm-diameter, 71.12-mm-long, vacuum-arc-remelted (VAR) 4340 ogive-nose steel projectiles. These projectiles were launched with striking velocities between 0.4 and 1.3 km/s using a 20-mm powder gun into 0.5 m square limestone target faces with angles of obliquity of 15° and 30°. Next, we employed the initial conditions obtained from the experiments with a technique that we have developed to calculate permanent projectile deformation without erosion. With this technique we use an explicit, transient dynamic, finite element code to model the projectile and an analytical forcing function based on the dynamic expansion of a spherical cavity to represent the target. Due to angle of obliquity we developed a new free surface effect model based on the solution of a dynamically expanding spherical cavity in a finite sphere of incompressible Mohr–Coulomb target material to account for the difference in target resistance acting on the top and bottom sides of the projectile. Results from the simulations show the final projectile positions are in good agreement with the positions obtained from post-test castings of the projectile trajectories.     

Multiangular elements in plate bending

The problem of bending a thin plate is solved by the finite element method. Using a differential equation of the plate element equilibrium determines the potential energy by contour values of displacements and their first derivatives. In the equilibrium state they have to be such that the potential energy reaches its minimum. The suggested calculation algorithm enables the use of multiangular elements of arbitrary shape instead of integration in the area of this element in which curvilinear integrals appear along the element contour. Elaborated also is the program for calculation by computer and verified usability of the method for various elements based on the example of the square plate.     

受冲板壳结构的弹塑性力学特性分析

采用基于随动坐标系的 4节点假设应变场壳单元及显式有限元方法分析受冲板壳结构的弹塑性力学特性。材料模型采用弹塑性等向强化模型 ,接触搜寻采用一体化接触搜寻方法 ,接触力由罚参数法计算 ,算例表明 :该方法简明、直观、快捷、方便     

A semi-analytical approach to three-dimensional normal contact problems with friction

 We present a semi-analytical approach for three-dimensional elastostatic normal contact problems with friction. The numerical approach to iteration on contact area and stick zone size is supported by an underlying analytical solution relating normal and tangential surface tractions to surface displacements in three coordinate directions. The governing equations are fully coupled. The analytical surface displacement solutions for a basic loading element have been derived elsewhere (Li and Berger 2001), and the total surface displacements are constructed as a superposition of deflections due to overlapping pyramid load segments. This approach requires no interpolation scheme for the field variables, which distinguishes it from other numerical techniques such as the FEM, BEM, and meshless methods. A background grid is defined only on the contact surfaces, and iteration approaches are used to determine a convergent configuration for contact domain and stick zone size. The approach is exercised on several normal contact problems, with and without friction, and the results compare favorably to existing analytical and numerical solutions. Received: 10 July 2002 / Accepted: 3 December 2002 The authors appreciate the support of the UC Department of Mechanical Engineering and the UC Office of the Vice President for Research, who jointly provided funds for this work.     

Axisymmetric contact of an elastic layer underlain by rigid base

Axisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.     

基于有限元法的CTP成像滚筒及版材的数值仿真

利用有限元分析软件ANSYS建立CTP成像滚筒的几何模型与有限元模型,选择接触单元模拟版材和滚筒表面之间的关系,以滚筒本体、滚筒与版材组合以及对滚筒内部吸真空的3种组合下进行有限元静力分析,获得滚筒自身变形对版材影响的大小,以及滚筒内抽吸真空对版材和滚筒变形的影响。结果表明,3种情况下滚筒和版材的最大变形量及位置均有所不同。其中,吸真空组合分析说明,版材在与滚筒表面密合状态下变形情况随从滚筒,滚筒表面的导槽对版材变形会产生一定影响,真实反映了工作状态,研究结果可以为CTP成像滚筒的设计与优化提供理论依据。     

On the accuracy of the Hertz model to describe the normal contact of soft elastic spheres

The finite element method is used to investigate the validity of the Hertz model for normal contact under conditions that violate some of the assumptions on which the Hertz model was derived. The conditions investigated are: frictional contact, non-flat contact surface and large strains. The investigations were performed for the case of two elastic spheres in contact as well as that of a sphere in contact with a flat plate. The existence of friction for normal contact does not appear to lead to any erroneous predictions of the force-deflection relationship by the Hertz model. The Hertz model also does not appear to predict significant errors when the contact surface is not flat. However, large strains were found to cause important prediction errors by the Hertz model. Calibration curves for the corrections on the Hertz model are proposed.     

Contact algorithms for the material point method in impact and penetration simulation

The inherent no‐slip contact constraint in the standard material point method (MPM) creates a greater penetration resistance. Therefore, the standard MPM was not able to treat the problems involving impact and penetration very well. To overcome these deficiencies, two contact methods for MPM are presented and implemented in our 3D explicit MPM code, MPM3D. In MPM, the impenetrability condition may not satisfied on the redefined regular grid at the beginning of each time step, even if it has been imposed on the deformed grid at the end of last time step. The impenetrability condition between bodies is only imposed on the deformed grid in the first contact method, while it is imposed both on the deformed grid and redefined regular grid in the second contact method. Furthermore, three methods are proposed for impact and penetration simulation to determine the surface normal vectors that satisfy the collinearity conditions at the contact surface. The contact algorithms are verified by modeling the collision of two elastic rings and sphere rolling problems, and then applied to the simulation of penetration of steel ball and perforation of thick plate with a particle failure model. In the simulation of elastic ring collision, the first contact algorithm introduces significant disturbance into the total energy, but the second contact algorithm can obtain the stable solution by using much larger time step. It seems that both contact algorithms give good results for other problems, such as the sphere rolling and the projectile penetration. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of roughness pitch of surfaces on their wettability

The surface roughness factors, such as the Wenzel roughness factor and so on, are very interrelated to each other. Therefore, it makes a precise discussion difficult on how the surface roughness affects the wettability. We already reported the effect of the surface roughness on the wettability at a constant Wenzel roughness factor using two kinds of models, the hemisphere close packing model and the hemiround rod close lining model. Nevertheless, the pitch is proportional to the height in these models. Therefore, we could not independently discuss the influence of roughness height and roughness pitch on the wettability. We developed our new models which can independently describe the influence of the surface roughness height and the roughness pitch on the wettability. We simulated loose packing sphere models by periodically placing small ball bearings and the loose lining round rod models by winding fine wires. The wettability was measured by the sessile drop method for the non-wetting system using paraffin coated samples and aqueous solutions. These results show that there is a critical pitch which determines the maximum contact angle in both systems. These results can be explained by the ratio of the solid/liquid/vapor and liquid/vapor line length at the three phase line.