An approach to combining 3D discrete and finite element methods based on penalty function method

An algorithm combining three-dimensional (3D) discrete and finite element methods is proposed. This new approach is conducted by decomposing the calculation domain into a finite element (FE) calculation domain and a discrete element (DE) calculation domain; the interaction between the two sub-domains is processed by using a penalty function method. Following the established model that combines spherical DEs and FEs, the corresponding numerical code is developed. The vibration process of two cantilever beams under dynamic force is simulated. By comparing the results calculated with different penalty factors set and also with that calculated by the finite element code LS-DYNA, it is found that the calculated results are unanimous and the precision is almost the same as LS-DYNA, as long as the penalty factor is large enough. Moreover, the vibration processes of two plates under impact of rigid spheres are simulated and the accuracy of the model proposed in this paper is further proved in the field of contact mechanics by comparing the simulating results with that calculated by using LS-DYNA. Finally, the impact fracture behavior of a laminated glass plate is simulated, with the influence of model parameters taken into consideration. And the numerical experiments show that the combined model can be used to predict some macroscopical physical quantities, such as the impact force of impactor.     

Adaptive combined DE/FE algorithm for brittle fracture of plane stress problems

A novel adaptive combined DE/FE algorithm is proposed to simulate the fracture procedure of brittle materials of plane stress problems. The main concept of the approach is that a model is composed of the finite element completely at the initial stage without any discrete element generated until portion of the model grid becoming severely deformed; and then the model is fragmented into two subdomains, the finite element (FE) and the discrete element (DE) subdomains. The interface force between the two subdomains is calculated by using the penalty method. An extrinsic cohesive fracture model is employed to simulate the brittle fracture procedure only in the DE subdomain. The adaptive algorithm may allow for the use of the accurate and efficient FEs in the lower distorted region and the DEs which are automatically generated in the severely deformed FE region . The feasibility of the adaptive algorithm is validated by the impact fracture simulation of a glass beam. The comparison of calculation time consumption shows that the adaptive algorithm has a higher efficiency than the DEM. At last, the impact fracture behavior of a laminated glass beam is simulated, and the cracks propagation is compared with the experimental results showing that the adaptive algorithm can be implemented to capture some fracture characteristics of brittle materials.     

An accurate and robust contact detection algorithm for particle‐solid interaction in combined finite‐discrete element analysis

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.     

Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison

This study presents a methodology which integrates single-objective evolutionary algorithms (EAs) and finite element (FE) model updating for damage inference in three-dimensional (3D) structures. First, original well-known EAs, namely the genetic algorithm, differential evolution (DE) and particle swarm optimization (PSO), are combined with FE model updating for detecting damage in a 3D four-storey modular structure and their performances are compared. Next, to obtain more accurate results, hybrid Lévy flights–DE and hybrid artificial bee colony–PSO are developed for enhancing damage identification. With each method, the objective function composed of modal strain energy and mode shape residuals, taken from the FE model of the intact structure and the simulated damage responses, is initially created. Then, the performance of each algorithm combined with FE model updating for damage detection is assessed in terms of three characteristics: consistency, computational cost and accuracy, and the best performing algorithm is recommended.     

Isogeometric contact analysis using mortar method

In the present work, an isogeometric contact analysis scheme using mortar method is proposed. Because the isogeometric analysis is employed for contact analysis, the geometric exactness of the contact region is maintained without any loss of geometric data because of geometry approximation. Thus, the proposed method can overcome underlying shortcomings that result from the geometric approximation of contact surfaces in the conventional finite element (FE)‐based contact analysis. For an isogeometric contact analysis, the schemes for treating the contact conditions and detecting the real contact surfaces are essentially required. In the proposed method, the mortar method is adopted as a nonconforming contact treatment scheme because it is expected to be in good harmony with the useful characteristics of nonuniform rational B‐spline A new matching algorithm is proposed to combine the mortar method with the isogeometric analysis to guarantee consistent contact surface information with the nonuniform rational B‐spline curve. The present scheme is verified by patch test and the well‐known problems which have theoretical solutions such as interference fit and the Hertzian contact problem. It is shown that the problems with curved contact surfaces which are difficult to treat by conventional approaches can be easily dealt with. Copyright © 2011 John Wiley & Sons, Ltd.     

A contact algorithm for frictional crack propagation with the extended finite element method

We present an incremental quasi‐static contact algorithm for path‐dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non‐linear contact mechanics and embedded within a localized element by penalty method. Newton–Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ‘LATIN’ for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Improvement of a frictional contact algorithm for strongly curved contact problems

One of the challenges in contact problems is the prediction of the actual contact surface and the kind of contact that is established in each region. In numerical simulation of deep drawing problems the contact conditions change continuously during the forming process, increasing the importance of a correct evaluation of these parameters at each load step. In this work a new contact search algorithm devoted to contact between a deformable and a rigid body is presented. The rigid body is modelled by parametric Bézier surfaces, whereas the deformable body is discretized with finite elements. The numerical schemes followed rely on a frictional contact algorithm that operates directly on the parametric Bézier surfaces. The algorithm is implemented in the deep drawing implicit finite element code DD3IMP. This code uses a mechanical model that takes into account the large elastoplastic strains and rotations. The Coulomb classical law models the frictional contact problem, which is treated with an augmented Lagrangian approach. A fully implicit algorithm of Newton–Raphson type is used to solve within a single iterative loop the non‐linearities related with the frictional contact problem and the elastoplastic behaviour of the deformable body. The numerical simulations presented demonstrate the performance of the contact search algorithm in an example with complex tools geometry. Copyright © 2003 John Wiley & Sons, Ltd.     

Damage detection with genetic algorithms taking into account a crack contact model

This paper deals with the crack detection in structural elements by means of a genetic algorithm optimization method. The crack model takes into account the existence of contact between the interfaces of the crack. Many of the methods to detect a crack in beam-like structures are based on linear one dimensional models and are not straightforwardly applicable to structures such as beams or arcs with a breathing crack with or without contact. The present study addresses bi- and three-dimensional models to handle the dynamics of a structural element with a transverse breathing crack. The methodology is not restricted to beam-like structures since it can be applied to any arbitrary shaped 3D element. The crack is simulated as a notch or a wedge with a unilateral Signorini contact model. The contact can be partial or total. All the simulations are carried out using the general purpose partial differential solver FlexPDE, a finite element (FE) code. A genetic algorithm (GA) optimization method is successfully employed for the crack detection. The dynamic response at some points of the damaged structures are compared with the solution of the computational (FE) model using least squares for each proposed crack depth and location. An objective function arises which is then optimized to obtain an estimate of both parameters. Physical experiments were performed with a cantilever damaged beam and the resulting data used as input in the detection algorithm.     

Motorcyclist helmet composite outer shell characterisation and modelling

In this study a new finite element model of composite outer shell of motorcyclist helmet is proposed, by modelling each layer of the composite material that builds the laminated structure of the outer shell of the helmet. Elastic and rupture properties of the laminate are taken into account for developing the finite element (FE) model and are extracted experimentally. A coupled experimental–numerical method combined with experimental modal analysis on beam samples is used to obtain the elastic characteristics of each layer of the outer shell. The rupture properties for each layer are extracted by experimental impact tests. The FE model of the outer shell is then validated with experimental data for elastic and rupture behaviour.     

Simple Common Plane contact algorithm

The common‐plane (CP) algorithm is widely used in the discrete element method to model contact forces between interacting particles or blocks of rock. A new simple contact algorithm, similar to the CP algorithm, is proposed to model discontinuities such as joints, faults and material interfaces in an explicit finite difference code. The CP is defined as a plane separating interacting faces of grid cells, instead of blocks or particles used in the original CP method. The new method does not require iterations even for very stiff contacts. It is very robust and easy to implement, both in 2D and 3D parallel codes. Copyright © 2011 John Wiley & Sons, Ltd.     

Simulation of Impact Fracture Behavior of Laminated Glass Based on DEM/FEM and Cohesive Model

Strength of Materials - A computational method in the impact fracture behavior simulation for laminated safety glass is presented using the discrete element (DE)/finite element (FE) surface-center...     

A mixed finite element model for the elastic contact problem

The static elastic contact problem is approached using Lagrange multipliers, leading to a mixed finite element problem. A non-linear friction law is introduced explicitly and the non-local character of the friction phenomena is implicitly assumed. In order to avoid stress oscillations near singular points, a perturbed Lagrangian functional is considered. The algorithms herein proposed do not impose nodal dependencies over the contact surfaces, allowing for the independent discretization of both bodies. The method is able to model simultaneous contact over different regions of any geometrical shape. Computer code, examples and results presented here are restricted to axisymmetrical and bidimensional cases.     

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.     

Fracture and fragmentation of thin shells using the combined finite–discrete element method

A model for fracture and fragmentation of multilayered thin shells has been developed and implemented into the combined finite–discrete element code. The proposed model incorporates an extension of the original combined single and smeared fracture approach to multilayered thin shells; it then combines these with an interaction algorithm that is based on the original distributed potential contact force approach. The developed contact kinematics preserves both energy and momentum balance, whereas the developed fracture model is capable of modelling complex fracture patterns such as fracture of laminated glass under impact. Copyright © 2013 John Wiley & Sons, Ltd.     

Receding contact problem involving large displacements using the BEM

A new algorithm is presented for the boundary element analysis of the two-dimensional contact problem between elastic solids involving large displacements. The contact constraints are not applied node-on-node but node-on-element, using the element shape functions to distribute the geometry, displacements and tractions on each element in the contact zone. Thus, the discretizations performed along the two surfaces in contact need not necessarily be the same. The solution procedure is based on the updated Lagrangian approach and the resulting method is incremental. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacements without it being necessary to change the initial discretization of the boundary of the bodies. Only the frictionless static problem is dealt with, and the proposed algorithm is applied to the most representative receding contact problem: a layer pressed against an elastic foundation. The results obtained when the displacements are small are in good agreement with the analytical solution. When large displacements are considered, another nonlinearity appears and its influence will be shown in this paper.     

On propagation of short rolling contact fatigue cracks

Recent accidents involving railway rails have aroused demand for improved and more efficient rail maintenance strategies to reduce the risk of unexpected rail fracture. Numerical tools can aid in generating maintenance strategies: this investigation deals with the numerical modelling and analysis of short crack growth in rails. Factors that influence the fatigue propagation of short surface‐breaking cracks (head checks) in rails are assessed. A proposed numerical procedure incorporates finite element (FE) calculations to predict short crack growth conditions for rolling contact fatigue (RCF) loading. A parameterised FE model for the rolling‐sliding contact of a cylinder on a semi‐infinite half space, with a short surface breaking crack, presented here, is used in linear‐elastic and elastic–plastic FE calculations of short crack propagation, together with fracture mechanics theory. The crack length and orientation, crack face friction, and coefficient of surface friction near the contact load are varied. The FE model is verified for five examples in the literature. Comparison of results from linear‐elastic and elastic–plastic FE calculations, shows that the former cannot describe short RCF crack behaviour properly, in particular 0.1–0.2 mm long (head check) cracks with a shallow angle; elastic–plastic analysis is required instead.     

Combined interior‐point method and semismooth Newton method for frictionless contact problems

In the present paper, a solution scheme is proposed for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method with lower order elements. An approach combining the interior‐point method and the semismooth Newton method is proposed. In this method, an initial active set for the semismooth Newton method is obtained from the approximate optimal solution by the interior‐point method. The simplest node‐to‐node contact model is considered in the present paper, that is, pairs of matching nodes exist on the contact surfaces. However, the discussions can be easily extended to a node‐to‐segment or segment‐to‐segment contact model. In order to evaluate the proposed method, a number of illustrative examples of the frictionless contact problem are shown. The proposed combined method is compared with the interior‐point method and the semismooth Newton method. Two numerical examples that are difficult to solve using the semismooth Newton method are solved effectively using the proposed combined method. It is shown that the proposed method converges within far fewer iterations than the semismooth Newton methods or the interior‐point method. Copyright © 2009 John Wiley & Sons, Ltd.     

Automation of finite element formulations for large deformation contact problems

The aim of this paper is to present a general method for automation of finite element formulations of large deformation contact problems. A new automatic‐differentiation‐based notation is introduced that represents a bridge between the classical mathematical notation of contact mechanics and the actual computer implementation of contact finite elements. Automation of derivation of the required formulas (e.g. element residual and tangent matrix) combined with automatic code generation makes the finite element implementation possible at a moderate effort. Accordingly, several 3D contact formulations have been implemented in this work, including penalty and augmented Lagrangian treatments of contact constraints, and several contact smoothing techniques. A typical benchmark problem could thus be executed in an objective way leading to a comprehensive study of the efficiency and the accuracy of various formulations of 3D contact finite elements. Copyright © 2010 John Wiley & Sons, Ltd.     

二维自由振动问题的自适应有限元分析初探

自由振动反映结构动力特性,是抗震分析和结构设计的重要基础。近年来,基于单元能量投影（EEP）法的自适应有限元分析已在一系列线弹性及非线性问题中取得成功,而有限元线法（FEMOL）自适应分析在二维自由振动问题中的应用也被证实是有效的。在此基础上,该文进一步提出二维自由振动问题的自适应有限元分析方法。通过将特征值问题线性化,合理引入二维线性问题的EEP超收敛计算和自适应求解技术,该法可得到满足精度要求的自振频率和按最大模度量满足用户给定误差限的振型。该文以弹性薄膜为例,介绍了这一进展,并给出数值算例以表明该方法的有效性和可靠性。     

A novel discrete element method based on the distance potential for arbitrary 2D convex elements

A new 2‐dimensional discrete element method, which is able to simulate a system involving a large number of arbitrary convex elements, is proposed. In this approach, a novel distance potential function is defined using a normalized format of the penetrated distance between contact couples, while a holonomic and precise algorithm for contact interaction is established, accounting for the influence of the tangential contact force. Furthermore, the new contact detection algorithm is well suited for nonuniform blocks unlike the common no binary search method that requires uniform elements. The proposed method retains the merit of the combined finite‐discrete element method and avoids its deficiencies. Compared with the existing finite‐discrete element method, the distance potential function has a clear physical meaning, where the calculation of contact interaction avoids the influence of the element shape. Accordingly, the new method completely gets rid of the restraint of uniform element type and can be applied to arbitrary convex elements. The new method is validated with well‐known benchmark examples, and the results are in very good agreement with existing experimental measurement and analytical solutions. Finally, the proposed method is applied to simulate the Tangjiashan landslide.