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.     

Penalty function method for combined finite–discrete element systems comprising large number of separate bodies

Large‐scale discrete element simulations, the combined finite–discrete element method, DDA as well as a whole range of related methods, involve contact of a large number of separate bodies. In the context of the combined finite–discrete element method, each of these bodies is represented by a single discrete element which is then discretized into finite elements. The combined finite–discrete element method thus also involves algorithms dealing with fracture and fragmentation of individual discrete elements which result in ever changing topology and size of the problem. All these require complex algorithmic procedures and significant computational resources, especially in terms of CPU time. In this context, it is also necessary to have an efficient and robust algorithm for handling mechanical contact. In this work, a contact algorithm based on the penalty function method and incorporating contact kinematics preserving energy balance, is proposed and implemented into the combined finite element code. Copyright © 2000 John Wiley & Sons, Ltd.     

A combined finite‐discrete element method for simulating pharmaceutical powder tableting

The pharmaceutical powder and tableting process is simulated using a combined finite‐discrete element method and contact dynamics for irregular‐shaped particles. The particle‐scale formulation and two‐stage contact detection algorithm which has been developed for the proposed method enhances the overall calculation efficiency for particle interaction characteristics. The irregular particle shapes and random sizes are represented as a pseudo‐particle assembly having a scaled up geometry but based on the variations of real powder particles. Our simulations show that particle size, shapes and material properties have a significant influence on the behaviour of compaction and deformation. Copyright © 2005 John Wiley & Sons, Ltd.     

Combined single and smeared crack model in combined finite‐discrete element analysis

Large‐scale discrete element simulations, combined finite‐discrete element simulations as well as a whole range of related problems, involve a large number of separate bodies that interact with each other and in general deform and fracture. In this context there is a need for a robust fracture algorithm applicable to simultaneous multiple fracturing of large numbers of bodies. In this work a fracture model for both initiation and propagation of mode I loaded cracks in concrete in the context of the combined finite‐discrete element method is reported. The algorithm is based on accurate approximation of experimental stress–strain curves for concrete in tension. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

3D dynamics of discrete element systems comprising irregular discrete elements—integration solution for finite rotations in 3D

An algorithm for transient dynamics of discrete element systems comprising a large number of irregular discrete elements in 3D is presented. The algorithm is a natural extension of contact detection, contact interaction and transient dynamics algorithms developed in recent years in the context of discrete element methods and also the combined finite‐discrete element method. It complements the existing algorithmic procedures enabling transient motion including finite rotations of irregular discrete elements in 3D space to be accurately integrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Finite strain,finite rotation quadratic tetrahedral element for the combined finite–discrete element method

In the past, the combined finite–discrete element was mostly based on linear tetrahedral finite elements. Locking problems associated with this element can seriously degrade the accuracy of their simulations. In this work an efficient ten‐noded quadratic element is developed in a format suitable for the combined finite–discrete element method (FEMDEM). The so‐called F‐bar approach is used to relax volumetric locking and an explicit finite element analysis is employed. A thorough validation of the numerical method is presented including five static and four dynamic examples with different loading, boundary conditions, and materials. The advantages of the new higher‐order tetrahedral element are illustrated when brought together with contact detection and contact interaction capability within a new fully 3D FEMDEM formulation. An application comparing stresses generated within two drop experiments involving different unit specimens called Vcross and VRcross is shown. The Vcross and VRcross units of ～3.5 × 10⁴kg show very different stress generation implying different survivability upon collision with a deformable floor. The test case shows the FEMDEM method has the capability to tackle the dynamics of complex‐shaped geometries and massive multi‐body granular systems typical of concrete armour and rock armour layers. Copyright © 2009 John Wiley & Sons, Ltd.     

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

For many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.     

A mixed‐enhanced finite‐element for the analysis of laminated composite plates

This paper presents a new 4‐node finite‐element for the analysis of laminated composite plates. The element is based on a first‐order shear deformation theory and is obtained through a mixed‐enhanced approach. In fact, the adopted variational formulation includes as variables the transverse shear as well as enhanced incompatible modes introduced to improve the in‐plane deformation. The problem is then discretized using bubble functions for the rotational degrees of freedom and functions linking the transverse displacement to the rotations. The proposed element is locking free, it does not have zero energy modes and provides accurate in‐plane/out‐of‐plane deformations. Furthermore, a procedure for the computation of the through‐the‐thickness shear stresses is discussed, together with an iterative algorithm for the evaluation of the shear correction factors. Several applications are investigated to assess the features and the performances of the proposed element. Results are compared with analytical solutions and with other finite‐element solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

Large‐scale parallel finite‐element analysis using the internet: a performance study

This paper describes a parallel finite‐element system implemented using the domain decomposition method on a cluster of remote computers connected via the Internet. This technique is also readily applicable to a grid computing environment. A three‐dimensional finite‐element elastic analysis involving more than one million degrees of freedom was solved using this system, and a good approximate solution was obtained with high parallel efficiency of over 90% using remote computers located in three different countries. Copyright © 2005 John Wiley & Sons, Ltd.     

Unstructured,curved elements for the two‐dimensional high order discontinuous control‐volume/finite‐element method

Quadrilateral and triangular elements with curved edges are developed in the framework of spectral, discontinuous, hybrid control‐volume/finite‐element method for elliptic problems. In order to accommodate hybrid meshes, encompassing both triangular and quadrilateral elements, one single mapping is used. The scheme is applied to two‐dimensional problems with discontinuous, anisotropic diffusion coefficients, and the exponential convergence of the method is verified in the presence of curved geometries. Copyright © 2014 John Wiley & Sons, Ltd.     

Three‐dimensional finite‐element simulation of the dynamic Brazilian tests on concrete cylinders

We investigate the feasibility of using cohesive theories of fracture, in conjunction with the direct simulation of fracture and fragmentation, in order to describe processes of tensile damage and compressive crushing in concrete specimens subjected to dynamic loading. We account explicitly for microcracking, the development of macroscopic cracks and inertia, and the effective dynamic behaviour of the material is predicted as an outcome of the calculations. The cohesive properties of the material are assumed to be rate‐independent and are therefore determined by static properties such as the static tensile strength. The ability of model to predict the dynamic behaviour of concrete may be traced to the fact that cohesive theories endow the material with an intrinsic time scale. The particular configuration contemplated in this study is the Brazilian cylinder test performed in a Hopkinson bar. Our simulations capture closely the experimentally observed rate sensitivity of the dynamic strength of concrete in the form of a nearly linear increase in dynamic strength with strain rate. More generally, our simulations give accurate transmitted loads over a range of strain rates, which attests to the fidelity of the model where rate effects are concerned. The model also predicts key features of the fracture pattern such as the primary lens‐shaped cracks parallel to the load plane, as well as the secondary profuse cracking near the supports. The primary cracks are predicted to be nucleated at the centre of the circular bases of the cylinder and to subsequently propagate towards the interior, in accordance with experimental observations. The primary and secondary cracks are responsible for two peaks in the load history, also in keeping with experiment. The results of the simulations also exhibit a size effect. These results validate the theory as it bears on mixed‐mode fracture and fragmentation processes in concrete over a range of strain rates. Copyright © 2000 John Wiley & Sons, Ltd.     

A novel 3D mixed finite‐element model for statics of angle‐ply laminates

Analysis of angle‐ply laminates becomes critical and computationally involved because of the presence of extension–shear coupling. A refined three‐dimensional, mixed, 18‐node finite element (FE) model has been developed to analyse angle‐ply laminates under static loading. The minimum potential energy principle has been used for the development of the mixed FE model, where the transverse stress components (τ_xz, τ_yz and σ_z, where z is the thickness direction) have been incorporated as the nodal degrees of freedom, in addition to the three displacement fields. Further, continuity of transverse stress fields through the thickness of the plate and layerwise continuity of displacement fields have been enforced in the formulation. Because all the constitutive and the compatibility conditions have been ensured within the continuum, the present formulation is unique amongst the family of mixed FE models. Results have been obtained for various angle‐ply laminates and compared with analytical and finite‐element solutions, which have been found to be in good agreement with them. Some new results on angle‐ply with clamped–clamped support condition have also been presented to serve as benchmark results. Copyright © 2003 John Wiley & Sons, Ltd.     

A two‐grid method for expanded mixed finite‐element solution of semilinear reaction–diffusion equations

We present a scheme for solving two‐dimensional semilinear reaction–diffusion equations using an expanded mixed finite element method. To linearize the mixed‐method equations, we use a two‐grid algorithm based on the Newton iteration method. The solution of a non‐linear system on the fine space is reduced to the solution of two small (one linear and one non‐linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h^1/3). As a result, solving such a large class of non‐linear equation will not be much more difficult than solving one single linearized equation. Copyright © 2003 John Wiley & Sons, Ltd.     

Parametric code for generation of finite‐element model of nonwovens accounting for orientation distribution of fibres

A novel finite‐element modelling code developed to investigate the structural behaviour of nonwoven materials is presented. The technique allows modelling of a nonwoven fabric as a continuous–discontinuous medium with a given pattern of bond points and a large number of constituent fibres with arbitrary orientation distribution. The parametric feature of the code provides automatic modelling of nonwoven materials according to design parameters in a very efficient way. The effect of fibre length is also included for the first time in a finite element model of a nonwoven. The developed code is very flexible and it is possible to be extended to further studies such as damage behaviour.Copyright © 2013 John Wiley & Sons, Ltd.     

Geometric interpretation of finite‐dimensional eddy‐current formulations

This paper gives an explicit geometric interpretation of finite element formulations of the eddy‐current problem. The paper shows, step‐by‐step how the eddy‐current problem can be implemented in a finite element kind of software system exploiting familiar geometric ideas such as lengths of edges, areas of faces, volumes of tetrahedra, and the mutual interconnections between the simplices of a mesh. The approach is a specific case of the so‐called geometric techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

The maximum principle violations of the mixed‐hybrid finite‐element method applied to diffusion equations

The abundant literature of finite‐element methods applied to linear parabolic problems, generally, produces numerical procedures with satisfactory properties. However, some initial–boundary value problems may cause large gradients at some points and consequently jumps in the solution that usually needs a certain period of time to become more and more smooth. This intuitive fact of the diffusion process necessitates, when applying numerical methods, varying the mesh size (in time and space) according to the smoothness of the solution. In this work, the numerical behaviour of the time‐dependent solutions for such problems during small time duration obtained by using a non‐conforming mixed‐hybrid finite‐element method (MHFEM) is investigated. Numerical comparisons with the standard Galerkin finite element (FE) as well as the finite‐difference (FD) methods are checked. Owing to the fact that the mixed methods violate the discrete maximum principle, some numerical experiments showed that the MHFEM leads sometimes to non‐physical peaks in the solution. A diffusivity criterion relating the mesh steps for an artificial initial–boundary value problem will be presented. One of the propositions given to avoid any non‐physical oscillations is to use the mass‐lumping techniques. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical simulation study of shale gas reservoir with stress-dependent fracture conductivity using multiscale discrete fracture network model

The exploitation of shale gas has increasingly become the focus of worldwide energy industry. Due to the existence of natural/hydraulic fractures, most of the shale gas reservoirs exhibit high degree of heterogeneity and complexity which leads to the stress-dependent fracture conductivity of shale gas reservoir. Discrete fracture network (DFN) model is adopted in this research since the conventional continuum model cannot meet the numerical simulation requirements of fractured shale gas reservoir. A series of experiments about the fracture properties stress-dependent have been conducted on some shale core samples, the stress-dependent fracture conductivity correlation is selected and incorporated into the mathematical model to characterize the reduction of fracture conductivity potential with the reservoir pressure drop. The DFN model is applied to a shale gas reservoir with fracture network to study the effect of the stress-dependent fracture conductivity on the shale gas well performance. The results show that the effect of fracture conductivity reduction with pressure drop on the shale gas well performance depends on both the initial fracture conductivity and matrix permeability. The complex interactions between the fracture and matrix permeability should be considered when select the appropriate size of proppants for fracturing.