Elastic property prediction by finite element analysis with random distribution of materials for heterogeneous solids

In the present paper, finite element method is employed to predict the effective material properties of heterogeneous materials via random distributions of the constituent materials. With the random distributing strategy, massive parametric analysis via finite element becomes feasible for multi-phase heterogeneous solids. Using a two-phase bi-continuous material as an example, the effects of the specimen size with respect to the characteristic size of the micro-structural size and the element density on the predicted effective properties are considered. The numerical predictions of the effective properties are checked by two analytical bounds which were proposed by Hashin and Shtrikemn (1963) through the principle of variation and the matrix-fiber model. Some discussions on the finite element prediction are also made to clarify the status of the present work in the composite mechanics research.     

Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis

A two-dimensional numerical model of microstructural effects is presented, with an aim to understand the mechanical performance in polycrystalline materials. The microstructural calculations are firstly carried out on a square lattice by means of a 2-D Monte Carlo (MC) simulation for grain growth, then the conventional finite element method is applied to perform stress analysis of a plane strain problem. The mean grain size and the average stress are calculated during the MC evolution. The simulation result shows that the mean grain size increases with the simulation time, which is about 3.2 at 100 Monte Carlo step (MCS), and about 13.5 at 5000 MCS. The stress distributions are heterogeneous in materials because of the existence of grains. The mechanical property of grain boundary significantly affects the average stress. As the grains grow, the average stress without grain boundary effect slightly decreases as the simulation time, while the one with strengthening effect significantly decreases, and the one with weakening effect increases. The average stress and the grain size agree well with the Hall–Petch relationship.     

磁悬挂天平偏航电磁场的二维有限元分析

在磁悬挂天平偏航控制中，偏航线圈中的电流变化对模型姿态变化影响十分显著．为了提高天平的偏航控制精度，有必要对天平偏航电磁场进行更为精确的分析．该文采用有限单元法对磁悬挂天平偏航电磁场进行了分析，得到了比传统计算方法更为准确的结果，并在实验中进行了验证，从而为磁悬挂天平的偏航控制提供了参考．     

From the individual element test to finite element templates: Evolution of the patch test

This paper starts a sequence of three articles that follow an unconventional approach in finite element research. The ultimate objective is to construct high-performance elements and element-level error estimators for those elements. The approach takes off from our previous work in high-performance elements and culminates with the development of finite element templates. The present paper concentrates on the patch test and evolved versions of the test that have played a key role in this research. Following a brief review of the historical roots, we present the Individual Element Test (IET) of Bergan and Hanssen in an expanded context that encompasses several important classes of new elements. The relationship of the IET to the multielement forms A, B and C of the patch test and to the single-element test are investigated. An important consequence of the IET application is that the element stiffness equations decompose naturally into basic and higher-order parts. The application of this decomposition to the “sanitization” of the non-convergent BCIZ element is described and verified with numerical experiments. Two sequel papers in preparation are subtitled ‘the algebraic approach’ and ‘element-level error estimation’. These apply the fundamental decomposition to the derivation of templates for specific mechanical elements and to the construction of element-level error estimators, respectively.     

Wrinkling of sandwich column: comparison between finite element analysis and analytical solutions

Wrinkling analysis of sandwich columns was carried out. Two methods were used, namely finite element methods and analytical solutions. In the finite element methods, shell elements based on Reissner–Mindlin were employed across the beam thickness. A very fine element was used to model both the skin and the core across the beam thickness. The buckling mode was increased up to 100 in order to be able to model the wrinkling mode. The analytical solutions used energy methods and Raleigh–Ritz solutions developed earlier by the author. Finally, comparisons were made with experimental data taken from published results. Good agreements were achieved between the experimental results and both the finite element and analytical solution. The difference was less than 10%. Both finite element and analytical solutions were able to predict both symmetrical and asymmetrical wrinkling.     

An adaptive remeshing procedure for discontinuous finite element limit analysis

An adaptive remeshing procedure is proposed for discontinuous finite element limit analysis. The procedure proceeds by iteratively adjusting the element sizes in the mesh to distribute local errors uniformly over the domain. To facilitate the redefinition of element sizes in the new mesh, the interelements discontinuous field of elemental bound gaps is converted into a continuous field, ie, the intensity of bound gap, using a patch‐based approximation technique. An analogous technique is subsequently used for the approximation of element sizes in the old mesh. With these information, an optimized distribution of element sizes in the new mesh is defined and then scaled to match the total number of elements specified for each iteration in the adaptive remeshing process. Finally, a new mesh is generated using the advancing front technique. This adaptive remeshing procedure is repeated several times until an optimal mesh is found. Additionally, for problems involving discontinuous boundary loads, a novel algorithm for the generation of fan‐type meshes around singular points is proposed explicitly and incorporated into the main adaptive remeshing procedure. To demonstrate the feasibility of our proposed method, some classical examples extracted from the existing literary works are studied in detail.     

Multiscale analysis of stiffness and fracture of nanoparticle-reinforced composites using micromechanics and global–local finite element models

A combined micromechanics analysis and global–local finite element method is proposed to study the interaction of particles and matrix at the nano-scale near a crack tip. An analytical model is used to obtain the effective elastic modulus of nanoparticle-reinforced composites, then a global–local multi-scale finite element model with effective homogeneous material properties is used to study the fracture of a compact tension sample. For SiO₂ particle-reinforced epoxy composites with various volume fractions, the simulation results for effective elastic modulus, fracture toughness, and critical strain energy release rate show good agreement with previously published experimental data. It is demonstrated that the proposed parametric multi-scale model can be used to efficiently study the toughness mechanisms at both the macro and nano-scale.     

Micromechanical formulation and 3D finite element modeling of microinstabilities in composites

A 3D micromechanical formulation and a FE-model of fiber micro-buckling in materials with isotropic and transversal isotropic fibers in compression is presented. Three variants of geometrical modeling of the characteristic cell are proposed and compared. An appropriate one is then selected. An eigenvalue analysis of a characteristic cell is performed. The results show that the fiber anisotropy reduces significantly the critical loads and must be taken into account.     

Rapid implementation of material models within finite element analysis

This paper presents a simple procedure for obtaining a numerical approximation to the consistent tangent matrix, together with a straightforward implicit (Euler backward) integration algorithm. The combined algorithm is used to incorporate four models into the commercial finite element package ABAQUS/Standard; illustrating how it can be used to rapidly implement material models within finite element analysis. The models have been chosen, not only because they help to illuminate the structure of the algorithm, but also because they illustrate its wide ranging applicability and permit the procedure to be tested against analytical results and an existing, well established, model.     

Mechanical analysis of 3D braided composites: a finite element model

The analysis of 3D braided composites is more difficult due to its complex microstructure. A new type of finite element method is developed to predict the effective moduli and the local stress within 3D braided composites under the 3D mechanical loading. To verify the present method, the material properties of undamaged 3D braided composites predicted in this paper are compared with the previous work. To demonstrate this method, some examples are analyzed.     

Finite element simulation of low-density thermally bonded nonwoven materials: Effects of orientation distribution function and arrangement of bond points

A random and discontinuous microstructure is one of the most characteristic features of a low-density thermally bonded nonwoven material, and it affects their mechanical properties significantly. To understand their effect of microstructure on the overall mechanical properties of the nonwoven material, discontinuous models are developed incorporating random discontinuous structures representing microstructures of a real nonwoven material. Experimentally measured elastic material properties of polypropylene fibres are introduced into the models to simulate the tensile behaviour of the material for its both principle directions: machine direction and cross direction. Additionally, varying arrangements of bond points and schemes of fibres’ orientation distribution are implemented in the models to analyse the respective effects.     

Three-dimensional finite element analysis of finite deformation micromorphic linear isotropic elasticity

A finite deformation micromorphic materially linear isotropic elastic model is formulated and implemented for three dimensional finite element analysis. The model is based on the kinematics, balance equations and thermodynamic equations proposed by Eringen and Suhubi (1964). The constitutive equations are calculated in the reference configuration, and the resulting stresses are mapped to the current configuration. The balance of linear momentum and the balance of first moment of momentum are linearized to construct the consistent tangent for three dimensional finite element implementation for solution by the Newton–Raphson method. Three dimensional numerical examples are analyzed to demonstrate preliminarily the implementation.     

Discrete cohesive zone model for mixed-mode fracture using finite element analysis

The discrete cohesive zone model (DCZM) is implemented using the finite element (FE) method to simulate fracture initiation and subsequent growth when material non-linear effects are significant. Different from the widely used continuum cohesive zone model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses rod type elements and applies the cohesive law as the rod internal force vs. nodal separation (or rod elongation). These rod elements have the provision of being represented as spring type elements and this is what is considered in the present paper. A series of 1D interface elements was placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes were introduced within the interface element to extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations were examined. For pure mode I, the double cantilever beam configuration, using both uniform and biased meshes were analyzed and the results show that the DCZM is not sensitive to the mesh size. Results also show that DCZM is not sensitive to the loading increment, either. Next, the end notched flexure for pure mode II and, the mixed-mode bending were studied to further investigate the approach. No convergence difficulty was encountered during the crack growth analyses. Therefore, the proposed DCZM approach is a simple but promising tool in analyzing very general two-dimensional crack growth problems. This approach has been implemented in the commercial FEA software ABAQUS^® using a user defined subroutine and should be very useful in performing structural integrity analysis of cracked structures by engineers using ABAQUS^®.     

A priori error estimation of finite element models from first principles

The quality of finite element computational results can be assessed only by providing rational criteria for evaluating errors. Most exercises in this direction are based ona posteriori error estimates, based primarily on experience and intuition. If finite element analysis has to be considered a rational science, it is imperative that procedures to computea priori error estimates from first principles are made available. This paper captures some efforts in this direction.     

Two-dimensional and axisymmetric unit cell models in the analysis of composite materials

Unit cell models have been widely used for investigating fracture mechanisms and mechanical properties of composite materials assuming periodically arrangement of inclusions in matrix. It is desirable to clarify the geometrical parameters controlling the mechanical properties of composites because they usually contain randomly distributed particulate. To begin with a tractable problem this paper focuses on the effective Young’s modulus E of heterogeneous materials. Then, the effect of shape and arrangement of inclusions on E is considered by the application of FEM through examining three types of unit cell models assuming 2D and 3D arrays of inclusions. It is found that the projected area fraction and volume fraction of inclusions are two major parameters controlling effective elastic modulus of inclusions.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Parametric study of stress state development during twinning using 3D finite element modeling

A deformation twinning model which simulates the characteristic twin shear and corresponding grain reorientation has been developed using a 3D finite element method. This model has been used to study how twinning affects the stress state in both the parent grain and twin, and the stress states that are energetically favorable for twinning. The component of shear stress on the twin plane and direction is primarily responsible not only for whether twinning can occur, but also the energetically favorable twin volume fraction. A map predicting twin volume fraction as a function of parent grain deviatoric stress has been developed.     

Failure analysis and finite element simulation of key components of PDM

As one of the most commonly used downhole drilling tools, PDM (Positive Displacement Motor) is widely used in drilling and workover. Drilling practice shows that PDM is frequently scraped for the failure of key components. The coupled thermo-mechanical finite element model of rubber linings, finite element models of thrust bearing and universal shaft petals were established respectively, and the failure reasons were discussed by simulation. It was found that there are oval holes caused by thermal failure in general rubber lining, while no oval holes in the uniform wall thickness rubber lining. Rubber layer peeling and broken appear on the surfaces of rubber linings under the load of drilling fluid and rotor. Thrust bearings experienced serious wear, corrosion and rupture in the terrible downhole environment. The universal shaft petals appear fracture in the root, and wear on contact surfaces under torque and axial load. The results obtained in the paper show that the analyzing model and evaluation methods are quite reasonable and can be generally applied, which have great significance on the enhancement of structural design and repair for PDM in the future industry.     

Cone bit bearing seal failure analysis based on the finite element analysis

Failure analysis of cone bit bearing seals is important in reducing production cost and preventing in-service component failure. However, a generally accepted criterion for their failure has not yet been established because of complexities in both their material properties and the environment. In this study, a two-dimensional axisymmetric finite element analysis (FEA) numerical model was established. FEA software was developed based on the Mooney–Rivlin constitutive model of the rubber material, and the penalty function contact algorithm. The distributions of stress, strain and contact pressure were analyzed to establish their effect on failure. The locations and causes of the failure and preventive measures were determined by comparison with an actual failure case. It was found that stress concentration and uneven pressure distribution occur at the seal. Rubber rings are highly and unequally compressed. Metal ring structure mainly determines sealing performance. To reduce the occurrence of failure, the structure must be improved by: designing an appropriate angle-tapered metal ring end face structure instead of a plane to change the trend in pressure distribution, increasing the contact area of the metal ring end face to reduce contact pressure and make the contact pressure distribution more uniform to reduce sealing surface wear, reducing the radial thickness to reduce the compression of the rubber ring, and improving back support structures to reduce the stress concentration. Results from the study can prevent and minimize risk for future failures to increase bit life and reduce drilling costs.     

Expert systems and finite element structural analysis — a review

Finite element analysis of many engineering systems is practised more as an art than as a science. It involves high level expertise (analytical as well as heuristic) regarding problem modelling (e.g. problem specification, choosing the appropriate type of elements etc.), optical mesh design for achieving the specified accuracy (e.g. initial mesh selection, adaptive mesh refinement), selection of the appropriate type of analysis and solution routines and, finally, diagnosis of the finite element solutions. Very often such expertise is highly dispersed and is not available at a single place with a single expert. The design of an expert system, such that the necessary expertise is available to a novice to perform the same job even in the absence of trained experts, becomes an attractive proposition. In this paper, the areas of finite element structural analysis which require experience and decision-making capabilities are explored. A simple expert system, with a feasible knowledge base for problem modelling, optimal mesh design, type of analysis and solution routines, and diagnosis, is outlined. Several efforts in these directions, reported in the open literature, are also reviewed in this paper.