Interface Element Method Research Articles

A robust interface finite element formulation for modeling brittle material failure problems

AbstractFailure of many brittle materials and structures can be modeled using interface‐oriented finite elements combined with intrinsic cohesive zone models. The discontinuous Galerkin (DG) finite element method provides an innovative framework for modeling brittle crack propagation with zero‐thickness interface elements, which can accommodate extrinsic cohesive laws to avoid the artificial compliance required in intrinsic cohesive models. However, robust formulations and implementations of DG methods are critical in alleviating the well‐known convergence issues for both crack nucleation and propagation with reduced instability. This paper presents a robust interface element formulation by modifying the incomplete interior penalty Galerkin (IIPG) method, which successfully avoids the initial element interface penetration across elements that occurs prior to crack nucleation, and thereby greatly reduces the instability issue as cracks open. We further verified and validated our implementation by using a bar tension test and a beam fracturing benchmark. The robustness of our proposed interface element method was demonstrated by a micromechanics fiber/matrix debonding problem with 64 fibers embedded in a bulk matrix.

A fast local nonlinear solution technique based on the partitioned finite element and interface element method

AbstractIn this study, a fast partitioned solution method that considers contact nonlinearity and local material nonlinearity based on the partitioned finite element and interface element method is proposed. Combined with the local failure characteristics of hydraulic structures such as arch dams, the stiffness matrices of the linear and nonlinear regions of the structure are decomposed to reduce the size of the overall stiffness matrix. Furthermore, in the nonlinear iteration, only the stiffness matrix of the nonlinear partition is modified, thereby reducing the calculation amount of the overall solution and improving the solution efficiency. The results show that our proposed method exhibits improved solution speed and stability while achieving the same solution accuracy.

A DG-based interface element method for modeling hydraulic fracturing in porous media

Fracture propagation coupled with fluid flow in porous media has very important applications in fracking in oil and gas reservoirs, corrosion in ceramics, and degradation of human bones. Modeling fracture failure in porous media governed by the coupled solid and fluid field equations is challenging and time-consuming. This paper extends discontinuous Galerkin (DG) finite element methods to model crack openings in porous media through exploiting an easy construction of interfaces for potential crack paths by locally breaking continuous elements. Consequently, a finite element mesh for fracture apertures is completely and gracefully constructed using DG interface objects as well as the definitions of jumps of displacements across the DG interfaces defined for bulk matrices. Furthermore, rigid cohesive laws often adopted for crack openings can be naturally implemented in DG formulations without introducing artificial stiffness, which may eventually improve the performance for implicit formulations in handling crack openings in porous media. In this work, we perform a consistent, fully implicit, and fully coupled hybrid DG/continuous finite element formulation for three field equations including the solid, bulk fluid, and fluid in fracture apertures resulting from crack openings. We verify our DG formulation and implementation using the Khristianovich-Geertsma-DeKlerk analytical solutions. Finally, we further demonstrate a good performance of the proposed DG method by modeling fracking in an oil reservoir containing two nature fractures.

A review of mechanical properties and constitutive theory of rock mass anisotropy

Rock anisotropy is an intrinsic property of natural rock mass, and layered rock has the most significant effect on the stress distribution and deformation of a rock mass. With the development of rock mechanics theory and constitutive theory, the study of rock anisotropy has become one of the focuses and hotspots in the field of rock mechanics. Based on the rock isotropic self-consistent theory, the rock anisotropy theory of different media such as triclinic anisotropy, monoclinic anisotropy, and orthorhombic anisotropy has been greatly developed. Rock mechanical property test, not only limited to the traditional single-axis, triaxial compression test, Brazilian split test and pure bending beam tensile test, and meso-structural characteristic test (XRD, ultrasonic test, etc.), is also widely used. With the development of numerical analysis theory and computer technology, numerical analysis methods such as finite difference method, discrete element method, finite element method, boundary element method, and interface element method have played an important role in the study of rock anisotropy characteristics. According to the assumptions and reasoning methods of anisotropic failure criterion, it can be classified into two categories: continuous failure criterion and discontinuous piecewise failure criterion. Continuous medium failure criterion can also be classified into mathematical and empirical ones. Because of the complexity of rock anisotropy, the research on yield criterion and constitutive relation of rock anisotropy is still in the stage of theoretical research, and it is seldom applied in actual rock engineering. The physics model of rock has an important influence on the study of the anisotropic characteristics of rock. Therefore, the establishment of an appropriate rock physics model has a direct impact on the accurate determination of rock anisotropy parameters and P-S wave velocity. Finally, the key and difficult points of anisotropic rock research and the direction of future research are discussed and analyzed to provide a reference for engineering practice and related problems.

Dynamic investigation of aeroengine high pressure rotor system considering assembly characteristics of bolted joints

Bolted connection is the basic connection form of combined rotor system for aeroengine, and its connection performance directly determines the dynamic characteristics of the rotor system. However, there are few studies on the dynamic characteristics of the rotor considering joint interface assembly parameters. Thus, the mechanical model of the bolted joint is presented by characterizing the mechanical relationship between the adjacent nodes of the joint interface. Then, in term of the mechanics model of joint interface and finite element method, the rotor assembly dynamic model of drum-disk-shaft is established. The influence of rotational speed, unbalance and joint interface stiffness on the dynamic response of the rotor is analyzed. By establishing the finite element model (FEM) of the test-bed, the maximum error is 6.1% compared with the experimental mode, which verifies the rationality of the FEM considering connecting bolts pretightening. Finally, the FEM of the aeroengine high pressure rotor system is established to study the dynamic characteristics of the rotor system under different pre-tightening conditions, which provides a theoretical basis for detecting and identifying the performance of the bolt joint of the aeroengine rotor system.

On the crack opening and energy dissipation in a continuum based disconnected crack model

All crack models developed to date can be classified into discrete- and continuum-based approaches. While discrete models are advantageously capable of capturing the kinetics of fractures, continuum-based approaches still pique considerable interest due to their straightforward implementation within the finite element method (FEM) framework. The cracking element method (CEM), a recently developed numerical approach for simulating quasi-brittle fracturing, is based on the FEM and does not need remeshing, a nodal cover algorithm, nodal enrichment or a crack-tracking strategy. The CEM takes self-propagating disconnected cracking segments to represent crack paths and naturally captures crack initiation and propagation processes. However, as with other types of continuum-based approaches that employ discontinuous crack paths, one critical question remains: Can the crack openings can be reliably and accurately obtained? To answer this question, a detailed study on the released energy, kinetic model, and displacement between the upper and lower facets of a crack is required. Multiple tests are conducted in this paper, and the results of the CEM are compared with those of the interface element method (IEM), which explicitly describes the crack openings. For reference and comparison purposes, an a priori crack path obtained by using an equivalent crack path (cracked elements) previously obtained from the CEM is implemented for the IEM. The crack openings obtained by the CEM and IEM are subsequently compared, and the results indicate that the crack openings and dissipated energy obtained by the CEM generally agree well with those obtained by the IEM. These findings highlight the effectiveness of utilizing disconnected cracking segments and further demonstrate the robustness and reliability of the CEM.

Thermal Stress Analysis of Chip Scale Packaging by Using Novel Multiscale Interface Element Method

In this study, a multiscale interface element method (MIEM) is developed to evaluate the interfacial peel and shear stress distributions in multilayer packaging structures. A newly developed polygon interface element contained many sides that could easily connect with many other polygon elements of much smaller scale. Simple model and less computation can obtain accurate stress distributions. After verification of the validity of the developed model, MIEM is applied to analyze thermal stress distribution of the chip scale package (CSP). In general, a good qualitative agreement has been observed between the various results. Moreover, MIEM can directly obtain the stress value at the interface, which is also one of the advantages of this method in dealing with multilayer structures.

Influences of heat input, welding sequence and external restraint on twisting distortion in an asymmetrical curved stiffened panel

Welding distortion not only degrades the fabrication accuracy of ship hull blocks but also decreases the productivity due to correction works. The accurate prediction of welding-induced distortion will help control the dimension accuracy. In this study, a computational approach based on inherent strain theory and interface element method was employed to efficiently and precisely estimate welding-induced deformation for large welded structures generated during assembly process. In the proposed approach, the local shrinkage due to heat input were considered by inherent strain components. On the other hand, the gap as well misalignment between the two parts to be joined, and the change of stiffness during assembly process were taken into account by interface elements. Meanwhile, the geometrical nonlinearity was included in the developed computational approach. In the current study, the features of welding deformation in an asymmetrical curved stiffened panel were numerically investigated by mean of the new computational approach. In addition, the influences of heat input, welding sequence and external restraint on the twisting distortion of the curved stiffened panel were further studied.

Accurate evaluation of the configurational forces in single-crystalline NiMnGa alloys under mechanical loading conditions

To properly predict the mechanical response of a single-crystalline NiMnGa sample, the configurational forces on the twin interfaces in the sample have to be calculated accurately. However, the conventional displacement-based finite element (DB-FE) method usually yields large numerical errors in calculating the contact stress values on the twin interfaces, which will further influence the evaluations of the configurational forces. In this paper, an interface element (IE) method is incorporated into the conventional FE framework. Through this FE-IE method, the contact stress is treated as one of the primary unknowns on the twin interfaces. By solving the governing system of the model numerically, the contact stresses on the twin interfaces can be directly obtained, based on which the configurational forces can be calculated. The obtained results are further used to predict the global mechanical response of the NiMnGa sample. For a simple example, the theoretical values of the resultant contact forces and the configurational forces on the twin interfaces can be determined. By comparing the numerical results obtained from the DB-FE method and the FE-IE method with the theoretical values, it is found that the FE-IE method can generate more accurate numerical solutions. Furthermore, the influence of the cross-sectional shapes of NiMnGa samples on their mechanical response is investigated.

Finite Element Model to Simulate Crack Propagation Using Interface Elements and Its Verification in Tensile Test

Since the crack generation and its propagation caused by welding defects is one of the main hull damage patterns, the simulation of crack propagation process has an important significance for ship safety. Based on interface element method, a finite element model to simulate crack propagation is studied in the paper. A Lennard-Jones type potential function is employed to define potential energy of the interface element. Tensile tests of steel flat plates with initial central crack are carried out. Surface energy density and spring critical stress that are suitable for the simulation of crack propagation are determined by comparing numerical calculation and tests results. Based on a large number of simulation results, the curve of simulation correction parameter plotted against the crack length is calculated.

Interfacial delamination of double-ceramic-layer thermal barrier coating system

Thermal barrier coating system (TBCs) must withstand the most demanding high temperature conditions where state-of-the-art top coat material Y2O3–stabilized ZrO2 may undergo significant sintering and phase change. The concept of double-ceramic-layer (DCL) TBCs seems to be an effective way to meet the need for both thermal stability and transformation toughening. In this paper, a virtual crack closure technique based interface element method is introduced to study the mechanics associated with the interfacial delamination of DCL TBCs. The evolution of energy release rate of interfacial delamination is explored for DCL TBCs with various geometrical and material parameters. Analysis of fracture mechanisms of delamination reveals that considering the integrated thermal and mechanical functionalities of coatings an optimal thickness ratio of outer to inner ceramic layers exists, which can be preliminarily evaluated by running numerical calculations of fracture parameters and performing thermal life experiments over a wide range of thickness ratios of outer to inner coating layers. In addition, the influence of separation centered at the interface of two ceramic layers is also examined. It is demonstrated that the local separation between two ceramic layers makes delamination readily to form and propagate at the interface between the inner coating and the underlying layer.

Stability Analysis of Unloading Slope by Interface Element Method

Mechanics behavior of unloading rock slope is essentially different from the natural rock slope . But, stability analysis of rocky slope during and after excavating still need these parameters and constitutional relation came from the natural rock slope, thus, the difference between the unloading rock mass and natural rock mass is neglected. The calculation result is quite different from the monitoring result. In order to analyze the stability of unloading rock slope properly, corresponding mechanics parameters including mechanics state, unloading degree and others should be determined and applied. In this paper, IEM - Sample Element Method and Interface Element Method expounded systematically and used to determine the corresponding mechanics parameters of a layered rock slope- Xishan slope of the Jiangyin Yangtze River Bridge. Then, IEM computer program based on Interface Element Method used to calculate the displacement of Xishan slope. Compare with displacement site-monitoring results, IEM is better than Finite Element Method.

A new Interface Element Method on Computation of the Interface Crack Propagation Energy Release Rate

A new interface element method was proposed to calculate the strain energy release rates(SERR) based on the virtual crack closure technique (VCCT). A Lagrange multiplier was introduced between the node pair at crack tip to obtain the internal forces. Then from the VCCT, the SERR was solved by using the forces and displacements near the crack tip. Examples for stationary cracks under the two typical cases are given. Meanwhile, the relationship curves between crack energy release rate and the length of crack, plate depths were plotted respectively.The example shows that the interface element used to calculate the SERR is simple, efficient, and highly accurate in analysis of 2D crack growth problems, and without requiring the special singularity element or collapsed element at crack tip.

Lower‐dimensional interface elements with local enrichment: application to coupled hydro‐mechanical problems in discretely fractured porous media

SUMMARYIn this study, we develop lower‐dimensional interface elements to represent preexisting fractures in rock material, focusing on finite element analysis of coupled hydro‐mechanical problems in discrete fractures–porous media systems. The method adopts local enrichment approximations for a discontinuous displacement and a fracture relative displacement function. Multiple and intersected fractures can be treated with the new scheme. Moreover, the method requires less mesh dependencies for accurate finiteelement approximations compared with the conventional interface element method. In particular, for coupled problems, the method allows for the use of a single mesh for both mechanical and other related processes such as flow and transport. For verification purposes, several numerical examples are examined in detail. Application to a coupled hydro‐mechanical problem is demonstrated with fluid injection into a single fracture. The numerical examples prove that the proposed method produces results in strong agreement with reference solutions. Copyright © 2012 John Wiley & Sons, Ltd.

CM-KR-1 Interface elements for coupling independently modeled finite element domains

A new method for non-matching interfaces on the boundaries of the finite elements in partitioned domains is presented by introducing interface elements.The interface element method(IEM)satisfies the continuity conditions exactly through interfaces without recourse to the Lagrange multiplier technique.The moving least square(MLS) approximation is implemented to construct the shape functions of the interface elements.The compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method,and the completeness of the shape functions of the interface elements guarantees the convergence of numerical solutions.Moreover,the coupling between the fluid and solid domains with dissimilar finite element meshes can be achieved by using the IEM.

MD-ISE-FE Multiscale Modeling and Numerical Simulation of Thermal Conductivity of Cu Film Interface Structure

With the devices miniaturization, the properties of materials at the micro/nano scale were much different from what at Macro-scale because of the scale effect. The Interface Stress Element (ISE) was introduced into the multi-scale model. These three methods, Molecular Dynamics (MD), ISE and Finite Element (FE) were effectively combined by designing a handshake region and using the transition interface element method. The multi-scale model of film was built based on MD-ISE-FE. The sequential coupling method was used to calculate, and then, the results of the FE and ISE region were applied to the MD region. The EAM potential was used to simulate. The results were the basically same with the other experimental and simulation results in the reference. It indicated that the multi-scale analysis method could be applied to calculate the thermodynamics properties of the interface structure at the Micro/nano scale.

Analysis of Shield Tunnel for Water Conveyance Based on the Interface Element Method

The shield tunnel for water conveyance is usually composed of two-layer liner tube. The outer layer is fabricated reinforced concrete structure consisting of the sectors of liner tube which are connected by binder bolt, and the inner layer is liner tube of depositing reinforced concrete. Under the action of inner and outer water pressure, there will be some discontinuous deformation on the crack sections and the interface between liner and soil, which bring great difficulty to the establishment of the model. Based on the interface stress element theory of discontinuous mechanics, this paper has proposed a computing model of shield tunnel for water conveyance in accordance with the project of transporting water through Yellow River for diverting water from the South to the North. This model can reflect the discontinuous deformation characteristics of various cracks. The effects of binder bolt and reinforced bar can also be well simulated. The theoretical analysis and practical computation results show that the model suggested in this paper is effective in simulating and computing, thus being regarded as an ideal model of shield tunnel for water conveyance.

A Coupled Finite Element and Element-Free Galerkin Method for Rigid Plastic Problems

The analysis for rigid plastic forming problems with finite element method can lose considerable accuracy due to severely distortional meshes. By measuring the mesh equality of elements, a coupling algorithm for rigid plastic problems have been proposed based on the interface element method, which converts the FE analysis into the EFG computation to preserve the accuracy in the region where meshes have been severely distorted. Numerical example shows that the present algorithms exploit the respective advantages of both the FE method whose computational efficiency is high and the EFG method which can throws out mesh distortions and be suitable for rigid plastic forming analysis.

Numerical Simulation of Fracture Propagation of Concrete on Meso-Level

In the paper, concrete on meso-level is taken as three phases composites consisting of aggregate、matrix and bond between matrix and aggregate. Model and arithmetic of Interface Element Method (IEM) is introduced and used to study the fracture characteristic and process of concrete under uniaxial load.

A Coupled Finite Element and Meshless Local Petrov-Galerkin Method for Large Deformation Problems

Based on the interface element method, a coupling algorithm for the large deformation problems has been proposed, which converts the FE analysis into the MLPG computation to preserve the accuracy in the region where meshes have been severely distorted. Numerical example shows that the present method exploits the respective advantages of both the FE method whose computational efficiency is high and the MLPG method which is suitable for large deformation.