Computational fracture mechanics: Research and application

This paper focuses on the impact of computational methodology on furthering the understanding of fundamental fracture phenomena. The current numerical approaches to the solution of fracture mechanics problems, e.g. finite element (FE) methods, finite difference methods and boundary element methods, are reviewed. The application of FE methods to the problems of linear elastic fracture problems is discussed. Particular emphases are placed on the stress intensity factors, energy release rate in mixed mode fracture and dynamic crack propagation. Numerical solutions of ductile fracture problems are surveyed. A special focus is placed on stable crack growth problems. The need for further research in this area is emphasized. The importance of large strain phenomena and accurate modeling of non-linearities is highlighted. An expanded version of fracture mechanics methodology is given by Liebowitz [Advances in Fracture Research 3. Pergamon Press, Oxford (1989)]; additional treatment is given in this paper to numerical results incorporating error estimates and algorithms for mesh design into the FE code. The adaptive method involves various stages which includes FE analysis, error estimation/indication, mesh refinement and fracture/failure analysis iteratively. Reference is made to integrate expert knowledge and a hierarchical, rule-based, decision process to fracture mechanics for the purpose of designing practical fracture-proof engineering products. Some further areas of research in adaptive finite element analysis are discussed.     

An efficient multi‐layer planar 3D fracture growth algorithm using a fixed mesh approach

We present a planar three‐dimensional (3D) fracture growth simulator, based on a displacement discontinuity (DD) method for multi‐layer elasticity problems. The method uses a fixed mesh approach, with rectangular panel elements to represent the planar fracture surface. Special fracture tip logic is included that allows a tip element to be partially fractured in the tip region. The fracture perimeter is modelled in a piece‐wise linear manner. The algorithm can model any number of interacting fractures that are restricted to lie on a single planar surface, located orthogonal to any number of parallel layers. The multiple layers are treated using a Fourier transform (FT) approach that provides a numerical Green's function for the DD scheme. The layers are assumed to be fully bonded together. Any fracture growth rule can be postulated for the algorithm. We demonstrate this approach on a number of test problems to verify its accuracy and efficiency, before showing some more general results. Copyright © 2001 John Wiley & Sons, Ltd.     

Fuzzy expertise and its application to R & D management

Applications of fuzzy set theory to various problems of data processing influenced greatly the analysis of expert opinion results. The authors developed models based on the fuzzy set concept for expert assessments using quantitative and qualitative scales typical in R & D management. The approach is illustrated by the solution of the problem of ranking of the factors influencing practical applications of research results.     

Phase-field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric-meshfree approach

Phase-field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric-meshfree approach is developed for the phase-field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric-meshfree approach uses moving least-squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase-field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowledge of crack paths. Furthermore, the intergranular and transgranular crack propagation patterns in polycrystalline materials can be simulated by the present approach. A series of numerical examples that deal with the isotropic and anisotropic fracture are investigated to demonstrate the robustness and effectiveness of the proposed approach.     

FMS Designer: An expert system for flexible manufacturing system design

Implementation of flexible manufacturing technology in the batch manufacturing environment has created major problems for designers and engineers who are responsible for specification and design of flexible manufacturing systems (FMS). The FMS design task appears to be an excellent application for expert systems techniques. This paper describes current results of an ongoing research effort to develop an expert system which analyses the output from an FMS simulation model, determines whether operational and financial objectives are met, identifies design deficiencies or opportunities for improvement, and proposes designs which overcome deficiencies or exploit improvement opportunities. An overview of the FMS design expert system is given and a case study is presented to illustrate how the system operates. Areas for future research are also discussed.     

基于CBR的机载雷达故障诊断专家系统研究

以故障诊断的理论和方法为基础,综合运用神经网络、基于案例推理(CBR)和专家系统理论,对雷达装备的故障诊断问题进行研究,形成一个集成的智能诊断专家系统。介绍了系统的总体结构和工作原理,并给出具体的诊断实例,此方法充分利用神经网络和CBR的优点,将提高雷达装备故障诊断的正确性和效率。     

General BE approach for three-dimensional dynamic fracture analysis

A general mixed boundary element approach for three-dimensional dynamic fracture mechanics problems is presented in this paper. A mixed traction-displacement integral equation formulation in the frequency domain is used. The hypersingular and strongly singular kernels are regularized by analytical transformations yielding an easy to implement BE approach. Nine-node quadrilateral and six-node triangular continuous quadratic elements are used for external boundaries and crack surfaces. The crack front elements have their mid node at one quarter of the element length allowing for a proper representation of the crack surface displacement. The present approach is intended for the frequency domain analysis of fracture mechanics problems of any general 3D geometry; i.e. boundless or bounded regions, single or multiple, surface or internal cracks. Transient dynamic problems are studied using the FFT algorithm. The numerical results presented show the robustness and accuracy of the approach which requires a reasonable number of elements and degrees of freedom.     

Issues in expert system development

The explicit representation of domain knowledge and its separation from the processes which manipulate it and the representation formalism particular to artificial intelligence allow expert systems to solve problems which are characterized by a high combinatoric complexity or which are sufficiently ill defined as to not have reasonable software engineering solutions. The expert system approach to problem-solving differs radically from its conventional system development counterpart. This paper defines the expert system and introduces the production system architecture. The relative strengths and weakenesses of expert system and software engineering approaches to problem solving are discussed. Also addressed are criteria for identifying problems amenable to expert system solution and some justifications for system development.Paper presented at the Ninth International Thermal Expansion Symposium, December 8–10, 1986, Pittsburgh, Pennsylvania, U.S.A.     

An implementation of the stiffness derivative method as a discrete analytical sensitivity analysis and its application to mixed mode in LEFM

In this work, an improvement in the stiffness derivative method based on a shape design sensitivity analysis is proposed, so that the error inherent in the finite difference procedure is avoided. For a global estimation of G from a given finite element solution, this approach is shown to be equivalent to the well-known J-integral when the latter is numerically implemented through its equivalent domain integral. However, it is verified that its direct application to 2D mixed mode problems of linear elastic fracture mechanics through the field decomposition technique yields estimates for G_I and G_II which are in general more accurate for the proposed method. The importance of the velocity field is also remarked and some suggestions for its choice are given.     

On the convergence of 3D free discontinuity models in variational fracture

Free discontinuity problems arising in the variational theory for fracture mechanics are considered. A Γ -convergence proof for an r-adaptive 3D finite element discretization is given in the case of a brittle material. The optimal displacement field, crack pattern and mesh geometry are obtained through a variational procedure that encompasses both mechanical and configurational forces. Possible extensions to cohesive fracture and quasi-static evolutions are discussed.     

Problems of fracture mechanics of solid bodies with V-shaped notches

We present a survey of the research into the problems of fracture mechanics of solid bodies with V-shaped notches. The methods used for the solution of plane problems of the theory of elasticity in the domains with corner points on the boundary contours are analyzed. Special attention is given to the unified approach to the solution of the problems of stress concentration near sharp and rounded V-shaped notches in elastic domains. The fracture criteria for solid bodies with V-shaped notches are analyzed. On the basis of the solution of plane elastoplastic problem within the framework of the model of plastic strips for a plane with infinite rounded V-shaped notch, we propose a new deformation fracture criterion for quasibrittle bodies with sharp and rounded V-shaped notches.     

Decision support system for rapid prototyping process selection through integration of fuzzy synthetic evaluation and an expert system

A new method is proposed for selecting the most appropriate rapid prototyping process according to user's specific requirements by using the expert system and fuzzy synthetic evaluation. The selection process is divided into two stages. First, it is necessary to generate feasible alternatives, which are executed under the expert system environment. Second, given those feasible alternatives, the fuzzy synthetic evaluation approach is employed to produce a ranking order of the alternatives and to finalize the most suirapid prototyping system. One distinctive characteristic of this method is that quantitative as well as qualitative measures are employed, providing more accurate results. The decision system developed based on the proposed method is composed of four modules: a database to store the specifications of various rapid prototyping processes; a knowledge-based expert system for determining the feasible alternatives; a fuzzy synthetic evaluation model to select the most suitable rapid prototyping process; and a user interface and an expert interface to interact with the system. The fuzzy synthetic evaluation approach used in the system is illustrated in detail by a numerical example. Furthermore, a Java-enabled solution, together with web techniques, is employed for developing such a networked decision support system. Finally, two examples of rapid prototyping process selection are designed to demonstrate the application of the system. The system has been implemented and can run at a rapid prototyping and manufacturing networked service platform that the authors have developed.     

Modelling of mixed mode debonding in externally FRP reinforced beams

In this paper a refined model able to analyze edge debonding problems in beams strengthened with externally bonded composite laminated plates, is presented. The structural system is viewed as composed by three physical different components: the base beam (made of steel or concrete), the adhesive layer and the bonded plate. Each component may be comprised by one or several mathematical layers which adopts the first-order shear deformation laminate theory. Bonding and continuity conditions between different layers are simulated by using the interface modelling technique. Strong and collapsed interface models are introduced in order to capture stress singularities and to reduce the complexity of the analysis, respectively. Governing equations for displacement fields complemented with boundary and continuity conditions, are obtained by a variational approach. According to a fracture mechanics approach, the analysis is carried out by evaluating the total and individual mode components of energy release rate (ERR).Applications for typical strengthened systems, carried out by numerical integration procedures, are proposed in which the energy release rates are evaluated by means of interface displacement jumps, leading to a very efficient numerical procedure. The approximations introduced in the model with respect to the adopted number of mathematical layers are analyzed and comparisons with existent models are given. For the simpler two-layer model of the structure, comparisons are given with the closed-form solutions obtained in [Greco F, Nevone Blasi P, Lonetti P. An analytical investigation of debonding problems in beams strengthened using composite plates. Eng Fract Mech 2006, in press]. The convergence to the results from continuum analysis is investigated when a refined assembly of layers is adopted, by means of comparisons with predictions from very careful FE solutions. Finally, the effect of different debonding modes on the overall behaviour of the structural system is analyzed. These results show the capability and the accuracy of the proposed approach to predict debonding failure behaviour in both steel and concrete strengthened beams. As a matter of fact, the proposed approach involves reduced computational cost with respect to FE solutions based on 2D continuum elements and the use of a multi-layer structural model leads to avoid some complexities related to the classical elasticity theory for bimaterial interface cracks.     

Controlling the onset of numerical fracture in parallelized implementations of the material point method (MPM) with convective particle domain interpolation (CPDI) domain scaling

The material point method is well suited for large‐deformation problems in solid mechanics but requires modification to avoid cell‐crossing errors as well as extension instabilities that lead to numerical (nonphysical) fracture. A promising solution is convected particle domain interpolation (CPDI), in which the integration domain used to map data between particles and the background grid deforms with the particle, based on the material deformation gradient. While eliminating the extension instability can be a benefit, it is often desirable to allow material separation to avoid nonphysical stretching. Additionally, large stretches in material points can complicate parallel implementation of CPDI if a single particle domain spans multiple computational patches. A straightforward modification to the CPDI algorithm allows a user‐specified scaling of the particle integration domain to control the numerical fracture response, which facilitates parallelization. Combined with particle splitting, the method can accommodate materials with arbitrarily large failure strains. Used with a smeared damage/softening model, this approach will prevent nonphysical numerical fracture in situations where the material should remain intact, but the effect of a single velocity field on localization may still produce errors in the post‐failure response. Details are given for both 2‐D and 3‐D implementations of the scaling algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

The 3‐D BEM implementation of a numerical Green's function for fracture mechanics applications

The use of Green's functions has been considered a powerful technique in the solution of fracture mechanics problems by the boundary element method (BEM). Closed‐form expressions for Green's function components, however, have only been available for few simple 2‐D crack geometry applications and require complex variable theory. The present authors have recently introduced an alternative numerical procedure to compute the Green's function components that produced BEM results for 2‐D general geometry multiple crack problems, including static and dynamic applications. This technique is not restricted to 2‐D problems and the computational aspects of the 3‐D implementation of the numerical Green's function approach are now discussed, including examples. Copyright © 2000 John Wiley & Sons, Ltd.     

An expert system using priorities for solving multiple-criteria facility layout problems

In this paper we develop an expert system for multiple-criteria facility layout problems. The facility layout problem is identified as an ill-structured problem; our approach for solving it is based on expert systems and multiple-criteria decision making (MCDM). The expert system interacts with the decision maker (DM), and reflects the DM's preferences in the selection of rules and priorities. The inference engine is a forward-chaining reasoning procedure which is discussed in detail. The approach consists of two parts: (a) construction of a layout based on a set of rules and restrictions, and (b) improvement of the layout based on interaction with decision maker. The MCDM expert system approach considers and incorporates the multiple criteria in these two parts as follows. In (a) it uses priorities on the selection of rules, adjacency of departments, and departments for construction purposes. In (b) it uses different objectives such as materials handling cost, flexibility, and materials handling time for paired comparison of generated layouts for improvement purposes. Some experiments with the developed computer package are reported and an example is solved.     

A direct traction BIE approach for three-dimensional crack problems

A boundary element (BE) approach based on the traction boundary integral equation for the general solution of three-dimensional (3D) crack problems is presented. The hypersingular and strongly singular integrals appearing in the formulation are analytically transformed to yield line and surface integrals which are at most weakly singular. Regularization and analytical transformation of the boundary integrals is done prior to any boundary discretization. The integration process does not require of any change of coordinates and the resulting integrals can be numerically evaluated in a simple and efficient way. In order to show the generality, simplicity and robustness of the proposed approach, different flat and curved crack problems in infinite and finite domains are analyzed. A simple BE discretization strategy is adopted. The results obtained using rather course meshes are very accurate. The emphasis of this paper is on the effective application of the proposed BE approach and it is pretended to contribute to the transformation of hypersingular boundary element formulation in something as clear, general and easy to handle as the classical formulation but much better suited for fracture mechanics problems.     

Stress intensity factor analysis for arbitrary shaped crack by local weight functions and expert systems for failure analysis

A theory has been proposed for 3D mixed mode weight function computations. This theory is based on the energy balance equation for the local perturbation of the crack front. 3D mixed mode weight functions for arbitrary loaded and shaped cracks are obtained from three reference stress intensity data. A good accuracy of the proposed technique has been demonstrated. The above approach has been applied as a background of the expert system for defects assessment analysis in structures.     

Application of expert systems and pattern recognition methodologies to facilities layout planning

This paper deals with two basic concepts of artificial intelligence (AI), from a facilities layout problem domain perspective. In this work, the facilities layout problem is treated as a multi-objective situation. From conventional multi-objective perspective, the philosophy underlying this work is not a different one. However, the qualitative constraints are handled via a symbolic manipulation structure. The two conceptualizations are: (a) an expert system and (b) a pattern recognition system. In the expert system, the heuristics used are based on the augmented transition networks of natural language processing. In the pattern recognition system, the use of productions rules to capture the expert knowledge is illustrated. For both the systems example problems are given.     

FESOLE-fuzzy expert system for determining the optimal level of enforcement

Electronic payment for using road infrastructure is an area that is gaining importance in the realm of intelligent transportation systems (ITS). While preparing such an electronic fee collection system, the level of enforcement needed must be determined. This is not a trivial task, because it is affected by many technical and monetary factors. At the same time, it cannot be expected that all decision makers are deeply involved in this field and are able to make an optimal decision depending on the recommendations of external experts. In order to decrease the possibility of manipulating this decision process by lobbyists and to save the money used for external consultants, a decision support system is needed. This paper describes a fuzzy expert system for determining the optimal level of enforcement ? FESOLE. It bridges a missing part in the research concerning ITS. The author focuses mainly on the major technical features of this model. A fuzzy expert system is used to approach this problem. It can extract and exploit the knowledge of human experts and convert it to a robust computational model. Suitability of this methodology for a given task is also demonstrated.