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This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

The purpose of this paper is to provide a theoretical analysis of the fracture behavior of multiple axisymmetric interface cracks between a homogeneous isotropic layer and its functionally graded material (FGM) coating under torsional loading.

In this paper, the authors employ the distributed dislocation technique to the stress analysis, an FGM coating-substrate system under torsional loading with multiple axisymmetric cracks consist of annular and penny-shaped cracks. First, with the aid of the Hankel transform, the stress fields in the homogeneous layer and its FGM coating are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations which are employed to calculate the SIFs.

From the numerical results, the following key points were observed: first, for two types of the axisymmetric interface cracks, the SIFs decrease with growing in the values of the non-homogeneity. Second, the SIFs increase with increases in interface crack length. Third, the magnitude of the SIFs decreases with increases in the FGM coating thickness. Fourth, the interaction between cracks is an important factor affecting the SIFs of crack tips.

New analytical dislocation solution in an FGM coating-substrate system is developed.

In this study composite and sandwich beams with homogeneous core and homogeneous or Functional Graded Materials (FGM) faces under three point bending have been confronted. The purpose of this paper is to study numerically sandwich beams with homogeneous core and homogeneous or FGM faces under three point bending and to compare the results for the stress and displacement fields with those resulted of coating – substrate and homogeneous beams. Considering a crack in the lower face sheet to study the influence of the material gradation on the stress intensity factors.

At first a static finite element analysis is performed throughout the composite and sandwich beams, which is taking into account the graded character or not of the faces. For this reason five plane models are considered in order to have a comparable study for the stress and displacement fields of composite beams, which are subjected to three point bending. Second a crack in the lower face is considered parallel to the axis of gradation. When subjected to three point bending, this crack will propagate slowly perpendicular to the lower face.

Computed distributions of the stress fields across the core material and near the interfaces are given for different materials gradation of the faces; and possible crack-initiation positions have been identified. Stress intensity factors are calculated using finite element method, and assuming linear fracture mechanics and plane strain conditions.

The originality of the proposed analysis is to investigate for the first time numerically the influence of the FGMs or homogeneous faces in the core material of sandwich beams under three point bending relative to the coating – substrate and to the homogeneous beams. Second to study the influence of a crack in the lower graded face sheet on the overall behavior of the composite beam and to investigate the influence of the material gradation on the values of stress intensity factors.

Ceramic materials and glasses have become important in modern industry as well as in the consumer environment. Heat resistant ceramics are used in the metal forming processes or as welding and brazing fixtures, etc. Ceramic materials are frequently used in industries where a wear and chemical resistance are required criteria (seals, liners, grinding wheels, machining tools, etc.). Electrical, magnetic and optical properties of ceramic materials are important in electrical and electronic industries where these materials are used as sensors and actuators, integrated circuits, piezoelectric transducers, ultrasonic devices, microwave devices, magnetic tapes, and in other applications. A significant amount of literature is available on the finite element modelling (FEM) of ceramics and glass. This paper gives a listing of these published papers and is a continuation of the author's bibliography entitled “Finite element modelling of ceramics and glass” and published in Engineering Computations, Vol. 16, 1999, pp. 510‐71 for the period 1977‐1998.

The form of the paper is a bibliography. Listed references have been retrieved from the author's database, MAKEBASE. Also Compendex has been checked. The period is 1998‐2004.

Provides a listing of 1,432 references. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

This paper makes it easy for professionals working with the numerical methods with applications to ceramics and glasses to be up‐to‐date in an effective way.

The purpose of this study is to investigate Thermo-mechanical limit elastic speed analysis of functionally graded (FG) rotating disks with the temperature-dependent material properties. Three different material models i.e. power law, sigmoid law and exponential law, along with varying disk profiles, namely, uniform thickness, tapered and exponential disk was considered.

The methodology adopted was variational principle wherein the solution was obtained by Galerkin’s error minimization principle. The Young’s modulus, coefficient of thermal expansion and yield stress variation were considered temperature-dependent.

The study shows a substantial increase in limit speed as disk profiles change from uniform thickness to exponentially varying thickness. At any radius in a disk, the difference in von Mises stress and yield strength shows the remaining stress-bearing capacity of material at that location.

Rotating disks are irreplaceable components in machinery and are used widely from power transmission assemblies (for example, gas turbine disks in an aircraft) to energy storage devices. During operations, these structures are mainly subjected to a combination of mechanical and thermal loadings.

The findings of the present study illustrate the best material models and their grading index, desired for the fabrication of uniform, as well as varying FG disks. Finite element analysis has been performed to validate the present study and good agreement between both the methods is seen.

Discusses the prospects of integration of functionally graded materials coating methods and computer modelling methods, which developed independently earlier. It is shown that combining these two approaches will result in the development of a powerful technology that can draw on the experience gained from MicroElectroMechanical Systems (MEMS). A goal of this review paper is to emphasise the main problems and to discuss already known examples of functionally graded tool synthesis based on rapid prototyping methods.

Frictional sliding contact problems between laterally graded orthotropic half-planes and a flat rigid stamp are investigated. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members.

The solution procedure is based on a finite element (FE) approach which is conducted with an efficient FE analysis software ANSYS. The spatial gradations of the orthotropic stiffness constants through the horizontal axis are enabled utilizing the homogeneous FE approach. The Augmented Lagrangian contact algorithm is used as an iterative non-linear solution method in the contact analysis.

The accuracy of the proposed FE solution method is approved by using the comparisons of the results with those computed using an analytical technique. The prominent results indicate that the surface contact stresses can be mitigated upon increasing the degree of orthotropy and positive lateral gradations.

One can infer from the literature survey that, the contact mechanics analysis of orthotropic laterally graded materials has not been investigated so far. In this study, an FE method-based computational solution procedure for the aforementioned problem is addressed. The presented study aims at guiding engineering applications in the prediction of the contact response of orthotropic laterally graded members. Additionally, this study provides some useful points related to computational contact mechanics analysis of orthotropic structures.

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

The purpose of this paper is to introduce a numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) functionally graded material (FGM) plate subjected to tensile mechanical load.

For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral.

According to the numerical analysis, all parameters above played an important role in determining the J-integral.

The present study consists in investigating the simulation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate under Mode I. The J-integral is determined for various load applied. The cracked plate is joined by bonding an FGM layer to TiB plate on its double side. The determination of the gain on J-integral by using FGM layer is highlighted. The calculation of J-integral of FGM’s involves the direction of the radius of the notch in order to reduce the J-integral.

This paper gives a bibliographical review of the finite element modelling and simulation of indentation testing from the theoretical as well as practical points of view. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1990 and 2002. At the end of this paper, 509 references are listed dealing with subjects such as, fundamental relations and modelling in indentation testing, identification of mechanical properties for specific materials, fracture mechanics problems in indentation, scaling relationship for indentation, indenter geometry and indentation testing.