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The purpose of this paper is to deal with large deformation analysis of plane beams composed of functionally graded (FG) elastic material with a variable Poisson’s ratio.

The material is assumed to be linear elastic, with a Poisson’s ratio varying according to a power law along the thickness direction. The finite element used is a plane beam of any-order of approximation along the axis, and with four transverse enrichment schemes, which can describe constant, linear, quadratic and cubic variation of the strain along the thickness direction. Regarding the constitutive law, five materials are adopted: two homogeneous limiting cases, and three intermediate FG cases. The effect of both finite element kinematics and distribution of Poisson’s ratio on the mechanical response of a cantilever is investigated.

In accordance with the scientific literature, the second scheme, in which the transverse strain is linearly variable, is sufficient for homogeneous long (or thin) beams under bending. However, for FG short (or moderate thick) beams, the third scheme, in which the transverse strain variation is quadratic, is needed for a reliable strain or stress distribution.

In the scientific literature, there are several studies regarding nonlinear analysis of functionally graded materials (FGMs) via finite elements, analysis of FGMs with constant Poisson’s ratio, and geometrically linear problems with gradually variable Poisson’s ratio. However, very few deal with finite element analysis of flexible beams with gradually variable Poisson’s ratio. In the present study, a reliable formulation for such beams is presented.

The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.

The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.

The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.

The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

The purpose of this paper is to achieve numerical simulation of cohesive crack growth in concrete structures.

The extended finite element method (XFEM) using four-node quadrilateral element associated with the fictitious cohesive crack model is used. A mixed-mode traction-separation law is assumed for the cohesive crack in the fracture process zone (FPZ). Enrichments are considered for both partly and fully cracked elements, and it thus makes the evolution of crack to any location inside the element possible. In all. two new solution procedures based on Newton-Raphson method, which differ from the approach suggested by Zi and Belytschko (2003), are presented to solve the nonlinear system of equations. The present formulation results in a symmetric tangent matrix, conveniently in finite element implementation and programming.

The inconvenience in solving the inversion of an unsymmetrical Jacobian matrix encountered in the existing approach is avoided. Numerical results evidently confirm the accuracy of the proposed approach. It is concluded that the developed XFEM approach is especially suitable in simulating cohesive crack growth in concrete structures.

Multiple cracks and crack growth in reinforced concretes should be considered in further studies.

The research paper presents a very useful and accurate numerical method for engineering application problems that has ability to numerically simulate the cohesive crack growth of concrete structures.

The research paper provides a new numerical approach using two new solution procedures in solving nonlinear system of equations for cohesive crack growth in concrete structures that is very convenient in programming and implementation.

The purpose is to analyze the mechanical behavior of the arterial wall in the degraded region of the arterial wall and to determine the stress distribution, as an important factor for predicting the potential failure mechanisms in the wall. In fact, while the collagen fiber degradation process itself is not modeled, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed. To do so, a local weakness in the media layer is considered by defining representative volume elements (RVEs) with different fiber collagen contents in the degraded area to investigate the mechanical response of the arterial wall.

A three-dimensional (3D) large strain hierarchical multiscale technique, based on the homogenization and genetic algorithm (GA), is utilized to numerically model collagen fiber degradation in a typical artery. Determination of material constants for the ground matrix and collagen fibers in the microscale level is performed by the GA. In order to investigate the mechanical degradation, two types of RVEs with different collagen contents in fibers are considered. Each RVE is divided into two parts of noncollagenous matrix and collagen fiber, and the part of collagen fiber is further divided into matrix and collagen fibrils.

The von Mises stress distributions on the inner and outer surfaces of the artery and the influence of collagen fiber degradation on thinning of the arterial wall in the degraded area are thoroughly studied. Comparing the maximum stress values on outer and inner surfaces in the degraded region shows that the inner surface is under higher stress states, which makes it more prone to failure. Furthermore, due to the weakness of the artery in the degraded area, it is concluded that the collagen fiber degradation considerably reduces the wall thickness in the degraded area, leading to an observable local inflation across the degraded artery.

Considering that little attention has been paid to multiscale numerical modeling of collagen fiber degradation, in this paper a 3D large strain hierarchical multiscale technique based on homogenization and GA methods is presented. Therefore, while the collagen fiber degradation process itself is not modeled in this study, zones with reduced collagen fiber content (corresponding to the degradation process) are assumed.

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.

Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.

With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so‐called “meshless” scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill‐time errors that might be addressed by introducing suitable projections. The general question of “rate of convergence” of these schemes requires analysis. Numerical results here suggest first‐order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods.

This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed “on‐the‐fly” for each “active point” to form a dynamic virtual mesh of active elements that evolves with the moving interface.

A 4‐node flat shell quadrilateral finite element with 6 degrees of freedom per node, denoted QC5D‐SA, is presented. The element is an assembly of a modification of the drilling degree of freedom membrane presented by Ibrahimbegovic et al., and the assumed strain plate element presented by Bathe and Dvorkin. The part of the stiffness matrix associated with in—plane displacements and rotations is integrated over the element domain by a modified 5‐point reduced integration scheme, resulting in greater efficiency without the sacrifice of rank sufficiency. The scheme produces a soft higher order deformation mode which increases numerical accuracy. A large number of standard benchmark problems are analyzed. Some examples show that the effectiveness of a previously proposed “membrane locking correction” technique is significantly reduced when employing distorted elements. However, the element is shown to be generally accurate and in many cases superior to existing elements.

The main aim of this study is to determine the fracture toughness and accordingly to predict the fracture initiation, crack propagation and mode of crack extension accurately in polypropylene subsea pipes subjected to internal pressure.

Tensile test was performed following the ISO 527–1 standard. An elastic-plastic constitutive model was developed based on the tensile test results, and it is implemented in the FEA model to describe the constitutive behaviour of the polypropylene material. Three-point bend tests with linear-elastic fracture mechanics (LEFM) approach were conducted following ISO-13586 standard, from which the average fracture toughness of the polypropylene pipe material in crack-opening mode was found as KIc = 3.3 MPa√m. A numerical model of the experiments is developed based on the extended finite element method (XFEM), which showed markedly good agreement with the experimental results.

The validated XFEM modelling approach is utilised to illustrate its capabilities in predicting fracture initiation and crack propagation in a polypropylene subsea pipe subjected to an internal pressure containing a semi-elliptical surface crack, which agrees well with existing analytical solutions. The XFEM model is capable of predicting the crack initiation and propagation in the polypropylene pipe up to the event of leakage.

The methodology proposed herein can be utilised to assess the structural integrity and resistance to fracture of subsea plastic pipes subjected to operational loads (e.g. internal pressure).

The purpose of this paper is to focus on MHD unsteady flow of Carreau fluid over a variable thickness melting surface in the presence of chemical reaction and non-uniform heat sink/source.

The flow governing partial differential equations are transformed into ordinary ones with the help of similarity transformations. The set of ODEs are solved by a shooting technique together with the R.K.–Fehlberg method. Further, the graphs are depicted to scrutinize the velocity, concentration and temperature fields of the Carreau fluid flow. The numerical values of friction factor, heat and mass transfer rates are tabulated.

The results are presented for both Newtonian and non-Newtonian fluid flow cases. The authors conclude that the nature of three typical fields and the physical quantities are alike in both cases. An increase in melting parameter slows down the velocity field and enhances the temperature and concentration fields. But an opposite outcome is noticed with thermal relaxation parameter. Also the elevating values of thermal relaxation parameter/ wall thickness parameter/Prandtl number inflate the mass and heat transfer rates.

This is a new research article in the field of heat and mass transfer in fluid flows. Cattaneo–Christov heat flux model is used. The surface of the flow is assumed to be melting.

This paper aims to describe the theoretical background and main hypotheses at the basis of SAFIR^®, a nonlinear finite element software for modeling structures in fire. The paper also explains how to use the software at its full extent. The discussed numerical modeling principles can be applied with other similar software.

Following a general overview of the organization of the software, the thermal analysis part is explained, with the basic equations and the different possibilities to apply thermal boundary conditions (compartment fire, localized fire, etc.). Next, the mechanical analysis part is detailed, including the time integration procedures and the different types of finite elements: beam, truss, shell, spring and solid. Finally, the material laws are described. The software capabilities and limitations are discussed throughout the paper.

By accommodating multiple types of finite elements and materials, by allowing the user to consider virtually any section type and to input the fire attack in multiple forms, the software SAFIR^® is a comprehensive tool for investigating the behavior of structures in the fire situation. Meanwhile, being developed exclusively for its well-defined field of application, it remains relatively easy to use.

The paper will improve the knowledge of readers (researchers, designers and authorities) about numerical modeling used in structural fire engineering in general and the capabilities of a particular software largely used in the fire engineering community.

At each New Year we stand at the threshold of fresh scenes and hopes, of opportunities and pastures new. It is the time for casting off shackles and burdens that have weighed us down in the old year; almost a new chapter of life. We scan the prevailing scene for signs that will chart the year's unrolling and beyond, and hope profoundly for a smooth passage. The present is largely the product of the past, but of the future, who knows? Man therefore forever seems to be entering upon something new—a change, a challenge, events of great portent. This, of course, is what life is all about. Trends usually precede events, often by a decade or more, yet it is a paradox that so many are taken by surprise when they occur. Trends there have been and well marked; signs, too, for the discerning. In fields particular, they portend overall progress; in general, not a few bode ill.