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The far-field methodology, developed by J. C. Maxwell in 1873 for the evaluation of the electrical conductivity of a particle-reinforced material, is utilised to estimate the effective third order elastic constants of composite media containing a random distribution of spherical particles. The results are explicit analytical relationships derived using a perturbation solution, that are in a broad agreement with previous studies employing different homogenisation schemes. In contrast to other homogenisation schemes, Maxwell's methodology relies only on the far-field asymptotics. Therefore, the methodology may be more suitable for the evaluation of effective mechanical and physical properties of composites where the far-field asymptotics are known or can be derived. The main fundamental result of this work is the first demonstration that the Maxwell methodology may be applied to weakly nonlinear problems. Therefore, it can offer a new, simple method to analyse homogenisation problems in many other fields. • First application of the Maxwell far-field methodology to nonlinear elasticity. • The derived relationships encompass results of classical micro-mechanics. • Obtained relationships generalise several particular cases investigated before. • Methodology is applicable to homogenisation problems in mechanics and physics. [ABSTRACT FROM AUTHOR]

The plasticity-induced crack closure phenomenon has been the subject of many previous theoretical and experimental studies. From these studies it was found that in the absence of applied loading, a fatigue crack is likely to be partially closed due to the plastic wake, which is generated behind the tip of a propagating crack. This partial, or residual, closure has many implications for theoretical modelling as well as practical applications. However, no theoretical models have been developed to evaluate what part of a propagating fatigue crack is closed in the free from stress state. Direct 3D FE simulations of the plasticity-induced crack closure are very challenging, time consuming, and are not feasible for a large number of fatigue cycles. Therefore, the current paper utilises a 2D strip-yield idealisation and the distributed dislocation technique to investigate the effects of the stress amplitude and R-ratio of fatigue loading on the residual crack closure. The outcomes of this work may assist in the evaluation of the adequacy and limitations of the current analytical and computational models describing the behaviour of structures containing fatigue cracks, as well as in the interpretation of data from nondestructive defect inspections. [Display omitted] • Evaluation of the closed part of a fatigue crack when free from applied stress. • Analytical strip-yield model solved using the distributed dislocation technique. • Parametric study for a range of parameters of constant amplitude fatigue loading. • Assessment of the adequacy of slit and breathing crack models. [ABSTRACT FROM AUTHOR]

This study utilises a third-order expansion of the strain energy density function and finite strain elastic theory to derive an analytical solution for an isolated, spherical void subjected to axisymmetric loading conditions. The solution has been validated with previously published results for incompressible materials and hydrostatic loading. Using this new solution and a homogenisation methodology, the effective linear and nonlinear properties of a material containing a dilute distribution of voids are derived. The effective nonlinear elastic properties are shown to be typically much more sensitive to the concentration of voids than the linear elastic properties. The derived analytical expressions for effective material properties may be useful for the development and justification of new experimental methods for the evaluation of porosity and theoretical models describing the evolution of mechanical damage associated with void nucleation and growth (e.g. creep). [ABSTRACT FROM AUTHOR]

• Crack tip opening load values were analysed for several loading sequences; • Analysed sequences have a high R-ratio content with no large overloads; • Measured values are well correlated with preceding min and max load values; • No significant memory effects beyond two previous turning points have been found; • New data driven approach for the evaluation of crack tip opening loads is suggested. In this paper, we present a new data-driven approach for the evaluation of crack tip opening load (P o p ) values under variable amplitude loading. These values are analysed for CT specimens manufactured from common aircraft grade aluminium alloys and subjected to several load sequences, all of which have a relatively high R-ratio content without significant overloads and underloads. Direct experimental measurements and outcomes of numerical simulations indicate that the P o p change abruptly from cycle to cycle. For this type of fatigue loading (including a military transport aircraft load spectrum with more than 400,000 turning points) and materials, it was found that P o p is well described by a linear function of the preceding minimum and maximum values of the applied loading. This finding provides a new simple way to evaluate the effective stress intensity factor range, which is often considered as a fatigue crack driving force. It is also verified via the use of machine learning that the proposed approach is capable of predicting the mean stress (R-ratio) effect on P o p for block loading. Therefore, the developed data-driven approach is a promising alternative to the computational methods, which currently dominate advanced fatigue life assessment procedures. [ABSTRACT FROM AUTHOR]

Highlights • A new theoretical relationship for the distribution of SIF for elliptical and part-elliptical cracks was developed. • A new way for evaluating of the quality of alternative K-solutions and fitting equations was suggested. • The relationship proposed here can assist in the development of SIF parametric equations from FE results. Abstract Stress intensity factors for cracks of elliptical or part-elliptical shapes in structural components, e.g. plates, bars and pressure vessels, are normally obtained using numerical methods. Due to the lack of exact benchmark solutions, the evaluation of the accuracy and quality of the numerical results and the corresponding fitting equations are largely based on the comparison against the outcomes of the previous numerical studies. In this work, a new relationship for the exact distribution of the stress intensity factor along the crack front is derived based on the divergence theorem for the compliance function. The application of the developed theoretical relationship is demonstrated towards the evaluation of the quality of previously obtained empirical equations for elliptical, semi-elliptical and part-elliptical cracks. [ABSTRACT FROM AUTHOR]

A new method for the analysis of plasticity-induced closure of finite cracks is developed based on the distributed dislocation technique. The method is applied to analyse closure and opening processes for an embedded fatigue crack propagating under constant amplitude cyclic loading. The obtained solution and presented results can serve as a benchmark for numerical procedures utilising the same yield-strip methodology. Comparison with past numerical studies reveals similar trends, though there are some differences in the crack tip opening values, particularly for low and negative R-ratios. The latter may indicate the need for a better approach to the discretisation of the contact, direct and reverse plasticity zones in the numerical procedures which utilise the same methodology. The developed method is general, and it can be adapted to evaluate the crack tip opening stress for other crack geometries and loading conditions. [Display omitted] • Analytical method for analysis of cracks with arbitrary plastic wake is developed. • Exact solutions for a crack growing under constant amplitude loading is presented. • The effects of R-ratio and maximum load amplitude on crack closure are investigated. • Solutions are compared with numerical studies using the same yield-strip methodology. [ABSTRACT FROM AUTHOR]

Large aortic aneurysm and acute and chronic aortic dissection are pathologies of the aorta requiring surgery. Recent advances in medical intervention have improved patient outcomes; however, a clear understanding of the mechanisms leading to aortic failure and, hence, a better understanding of failure risk, is still missing. Biomechanical analysis of the aorta could provide insights into the development and progression of aortic abnormalities, giving clinicians a powerful tool in risk stratification. The complexity of the aortic system presents significant challenges for a biomechanical study and requires various approaches to analyse the aorta. To address this, here we present a holistic review of the biomechanical studies of the aorta by categorising articles into four broad approaches, namely theoretical, in vivo , experimental and combined investigations. Experimental studies that focus on identifying mechanical properties of the aortic tissue are also included. By reviewing the literature and discussing drawbacks, limitations and future challenges in each area, we hope to present a more complete picture of the state-of-the-art of aortic biomechanics to stimulate research on critical topics. Combining experimental modalities and computational approaches could lead to more comprehensive results in risk prediction for the aortic system. [ABSTRACT FROM AUTHOR]

In this paper, plasticity effects at the tip of an edge through-the-thickness crack are investigated by invoking the strip-yield model and the first order plate theory. The latter theory is the simplest extension of the classical plane theories of elasticity, which is capable of accounting for three-dimensional effects and, in particular, the plate thickness effect. By utilising the distributed dislocation technique, new results are obtained on the interaction of the free boundaries (free edge and free plate planes) with the crack tip plasticity region. Numerical results for the crack tip opening displacement and global constraint factor are first presented at various crack length to plate thickness and applied stress to yield stress ratios. The results are validated against past 3D solutions for an embedded crack as well as analytical solutions obtained under the plane stress or plane strain assumption. The new model and results can be utilised in advanced fracture and fatigue analyses of cracks emanating from a free surface. [ABSTRACT FROM AUTHOR]

Numerous solutions of the plane theory of elasticity, derived over the past hundred years, provide a very good approximation to the in-plane stress components. However, an accurate evaluation of the out-of-plane (or transverse) stresses is often impossible as the three-dimensional stress field may not follow either plane stress or plane strain assumptions, specifically, near the edges formed by notches, cracks and other stress concentrators. For relatively simple geometries and loading conditions, the 3D stress and displacement fields can be analytically evaluated using the first-order plate theory. This theory can be considered as an elementary extension of the plane theory of elasticity and it retains the simplicity of the two-dimensional formulation. However, the derivation of exact solutions within this theory is far more difficult. In this paper, we present the governing equations of the first-order plate theory in arbitrary curvilinear coordinates, and based on these equations we develop a simplified method for the evaluation of the out-of-plane displacements and stress components. Several examples are considered to demonstrate the effectiveness and the accuracy of the new method. Due to simplicity it can be applied to investigate many 3D elastic problems involving sharp wedges and plate geometries weakened by cracks, notches and other stress concentrators. All these problems currently represent a great challenge for analytical approaches. [ABSTRACT FROM AUTHOR]

On the basis of the non-linear theory of elasticity and the invariant based formulation developed by Ogden, we analyse the effect of homogeneous stress on the propagation of Lamb waves. Using the theory of incremental deformations superimposed on large deformations, we derive the equations governing the propagation of small amplitude waves in a pre-stressed plate. By enforcing traction-free boundary conditions at the surfaces of the plate, we further obtain the characteristic equations for symmetric and anti-symmetric Lamb wave modes and investigate the effect of stress on the phase velocity, i.e. the acoustoelastic effect. A comparison with experimental data exhibits a better correlation than previously published results. The outcomes of this study can be utilised in the development of new techniques for the measurement of applied stresses based on the acoustoelastic effect. In particular, a strong sensitivity of the phase velocity to the applied stress near the cut-off frequencies of higher-order Lamb wave modes is a very promising option, which seems to have been overlooked in previous studies. [ABSTRACT FROM AUTHOR]

• Field of residual micro-strains changes with accumulation of HCF damage. • Hydrostatic residual micro-stress has a tendency to decrease with increasing HCF damage. • Only severe fatigue damage can be evaluated with the Neutron Diffraction method. • The full-width at half-maximum of the diffraction peak increases at high levels of damage. One of the most successful applications of the Neutron Diffraction (ND) method is the evaluation of residual stress, specifically in welded structures, and many examples exists in the literature. The present study explores the feasibility of applying the ND method to the evaluation of early high-cycle fatigue damage (i.e. the damage prior to formation of fatigue micro- or macro-cracks). In metals and advanced alloys early fatigue damage is normally associated with the accumulation of irreversible and highly localised micro-plastic strains. These strains change the micro-strain/stress field on various scale levels. In this study we attempt to measure these changes applying the ND method to G350 steel fatigue samples, which have been relieved from residual stress and subjected to various degrees of high-cycle fatigue damage. Multiple measurements of the strain/stress field in each sample have been undertaken using the ND method with an incoming beam of 0.5×0.5 mm2. The outcomes demonstrate that it is feasible to evaluate severe fatigue damage using the ND method, and, in general, the severity of the fatigue damage correlates relatively well with the averaged hydrostatic component of the residual stresses measured by the ND. However, more accurate evaluation may require higher spatial resolution (smaller gauge length) and, possibly, a larger number of measurement points to improve the quality of the experimental data. [ABSTRACT FROM AUTHOR]

Three-dimensional effects near crack front were subject of many analytical, numerical and experimental studies over the past 50 years. These studies were facilitated by obvious discrepancies between experimental evidences and predictions of two-dimensional theories of elasticity, which singular solutions currently form through a framework of contemporary Fracture Mechanics. In particular, the classical plane solutions of the theory of elasticity fail to describe the displacement, stress and strain fields in the close vicinity of the crack tip. Subsequently, the existing experimental techniques for determining stress intensity factor fully rely on the measurements taken outside the region affected by the three-dimensional effects, and, in particular, by 3D corner (vertex) singularity. In the present paper, we attempt for the first time to develop and validate an experimental procedure for accurate evaluation of mode I stress intensity factor from surface measurements of the transverse (out-of-plane) displacements over the area encapsulating the crack tip with a radius less than five per cent of the plate thickness. The proposed procedure can have several advantages in comparison with the existing experimental techniques. These are discussed in the paper. [ABSTRACT FROM AUTHOR]

We consider the problem of a multi-layered medium composed of an arbitrary number of perfectly bonded isotropic layers, with different thicknesses and elastic properties, when an edge dislocation of arbitrary orientation is present along one of the interfaces. A new effective solution is obtained for the complete stress and displacement fields induced by the interfacial edge dislocation in the multi-layered medium. The solution for the stress field due to the interfacial edge dislocation can be utilized to formulate governing equations for multiple interacting cracks in a multi-layered medium, with no restriction on the crack orientation, position and loading. The edge dislocation solution is validated directly by comparing it to available edge dislocation solutions and indirectly by revisiting some previously examined interfacial crack problems. [ABSTRACT FROM AUTHOR]

Prof. Lazzarin received the recognition for his distinguished contributions into the analysis of stresses in structural components weakened by sharp and blunt notches. He has been instrumental in developing the strain energy density approach for the evaluation of fracture initiation and characterisation of fatigue life. Some of the latest works of Prof. Paolo Lazzarin were devoted to the investigation of 3D effects in structures weakened by various stress concentrators. In this paper we continue to elucidate the role of 3D effects and apply the advanced digital image correlation technique to investigate experimentally the displacement and strain fields near a sharp notch front. The outcomes of this study are compared with the previous analytical and numerical results. In particular, we demonstrate the variation of the strain field across the thickness near the notch front, which cannot be described with the classical solutions of the plane theory of elasticity. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to considering the effect of seasonal changes in soil temperature on the performance of a horizontal geo heat exchanger. It is different from the existing models which consider seasonal changes in soil temperature by applying a real energy balance on the ground surface. In the new model, the seasonal changes in soil temperature, which are affected by the thermal interaction between the ground and the atmosphere, are expressed as an internal source term. The value of the internal source term depends on the soil density, soil specific heat, soil temperature difference during summer and winter, and time period. The simulation results show that the new approach, which takes into account the effect of periodic soil temperature fluctuations on the performance of the horizontal geo heat exchanger, is valid. [ABSTRACT FROM AUTHOR]

Brittle matrix composites such as fiber-reinforced cements and ceramics are often bonded to dissimilar materials such as metals or other ceramics. The mismatch in elastic properties can affect the growth of matrix cracks located near the bonded interface. In this paper, a bonded system comprising of an elastic layer sandwiched between two identical elastic half-spaces is considered. A mathematical model is developed based on the distributed dislocation technique, for the analysis of a bridged straight crack embedded in the elastic layer. The bridging tractions are considered to be dependent on the crack opening displacement. The stress field is assumed to be plane stress or plane strain and all three-dimensional effects are disregarded. The numerical results include the critical stress required to initiate failure of the matrix and the failure of fibers bridging the crack. The dependencies of these critical values upon the thickness of the composite layer as well as the mismatch in elastic properties are presented in dimensionless form. The results can be used to estimate the residual strength of bonded composites with a flaw near the material interface. [ABSTRACT FROM AUTHOR]

The fundamental problem of finding the effective linear and nonlinear elastic properties of a particulate composite subjected to finite elastic deformations is solved when the matrix and particulate phases are assumed to be weakly nonlinear. Weak nonlinearity is adequate to describe common engineering materials and composites loaded in the elastic regime. A nonlinear analogue of the Eshelby solution for the axisymmetric deformation of spherical particles is derived. Based on this solution, explicit asymptotic expressions for the effective linear and third-order (nonlinear) elastic moduli are derived in the case of a dilute distribution of spherical particles based on a general homogenisation methodology proposed by Hill. It is demonstrated that the current solutions correctly recover well-known relationships for the linear material properties of particulate composites as well as previously derived expressions for the effective nonlinear properties for certain special cases considered previously (e.g. hydrostatic loading, and a neo-Hookean matrix containing voids). The obtained theoretical results also agree with limited experimental data available in the literature. • A nonlinear analogue of the Eshelby solution for a weakly nonlinear spherical inhomogeneity is derived using a perturbation analysis. • The perturbation solution is used to derive relationships for the effective third-order elastic constants of a particulate composite. • Our analytical results generalise particular cases investigated before. • The derived relationships encompass results of linear elastic micromechanics. • The relationships are partially validated against experimental data and numerical studies. [ABSTRACT FROM AUTHOR]

Highlights: [•] We solve the problem of a rigid inclusion pressed between two elastic half spaces. [•] A new distributed dislocation and Föppl integral approach is developed. [•] The solution can be applied to cylindrical inclusions of arbitrary shape. [•] The present approach does not experience any computational difficulties. [•] Simplified solutions are also presented. All results are validated. [ABSTRACT FROM AUTHOR]

Abstract: In hydraulic stimulations of oil and gas wells, injection of proppant (or small particles) is normally needed to avoid the closure of the created fractures under confining stresses. The residual openings of these fractures determine the efficiency and, in general, the success of the hydraulic stimulations. Despite the vast number of papers devoted to fluid driven fractures and hydraulic stimulation procedures, there has not been much research conducted on residual fracture profiles. This problem is characterised by a strong non-linearity and represents a challenge for numerical modelling. In this paper a simple semi-analytical method for calculating the residual openings of fractures partially filled with proppant is developed. It is based on the Distributed Dislocation Technique and Terzaghi's classical consolidation model. One of the results of simulations indicates that the proppant distribution and its mechanical properties have a significant influence on the residual fracture profiles. [Copyright &y& Elsevier]

Abstract: When a crack or sharp notch is subjected to anti-plane shear loading the boundary conditions negate the transverse shear stress components at the free surfaces and generate a coupled in-plane shear stress field, which can be singular. For sharp V-notches with zero notch opening angle (or cracks) this 3D phenomenon was known for a long period of time. However this mode was largely ignored in stress analysis of notched components. Till now it is still unclear how significant this mode is and whether it has to be taken into consideration in integrity and failure analysis of engineering structures. The present paper is aimed to investigate this singular mode by means of the 3D Finite Element method, which is applied to notched plates with different notch opening angles and plate thicknesses. The stress state associated with the coupled mode is localised and quickly decays with the distance from the notch tip. Therefore, the obtained theoretical results can be applied to a wide range of notched components provided that the boundaries are sufficiently far from the notch tip. Among these results is the effect of the plate thickness on the intensity of the coupled mode; the latter increases with the decrease of the plate thickness. Significance of these new results to failure and integrity assessments of plate and shell components with sharp notches, including through-the-thickness cracks, is discussed in the final section of the paper. [Copyright &y& Elsevier]

Abstract: A simplified approach for calculating the conductivity of narrow fractures filled with a sparse monolayer of proppant particles is developed. The proppant particles are modelled as rigid spheres and the deformation of the fracture faces is assumed to be purely elastic. Hertz contact theory and the principle of superposition are utilised to obtain the fracture opening profile as a function of the proppant concentration and the value of confining stress. The conductivity of the deformed fracture channel is determined by using computational fluid dynamics. It has been demonstrated that some optimal proppant concentration exists, which maximises the fracture conductivity. Based on the simplified approach developed in this paper, the optimal concentration has been obtained as a function of the confining stress and the material properties of the fractured medium. The results are compared with previously published experimental data, which also indicate the existence of an optimal proppant concentration. A reasonable agreement between theoretical and experimental results is observed. [Copyright &y& Elsevier]

Abstract: It is well-known that residual opening of hydraulically stimulated fractures significantly influences the production rate of a well. Despite the numerous studies carried out in the past, there still is a lack of simple mathematical models capable of foreseeing the residual opening of fractures filled with granular particles and subjected to a confining pressure. In this paper a mathematical model based on the Distributed Dislocation Technique was developed and implemented to predict the height of the residual opening of a single crack filled with granular particles after releasing the stimulated hydraulic pressure. The mechanical response of the proppant (granular particles) to the applied pressure in this work was simulated by Terzaghi''s classical consolidation model. Two limiting cases were investigated in detail in order to demonstrate the model behaviour and validate the computational technique. The developed model can be further utilised to predict the increase of the production rate during hydraulic fracture stimulations and investigate other important phenomena influencing well productivity, such as, for example, secondary cracking of the fractured media. [Copyright &y& Elsevier]

Abstract: The 3D Finite Element method is applied to mixed fracture under anti-plane loading of a straight through-the-thickness crack in a linear elastic plate. This coupled fracture mode represents one of three-dimensional phenomena, which are currently largely ignored in numerical simulations and failure assessment of structural components weakened by cracks. It arises due to the boundary conditions on the plate free surfaces, which negate the transverse shear stress components corresponding to classical mode III. Instead, a new singular stress state in addition to the well-known 3D corner singularity is generated. This singular stress state (or coupled fracture mode) can affect or contribute significantly to the fracture initiation conditions. The coupled singular mode exists even if the applied anti-plane loading produces no singularities (K III =0). In this case there is a strong thickness effect on the intensity of the coupled fracture mode. [Copyright &y& Elsevier]

Abstract: Objectives: To provide a brief summary of the background theory of interfacial fracture mechanics and develop an analytical framework that identifies the critical factors for the analysis of the initiation and propagation of adhesion failure in composite restorations. Methods: A conceptual framework utilizing interfacial fracture mechanics and Toya''s solution for a partially delaminated circular inclusion in an elastic matrix, which can be applied (with caution) to approximate polymer curing induced cracking about composite resins for class 1 cavity restorations. Results: The findings indicate that: (1) most traditional shear tests are not appropriate for the analysis of the interfacial failure initiation; (2) material properties of the restorative and tooth material have a strong influence on the energy realize rate; (3) there is a strong size effect; and (4) interfacial failure once initiated is characterized by unstable propagation along the interface almost completely encircling the composite. Significance: The work is important for the analysis of the reliability of composite class I restorations and provides an adequate interpretation of recent adhesion debonding experimental results utilizing tubular geometry of specimens. The approach clearly identifies the critical parameters including; curing strain, material modulii, size and interfacial strain energy release rate for reliable development of advanced restorative materials. [Copyright &y& Elsevier]

Abstract: A new approach to calculation of the elastic bulk modulus of low consolidated porous media in the vicinity of the percolation limit under dry and saturated conditions is developed based on a physical consolidation model of rocks and the classical contact theory developed by H. Hertz in 1882. The derived analytical relationships for the elastic bulk modulus, which take into account the structural architecture of packing, are compared with theoretical predictions from popular micromechanic theories, Hashin–Shtrikman strict bounds as well as with experimental results available for low consolidated granular materials. The latter comparison demonstrates a good agreement under both dry and water saturated conditions. [Copyright &y& Elsevier]

Abstract: Pipes transporting gas or liquid can be subjected to impulse loading as a result of an accident. In many previous studies the effects of the flowing media on the transient response of pipes were largely ignored or considered to be negligible. This paper aims to shed light on the significance of these effects. First, we present a simplified mathematical model of a pipe filled with a flowing liquid or gas and subjected to dynamic loading. This model is based on the well-known Bernoulli–Euler beam theory, but also incorporates forces generated by the internal flow which follows the pipe lateral deflections and generates the inertia, centrifugal and Coriolis flow accelerations. Further, we develop asymptotic analytical and numerical methods for the analysis of the governing equation. Finally, as example, we investigate in detail the effect of the flow parameters on the dynamic response of a cantilever pipe subjected to impulse loading. Special attention is given to the pipe whip phenomenon, which causes growing unlimited displacements of the pipe regardless of how small the value of the applied loading is. The developed theoretical methods provide a framework for analysis of many other dynamic problems of pipes with flowing media subjected to arbitrary boundary and loading conditions. [ABSTRACT FROM AUTHOR]

Abstract: Notched plates are often found in various applications ranging from microelectronic devices to large-scale civil structures. Stress analysis of plate components wherein the loading is uniformly distributed over the thickness, parallel to the plane of the plate, is normally based on plane stress or plane strain assumptions. Three-dimensional effects, such as the influence of the plate thickness on stress components, are largely ignored or considered as negligible for all practical purposes. This paper summarizes recent theoretical and numerical studies and discusses some important features of the three-dimensional singular solutions for sharp notches obtained within linear elasticity. Taking into account dimensionless considerations, the relationships between the intensities of the singular stress states corresponding to the three-dimensional linear elastic solutions and the plate thickness are established. The obtained relationships have many intriguing implications for the failure assessment of notched plates made of sufficiently brittle material. For example, based on a similar argument to the one used in classical linear-elastic fracture mechanics, it can be shown that a sufficiently thick plate with a sharp re-entrant corner should have virtually zero strength when subjected to antisymmetric (or mixed mode) loading. The theoretical conclusions drawn in this paper have direct applications to fracture testing and fracture assessment of plate components, and they set new goals for further experimental studies. [Copyright &y& Elsevier]

Abstract: Experiments have shown that the application of an overload cycle can act to retard crack growth and even potentially lead to crack arrest. This paper describes a new method for investigating fatigue crack growth after the application of an overload cycle under plane stress conditions. The developed method is based on the concept of plasticity-induced crack closure and utilises the distributed dislocation technique and a modified strip-yield model. The present results are compared to previous experimental data for several materials. A good agreement is found, with the predictions showing the same trends in the various stages of post-overload crack growth. [Copyright &y& Elsevier]

Abstract: Crack growth rates are significantly affected by the thickness of the specimen when all other parameters are kept constant. A quantitative estimation of the thickness effect is thus necessary to make predictions of crack growth rates more accurate and reliable. For this purpose a theoretical model was developed based on the strip-yield assumption and first-order plate theory. No empirical or fitting parameters were used in this work unlike some previous studies. The theoretical values obtained for the normalised load ratio parameter, U, were employed to describe experimental data, obtained under small-scale yielding conditions, at various load ratios and plate thicknesses. Such a representation considerably narrowed the scatter in the crack growth rates versus the effective stress intensity factor range, ΔK eff, demonstrating the potential of the theoretical model. [Copyright &y& Elsevier]

Abstract: Adhesive resin-based restorative materials have the potential to considerably strengthen teeth and offer more economically viable alternatives to traditional materials such as gold, amalgam or ceramics. Other advantages are direct and immediate placement and the elimination of the use of mercury. However, polymerization shrinkage during curing of an adhesive restoration and mismatch in mechanical properties can lead to the initiation and development of interfacial defects. These defects could have a detrimental effect on the longevity of the restored tooth. The current study is focused on some design issues of resin-based composites affecting the longevity of the tooth–restoration interface. The theoretical approach is based on self-consistent micromechanical modelling that takes into account the effect of the material properties, volume concentration of the dispersed particle phase as well as the shape of these particles on the overall thermomechanical properties of the composite. Results obtained for resin-based composites reinforced with spherical, disc and short fibre particles highlight the advantages of disc shaped and short fibre particles. [Copyright &y& Elsevier]

Abstract: Geometric singularities for perfect bond constitute a fairly well explored area in linear elasticity. In this paper, an effect of a thin plastic adhesive layer on the singular stress field at the interface corner of a glued bi-material wedge is studied within a simple model. Following the conventional one-dimensional analysis of bonded joints, the adhesive layer is treated as a layer of displacement discontinuity between two materials. A new characteristic equation for the determination of the characteristics of the singular stress field is derived based on the classical works of Williams and Bogy. The new characteristic equation is studied for certain particular composites and angles, which commonly occur due to joining dissimilar materials. The focus of this paper is the problem associated with elimination of the singular stress field, with the goal of providing an approach for designing singular-free adhesive joints. [Copyright &y& Elsevier]

Abstract: The purpose of this investigation was to adopt an analytical approach to analyse stresses at the restoration–dentine interface caused by polymerization shrinkage, occlusal and thermal loading with the primary focus on evaluating the effect of the material properties of the composite restoration on the strength of the interface. Some essential simplifications were employed to derive an explicit analytical solution. The results confirm previous findings that interfacial stresses due to polymerization shrinkage are increased with the higher modulus of elasticity of the restoration, while Poisson''s ratio of the restorative material has a very small influence on these stresses. Occlusal loading resulted in much lower interfacial stresses when compared to shrinkage and thermal loads. The obtained results were in a good agreement with other numerical and clinical studies. From the modelling analysis it was found that the majority of commercially available composite restorative materials are expected to create significant interfacial stresses when subjected to cold temperatures. In addition, it was shown that there is a considerable potential for interfacial stresses to be minimised by an appropriate selection of thermo-mechanical properties of the restorative material especially with the new finding on the negative temperature variation effect. [Copyright &y& Elsevier]

Abstract: Objective: The ultimate success or failure of a restored tooth is largely dependent on clinical management. Clinicians may choose from a number of restorative materials, different clinical techniques and cavity preparation procedures. The purpose of this study was to specifically examine aspects of the material choice holding other factors constant. Methods: The current paper adopts a fundamental result in the linear theory of elasticity on the singular stress distribution in a bi-materials wedge to analyze the fracture susceptibility of different materials used for the restoration of a tooth. Results: Comparable results are reported for amalgam, gold alloys and ceramic materials. It is shown that due to a wide variety of mechanical properties the application of resin-based composites could lead to improved or less fracture resistance of the restored tooth. Significance: This variety in the mechanical properties for resin-based composites could be partially responsible for the contradictory evidences reported by different clinical studies. The present work contributes evidence from an analytical model to assist the restorative dentist in selection of an appropriate restorative material and guide the manufacturing companies on the preferred physical properties of newer designed materials. [Copyright &y& Elsevier]

Abstract: The accuracy of flaw assessment techniques for welded joints is directly related to the accurate estimate of the yield collapse load. A careful finite element limit analysis can provide a very good and reliable assessment of the collapse load. Unfortunately, such an analysis is normally time-consuming and requires a substantial effort in order to validate the finite element calculations. In this paper we apply the classical upper bound theorem of plasticity to develop simplified solutions for a through crack in a tensile plate with a mismatched welded joint. The weld configuration is idealised as a simple sandwich model and the collapse load is derived analytically from a solution of an extreme-value problem. The theoretical solutions are then verified by independent finite element calculations. The proposed solutions seem to be very effective and accurate and can be easily generalized for many other weld geometries and loading conditions. [Copyright &y& Elsevier]

Abstract: Background: Numerous analyses for the shrinkage stress in the adhesive resin-based composite restorations mostly rely on numerical models. However, various finite element studies have inherent difficulties and inconsistencies associated with the use of different anatomy (tooth and restoration), boundary conditions (root and interfaces) and shrinkage models. As a consequence many numerical results remain inconclusive. Objective: The objective of this paper is to develop a simplified analytical model of shrinkage stress and investigate effects of material properties of the restorative material, size of the restoration and volumetric shrinkage on the magnitude of the shrinkage stress in the vicinity of the dental-restoration interface. Methods: The model is based on the following assumptions. The geometry is axisymmetric; all materials are linear-elastic; and the polymerization of the restoration material results in uniform volume shrinkage. An application of compatibility conditions leads to the system of five linear algebraic equations to five unknown variables, which can be easily resolved using standard techniques. Results: An explicit equation for the tensile stress at the interface was obtained. It was shown that higher Young''s modulus, Poisson''s ratio and volume shrinkage of the restorative material normally lead to larger tensile stress at the interface, which increases the risk of debonding. The results obtained based in this work, in general, are in a good agreement with published results of finite element studies. Significance: The model allows comparison of different adhesive restorative materials with respect to the fracture risk of the interface induced by the development of the shrinkage stress at the restoration–dentine interface during polymerization. The model can be used to validate more sophisticated computational models as well as to conduct various optimization studies and preliminary assessments of fracture risk. [Copyright &y& Elsevier]

Abstract: The stress singularities in angular corners of plates of arbitrary thickness with various boundary conditions subjected to in-plane loading are studied within the first-order plate theory. By adapting an eigenfunction expansion approach a set of characteristic equations for determining the structure and orders of singularities of the stress resultants in the vicinity of the vertex is developed. The characteristic equations derived in this paper incorporate that obtained within the classical plane theory of elasticity (M.L. Williams’ solution) and also describe the possible singular behaviour of the out-of-plane shear stress resultants induced by various boundary conditions. [Copyright &y& Elsevier]

• The critical angle hypothesis has been suggested more than forty years ago. • More than a dozen of past experimental studies have been analysed. • Experimental evidences are controversial. • The hypothesis is valid for a steady state crack propagation and sufficiently small plastic zone size. More than forty years ago, several researchers suggested a hypothesis that the front of a fatigue crack must intersect the free surfaces at a certain (critical) angle to ensure the finite energy flux at the terminal (vertex) point(s). Since its formulation, this hypothesis was under scrutiny in many studies, which utilised various materials, cyclic loading conditions and different specimen geometries. The outcomes of these studies were very divisive: from overwhelming confirmation of this hypothesis to total abjuration. In this paper, we first discuss the conditions, which can affect the shape of the crack front near free surfaces. Further, we demonstrate that the critical angle hypothesis seems to be valid when the plastic (or process) zone is much smaller than the size of the region controlled by 3D vertex singularity. As demonstrated in a number of past numerical studies, this size is related to the crack and specimen geometry, e.g., to the crack front length. Past experimental studies also indicate that fatigue crack fronts tend to intersect the free surface at the critical angle at the steady-state growth rather than when the crack propagation leads to the changes or evolution of the crack front, e.g., during propagation of fatigue cracks in round bars. [ABSTRACT FROM AUTHOR]

The paper reviews the current state-of-the art of modern computational tools which can be adopted to support Full-Scale Fatigue Tests (FSFTs) of airframes. A suite of validated and verified simulation tools could potentially deliver significant time and cost savings during the design, certification, and operation phases of both civilian and military aircraft. The review is largely derived from research articles published in international journals and conference proceedings over the past 10 years. An emphasis is placed on computer-based multiscale fatigue damage modelling techniques, probabilistic approaches, and experimental methods, which have emerged over the past decade for both metallic and composite structures. Finally, several recommendations are made on the further development of computational simulation tools for the purpose of augmenting physical fatigue testing of airframes. [ABSTRACT FROM AUTHOR]

• New analytical method for fatigue analysis of structures with surface cracks. • A good agreement is achieved with previous numerical and experimental studies. • The method allows for development of empirical closure models. This paper presents a new analytical method for the analysis of fatigue growth of surface cracks in various structural components. The method is based on a governing equation describing the front evolution of surface cracks of elliptical and part-elliptical shapes. This method avoids the need for various numerical schemes for the calculation of the incremental crack front advance, which were used in all previous studies. Plasticity-induced crack closure models can also be incorporated into the method or these models can be deducted from a correlation of experimental data and the method predictions. When the plastic constraint conditions change significantly along the crack front, the implementation of the plasticity induced crack closure models can significantly improve the accuracy of fatigue life predictions. The method is validated against previous theoretical and experimental studies. [ABSTRACT FROM AUTHOR]

Abdominal aortic aneurysm (AAA) is a pathological condition characterised by localised dilation of the infrarenal aorta, which can be fatal if rupture occurs. Current diagnostic criteria for repair are not patient-specific, but computational modelling may help to predict the potential growth and risk of AAA rupture accurately. This paper highlights how important using the Windkessel effect and fully-developed inflow velocity framework for the biomechanical analysis of AAA is; in other words, this research investigates how different boundary conditions in modelling methods affect the ability to correctly represent the biomechanics of AAA with complex non-linear parameters using a two-way fluid–structure interaction (FSI) technique. Time-averaged wall shear stress (TAWSS) is highly sensitive to boundary conditions, so unrealistic or simplified boundary conditions can lead to very different TAWSS results. This study also revealed that the use of outflow 3-element Windkessel boundary conditions on pulsatile pressure affects the flow pattern and increases the flow recirculation period. By accounting for the Windkessel effect and preventing backflow in numerical studies of AAA, the maximum displacement found in the distal branches can also be reduced. Models assuming plug velocity profiles overestimate peak wall stress by approximately 20% compared with models using fully developed parabolic inlet velocity profiles. This study incorporated a three-layer anisotropic material model and non-Newtonian fluid properties into the simulation, providing a more realistic representation of the effect of boundary condition selection on AAA mechanics. The results summarised from the parametric study could contribute to better prediction of AAA growth and rupture risk, and have important implications for the development of improved treatment strategies for AAA patients. • Fluid–structure interaction model enables more realistic representations for AAA. • Time-averaged wall shear stress is sensitive to boundary conditions. • Windkessel effect reduces maximum displacement on the distal branches of the aorta. • Plug velocity profiles overestimate peak wall stress by 20%. • Back-flows at abdominal aortic aneurysm outlets increase flow recirculation period. [ABSTRACT FROM AUTHOR]