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This paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.

In the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.

The reduced integration, performed by this linearly integrated formulation, plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy and, which is most important, presents no instabilities, unlike nodal integration methods without stabilization. As a consequence of using such a convenient linearly integrated local form, the derived meshfree and finite element numerical methods become fast and accurate, which is a feature of paramount importance, as far as computational efficiency of numerical methods is concerned. Three benchmark problems were analyzed with these techniques, in order to assess the accuracy and efficiency of the new integrated local formulations of meshfree and finite element numerical methods. The results obtained in this work are in perfect agreement with those of the available analytical solutions and, furthermore, outperform the computational efficiency of other methods. Thus, the accuracy and efficiency of the local numerical methods presented in this paper make this a very reliable and robust formulation.

Presentation of a new local mesh-free numerical method. The method, linearly integrated along the boundary of the local domain, implements an algorithm with no further integration required. The method is absolutely reliable, with remarkably-accurate results. The method is quite robust, with extremely-fast computations.

According to the microstructural characteristics of composite ceramic, the strain field distribution regularity of triangular symmetrical composite eutectic is obtained from the stress field distribution regularity of three-phase element in composite ceramic. In allusion to the damage of composite eutectic, it is introduced as a variable in this paper with the aim to determine the strain field distribution regularity of triangular symmetrical composite eutectic with damage behavior.

On the basis of the relationship between strain field and fiber inclusions volume fraction, the strain field of composite eutectic is analyzed.

The strain field of composite ceramic is distinctly dependent on the fiber inclusions volume fraction, fiber diameter and damage behavior of composite eutectic by quantitative analysis. The strain in matrix parallel to eutectic is the maximum linear strain and the main factor for the damage and fracture of eutectics.

The foundation of the strength research of composite eutectic is laid.

Recently, a new class of fatigue crack growth models based on elastoplastic stress‐strain histories at the crack tip region and strain‐life fatigue damage models have been proposed. The fatigue crack propagation is understood as a process of continuous crack initializations, over elementary material blocks, which may be governed by strain‐life data of the plain material. The residual stresses developed at the crack tip play a central role in these models, since they are used to assess the actual crack driving force, taking into account mean stresses and loading sequential effects. The UniGrow model fits this particular class of fatigue crack propagation models. The purpose of this paper is to propose an extension of the UniGrow model to derive probabilistic fatigue crack propagation data, in particular the derivation of the P–da/dN–ΔK–R fields.

An existing deterministic fatigue crack propagation model, based on local strain‐life data is first assessed. In particular, an alternative methodology for residual stress computation is proposed, based on elastoplastic finite element analysis, in order to overcome inconsistencies found in the analytical approximate approaches often used in literature. Then, using probabilistic strain‐life fields, a probabilistic output for the fatigue crack propagation growth rates is generated. A new probabilistic fatigue field is also proposed to take mean stress effects into account, using the Smith‐Watson‐Topper (SWT) damage parameter. The proposed models are assessed using experimental data available for two materials representative from old Portuguese bridges.

A new method to generate probabilistic fatigue crack propagation rates (P–da/dN–ΔK–R fields) is proposed and verified using puddle iron from old Portuguese bridges, usually characterized by significant scatter in fatigue properties. Also, a new probabilistic fatigue field for plain material is proposed to deal with mean stress effects.

A relation between the P–ε–N and the P–da/dN–ΔK–R fields is firstly proposed in this research. Furthermore, a new P–SWT–N field is proposed to deal with mean stress effects.

The weld region obtained during friction stir welding (FSW) of metallic materials (including aluminum alloys) contains typically well-defined zones, each characterized by fairly unique microstructure and properties. The purpose of this paper is to carry out combined experimental and numerical investigations of the mechanical properties of materials residing in different weld zones of FSW joints of thick AA2139-T8 plates.

Within the experimental investigation, the following has been conducted: first, optical-microscopy characterization of the transverse sections of the FSW joints, in order to help identify and delineate weld zones; second, micro hardness field generation over the same transverse section in order to reconfirm the location and the extent of various weld zones; third, extraction of miniature tensile specimens from different weld zones and their experimental testing; and finally, extraction of a larger size tensile specimen spanning transversely the FSW weld and its testing. Within the computational investigation, an effort was made to: first, validate the mechanical properties obtained using the miniature tensile specimens; and second, demonstrate the need for the use of the miniature tensile specimens.

It is argued that the availability of weld-zone material mechanical properties is critical since: first, these properties are often inferior relative to their base-metal counterparts; second, the width of the weld in thick metallic-armor is often comparable to the armor thickness, and therefore may represent a significant portion of the armor exposed-surface area; and finally, modeling of the weld-material structural response under loading requires the availability of high-fidelity/validated material constitutive models, and the development of such models requires knowledge of the weld-material mechanical properties.

The importance of determining the mechanical properties of the material in different parts of the weld zone with sufficient accuracy is demonstrated.

Crack damage detection for aluminum alloy materials using fiber Bragg Grating (FBG) sensor is a kind of structure health monitoring. In this paper, the damage index of full width at half maximum (FWHM) was extracted from the distorted reflection spectra caused by the crack-tip inhomogeneous strain field, so as to explain the crack propagation behaviors.

The FWHM variations were also investigated through combining the theoretical calculations with simulation and experimental analyses. The transfer matrix algorithm was developed to explore the mechanism by which FWHM changed with the linear and quadratic strain. Moreover, the crack-tip inhomogeneous strain field on the specimen surface was computed according to the digital image correlation measurement during the experiments.

The experimental results demonstrated that the saltation points in FWHM curve accorded with the moments of crack propagation to FBG sensors.

The interpretation of reflected spectrum deformation mechanism with crack propagation was analyzed based on both simulations and experiments, and then the performance of potential damage features – FWHM were proposed and evaluated. According to the correlation between the damage characteristic and the crack-tip location, the crack-tip of the specimen could be measured rapidly and accurately with this technique.

The purpose of this paper is to study techniques of pattern recognition in the strain field as structural health monitoring tools. The changes in the strain field may be very intense at the tip of a crack but smooth out very quickly. So trying to get information about damage occurrence from strain measurements is a difficult task, as the detected strain changes may be very small and masked by temperature drifting, load changes or any other environmental factor.

It drives to the need to include a large sensor array into the structure, which is not difficult when using optical fiber sensors. Experiments were done on a simple cantilever beam, instrumented with 32 sensors and submitted to loads and progressive damage conditions. The same approach was applied to a more complex structure, the wing of an unmanned air vehicle (UAV) made in composite materials.

Algorithms based on principal component analysis (PCA), damage indices and damage thresholds were used and shown to be simple and robust enough for this task.

The data treatment was done in a fully automated approach; an algorithm to compare and extract information from the multiple strain measurements was developed for this task.

Fatigue crack growth models based on elastic‐plastic stress‐strain histories at the crack tip region and strain‐life damage models have been proposed. The UniGrow model fits this particular class of fatigue crack propagation models. The residual stresses developed at the crack tip play a central role in these models, since they are applied to assess the actual crack driving force. This paper aims to assess the performance of the UniGrow model based on available experimental constant amplitude crack propagation data, derived for several metallic materials from representative Portuguese bridges. It also aims to discuss key issues in fatigue crack growth prediction, using the UniGrow model, in particular the residual stress computation and the suitability of fatigue damage rules.

The UniGrow model is assessed using data derived by the authors for materials from Portuguese riveted metallic bridges. Strain‐life data, from fatigue tests on smooth specimens, are used to propose a convenient fatigue damage model. Predicted crack growth rates are compared with experimental crack propagation data obtained by authors using fatigue tests on compact tension specimens. Since the UniGrow model is a residual stress‐based propagation model, elastoplastic finite element analysis is proposed for comparison with the analytical approach implemented in the original UniGrow model.

The use of the Smith‐Watson‐Topper damage parameter overestimates the stress R‐ratio effects on crack propagation rates, mainly if the material shows crack propagation rates with small to moderate sensitivity to stress R‐ratio, which is the case of the materials under investigation in this paper. Alternatively, the application of the Coffin‐Manson damage law leads to consistent fatigue crack growth predictions for the investigated range of positive stress R‐ratios. The stress R‐ratios effects may be solely attributed to the residual stresses. Their estimation, using an analytical approach, may lead to inconsistent results, which is demonstrated by an alternative elastoplastic finite element analysis.

Contributions for more accurate predictions of fatigue crack propagation rates, for several stress ratios, using a strain‐based approach is proposed. This approach is valuable since it may be used to reduce the time consuming and costly fatigue crack propagation tests. Furthermore, the proposed approach shows potential for an unified crack initiation and propagation approach.

The purpose of this paper is to introduce a computational time dependent modeling to investigate propagation of elastic-viscoplastic zones in the shock wave loaded circular plates.

Constitutive equations are implemented incrementally by the Von-Kármán finite deflection system which is coupled with a mixed strain hardening rule and physical-base viscoplastic models. Time integrations of the equations are done by the return mapping technique through the cutting-plane algorithm. An integrated solution is established by pseudo-spectral collocation methodology. The Chebyshev basis functions are utilized to evaluate the coefficients of displacement fields. Temporal terms are discretized by the Houbolt marching method. Spatial linearizations are accomplished by the quadratic extrapolation technique.

Results of the center point deflections, effective plastic strain and stress (dynamic flow stress) and temperature rise are compared for three features of the Von-Kármán system. Identifying time history of resultant stresses, propagations of the viscoplastic plastic zones are illustrated for two circumstances; with considering strain rate and hardening effects, and without them. Some of modeling and computation aspects are discussed, carefully. When the results are compared with experimental data of shock wave loadings and finite element simulations, good agreements between them are observed.

This computational approach makes coupling the structural equations with the physical descriptions of the high rate deformation through step-by-step spectral solution of the constitutive equations.

The purpose of this paper is to study mutual interaction between von Mises equivalent and hydrostatic stresses at the crack tip area of an elastoplastic material in order to obtain critical conditions for crack propagation under fatigue loading.

A5083-H111 aluminum alloy is used to obtain a Chaboche-type constitutive equation, which is introduced in a commercial finite elements package to evaluate stress distribution at crack tip area. A simplified three-dimensional (generalized plane strain) grid is used, resulting in fast and accurate results. Numerical simulations are performed to connect crack propagation rate with various combinations of fatigue stress amplitude, initial crack length and number of loading cycles. Distance between characteristic points of stresses distribution in the crack tip area are compared to experimental fatigue crack growth rates in order to assess the validity of the present approach.

It is found that saturation of plastic strains, i.e. maximization of von Mises equivalent stress, is a prerequisite for hydrostatic stress to take a critical-maximum value, outside the plastically saturated zone. At the point of maximum hydrostatic stress brittle fracture is initiated, driving to separation of the ligament up to crack tip, without formation of new plastic strains. The length of this ligament is defined as crack propagation step, showing good agreement with experimental data.

The present approach seems to constitute a reasonable and adequate method for the description of fatigue crack propagation in terms of continuum mechanics, not necessitating microscopic considerations or empirical criteria lacking theoretical or physical basis. In addition, it liberates from the notion of stress intensity factors, strongly disputed beyond linear elasticity. Improved constitutive equations and numerical models are expected to drive in a complete fatigue failure criterion similar to those of static loading.

Mechanical issues related to the information and growth of small cracks are considered to play a major role in very high cycle fatigue (VHCF) for metallic materials. Further efforts on better understanding in early stage of a crack are beneficial to estimating and preventing catastrophic damage for a long period service.

Dependent on the ultrasonic loading system, a novel method of in situ photomicroscope is established to study the crack behaviors in VHCF regime.

This in situ photomicroscope method provides advantages in combination with fatigue damage monitoring at high magnification, a large number of cycles, and efficiency. Visional investigation with attached image proceeding code proves that the method has high resolution on both size and time, which permits reliable accuracy on small crack growth rate. It is observed that the crack propagation trends slower in the overall small crack stage down to the level of 10–11 m/cycle. Strain analysis relays on a real-time recording which is applied by using digital image correlation. Infrared camera recording indicates the method is also suitable for thermodynamic study while growth of damage.

Benefiting from this method, it is more convenient and efficient to study the short crack propagation in VHCF regime.