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Enhancing the strength and ductility of metallic materials simultaneously is crucial for numerous industrial applications, yet it remains a formidable challenge due to the typical trade-off between these two properties. This study introduces an innovative approach to surmount this challenge by employing a composite bar design that leverages necking inhibition mechanisms for simultaneous improvements in both strength and ductility. The composite bars, comprising aluminum cores reinforced with spirally wound fiber-reinforced polymer (FRP) strands, were fabricated in various configurations to investigate different necking behaviors. Through uniaxial testing, the composite bars exhibited notable increases in both strength and ductility, attributed to the strategic design of the FRP winding angle and FRP content. This design effectively modulates the necking behavior, thereby enhancing the composite bars' mechanical properties. Analysis of the strain distribution further elucidated the role of the spiral FRP strands in necking prevention. The composite bar design method outlined in this study offers a viable strategy for enhancing the mechanical performance of metallic materials, significantly reducing the risk of abrupt failure under high loads and deformations. [ABSTRACT FROM AUTHOR]

A large number of structures in the United States and worldwide include nonductile reinforced concrete (RC) frames with columns and beams that are prone to shear failure. Due to the brittle nature of shear failures, accurate simulation of RC structures with shear-critical members is essential to predicting their overall capacity under severe loading scenarios (e.g., earthquakes) and designing effective retrofits and upgrades. In this paper, a previously developed gradient inelastic (GI) force-based (FB) beam-column element formulation capable of capturing axial-flexural interaction and predicting flexural failures is extended to account for axial-flexural-shear interactions in RC members in order to predict shear failures. The proposed shear-enhanced GI FB element formulation advances the original GI FB element formulation by developing higher-order cross section kinematics, i.e., beyond the plane sections assumption, and by developing a 3D concrete constitutive model. The higher-order cross section kinematics can simulate strain distribution of the cross section more accurately while using 3D concrete constitutive models at the element's cross sections permits simulation of axial-flexural-shear interactions. To incorporate the confinement effects of transverse steel reinforcement, through-the-depth stress equilibrium is strictly enforced in the transverse directions of the member's cross section. To eliminate strain localization phenomena, new gradient nonlocality relationships are introduced in addition to those of the original GI FB formulation. The proposed element formulation is implemented in the OpenSees structural analysis software and is shown to maintain continuous macroscopic section strain distributions over the element length during softening and discretization convergent responses, thereby eliminating the strain localization phenomena. In addition, the predictions of the shear-enhanced GI FB element formulation are compared with data available from experiments on RC beams and columns. [ABSTRACT FROM AUTHOR]

The present experimental study is focused on quantifying the initiation and propagation of desiccation cracking and strain localization in lime-treated compacted expansive soils subjected to controlled temperature and relative humidity conditions. Two bench-scale experimental setups were designed and developed in this study to capture the desiccation cracking and strain localization in soil specimens using digital image processing (DIA) and digital image correlation (DIC) techniques, respectively. A Python program was also developed for autodetection of optimum threshold intensity for crack segmentation, which considerably reduced the chances of noise in DIA and allowed accurate batch processing of multiple images. An open-source software Ncorr was used for two-dimensional DIC analysis to obtain strain localization plots during the desiccation process of soil. The effectiveness of the lime treatment technique for the stabilization of expansive soil was evaluated by considering the major issues of expansive soils such as swelling, shrinkage, unconfined compressive (UC) strength, and desiccation cracking. The results revealed that the lime treatment was ineffective in controlling the desiccation cracking of expansive soil. Only a small percentage of lime (2% or less) was found to slightly reduce the desiccation cracking. However, such small quantities of lime were not found enough to fully sway the swelling and shrinkage nature of the soil. A significant change in the crack pattern was observed in specimens treated with 3% or higher amount of lime. The total length of cracks increased up to 75% due to the addition of 6% lime compared with untreated soil. Similarly, more localized deformation zones were observed in strain localization plots of specimens treated with 3% or higher amounts of lime. [ABSTRACT FROM AUTHOR]

In the presence of softening section constitutive relations, classical beam theories predict erroneous strain singularities, and the corresponding force/flexibility-based (FB) beam-column element formulations result in strain localization and loss of response objectivity, i.e., divergence, rather than convergence, with progressive mesh refinements. To address this challenge, various FB element formulations have been proposed in the literature. One of these formulations is the so-called "gradient inelastic" (GI) FB formulation, which is a two-node element formulation that eliminates the strain localization and achieves response objectivity through strain gradient nonlocality relations. Although a single two-node GI element can effectively simulate an entire beam or column, simulating such a member via multiple two-node GI elements in series (e.g., to apply intermediate point loads, to more accurately capture geometric nonlinearities, or to represent cross-section variation) would not lead to accurate response predictions. This is because, in a model with multiple two-node GI elements in series, the nonlocality relations are not enforced at the intermediate/connection nodes between adjacent elements. Instead, end member boundary conditions (BCs) are enforced at those connection nodes because the two-node GI formulation has been designed to simulate an entire member. To tackle this shortcoming, this paper proposes an innovative multinode GI FB element formulation. To enforce the nonlocality relations at the connection nodes, two different sets of mathematically admissible section strain compatibility conditions (CCs) are adopted. The multinode formulations using both sets of CCs are evaluated through several simulation examples, including beams and columns subjected to various loads. The evaluations demonstrate the ability of both element formulations to produce objective softening responses, while one set of CCs is found to more closely predict the responses of previously tested RC beams under midspan loading. [ABSTRACT FROM AUTHOR]

A multiscale approach that couples the finite-element method (FEM) and the discrete-element method (DEM) is used to model and analyze the earthquake fault rupture–soil–foundation interaction (FR–SFI) problem. The approach obtains the soil constitutive responses from the DEM solutions of representative volume elements (RVEs) embedded at the FEM integration points, effectively bypassing the phenomenological hypotheses in conventional FEM simulations. The fault rupture surfaces and shear localization patterns under normal and reverse faults with or without foundation atop were adequately captured using the multiscale approach and verified with available centrifuge experimental and numerical results. An examination of the stress-strain responses and the microstructural evolutions of local RVEs revealed that the RVEs located in or immediately outside the shear bands behaved distinctly and might change their stress states from initially at rest to active under normal fault or passive under reverse fault. The micromechanics study also sheds light on the capability of heavy foundations to protect the superstructure due to rupture surface diversion under reverse fault and their possible detriment under normal fault. [ABSTRACT FROM AUTHOR]

Through natural selection, living systems have evolved elegant hierarchical structures with excellent mechanical properties and efficient biological functions. The helical tendrils of climbing plants are known for their intriguing geometry and superior deformability. Many engineering materials are vulnerable to plastic strain localization, and the efficiency of material usage can be significantly improved by suppressing strain localization. Inspired by plant tendrils, a novel structural design of ultraductile engineering materials is proposed in this work. A cylindrical metallic bar is considered as an example. In the proposed design, a number of strands are wound spirally about and bonded to the bar. The effectiveness of the design in improving the deformation capacity of the metallic bar is demonstrated by numerical simulations and experimental tests. In the postnecking process, the maximum principal strain in the composite bar is distributed more evenly than that in the bare bar. This work provides a way for improving the deformability and ductility of a diversity of engineering materials, which can prevent these materials from failing under excessive deformation. [ABSTRACT FROM AUTHOR]

Within the framework of second-order cone programming optimized micropolar continuum finite-element method (CosFEM-SOCP), the geotechnical strain localization can be adequately modeled. In most existing literatures, however, the constant internal characteristic length lc has been adopted and less attention has been paid to the evolution of lc. To more accurately predict the strain localization, response, and stability of a geotechnical system, one relationship for evolving lv that relies on the equivalent plastic strain is implemented and investigated. Based on one homogeneous slope example and one rigid strip footing example, it was found that geotechnical stability may not be significantly affected by evolving lv, indicating that constant lc can be simply applied to geotechnical stability analysis. For the rigid strip footing problem, nevertheless, the effects of evolving lv on the pressure–displacement response curves should not be ignored, and the influence range of the shear band predicted by CosFEM-SOCP with evolving lv is generally smaller than that predicted by CosFEM-SOCP with constant lc. Consequently, in order to more accurately predict the pressure–displacement response curves and the failure zone, the evolving lv will be adequately assessed and modeled. [ABSTRACT FROM AUTHOR]

This study investigates the effect of loading boundary conditions on the mechanical behavior of cuboidal sand specimens during plane strain (PS) testing. Deformation-controlled PS compression tests were performed with flexible boundaries (FB) on varying densities of sand. Further, rigid-frictional and rigid-lubricated boundary triaxial compression tests were performed on cuboidal specimens with aspect ratios of 2∶1 and 1∶1 , respectively. The results of PS testing with the loading boundary of different relative rigidity indicate a significant change in the observed response. The relatively rigid boundaries along the loading direction tend to overestimate the stress ratio compared with those with FBs. The FB-PS tests in the present study reveal no softening behavior, unlike those exhibited in conventional triaxial tests with rigid end boundaries. The imposed kinematic constraints for PS tests resulted in higher friction angle values compared with the triaxial tests. Local strain evolution and various deformation modes were analyzed using digital image analysis, which provides ensuing insights regarding its relation to the macro-scale global material response. [ABSTRACT FROM AUTHOR]

The influence of perturbation magnitude and extent of area on the emergence of localized instability in sand specimens subjected to biaxial loading has been explored within a numerical framework using a generalized 3D material model. In this regard, this article seeks to examine the effect of perturbation type in terms of material imperfection and subsequently attempts to characterize mesh dependency on localization onset in sands. Coupled undrained transient (globally undrained locally drained) analysis of Hostun RF sand has been performed to investigate the onset of instability by inducing material heterogeneity within the numerical model considering small strain formulation. For a given magnitude of perturbation, it is observed that instability onset requires a specific mesh convergence study, and with mesh refinement it practically becomes asymptotic to the theoretically predicted value estimated by bifurcation analysis. Perturbation magnitude significantly influenced onset strain of instability when compared with the effect of extent of the area for a fixed perturbation magnitude. However, all the sand specimens revealed emergence of localized instability modes in both cases. [ABSTRACT FROM AUTHOR]

Recent studies have shown that detection of the onset and evolution of micro shear bands (MSBs) in granular materials can be improved using measurements of the kinematic behavior of particles. Different methods such as the discrete-element method (DEM) or threedimensional (3D) imaging techniques have been used to measure the kinematics of individual particles within triaxial specimens. However, conventional kinematic techniques that use particle translation and/or rotation cannot detect the onset and growth of MSBs during the hardening phase of axisymmetric triaxial experiments. In order to expose the localized shearing and particle-scale behavior of triaxial specimens, a relative particle translation gradient (RPTG) concept is used to detect and expose the onset of strain localization before the peak principal stress ratio (PSR). RPTG measurements for four different granular materials are reported in this paper. The RPTG concept is used to expose the onset of MSBs during the hardening phase of the experiments. In addition, the contact number of individual particles is quantified and discussed in relation to particle rotation to investigate a particle-scale relationship between particle contacts and rotation. The effects of density, confining pressure, and particle shape on contact number are examined. [ABSTRACT FROM AUTHOR]

The main objective of this study was to quantify effect of fibers on the onset of strain localization in elastic-plastic cementitious composites. To this end, multidirectional fibers were embedded into an elastic-plastic cementitious matrix and the resulting composite was described by several different types of nonassociated Drucker-Prager hardening plasticity models. Diagnostic strain localization analyses were conducted, thus providing strain and stress levels at the onset of strain localization, along with corresponding directions and modes of strain localization. Several actual uniaxial tension and compression tests on plain cementitious composites and on high-performance steel fiber-reinforced cementitious composites were investigated. Results showed that the onset of strain localization was slightly delayed in uniaxial tension and more significantly delayed in uniaxial compression tests on high-performance fiber-reinforced cementitious composites as compared to the plain mortar. Specifically, the diagnostic strain localization analysis appears to detect the inception of a fiber-induced distributed cracking in uniaxial tension tests, and the onset of a fiber-induced delay of a major crack localization in a uniaxial compression test. [ABSTRACT FROM AUTHOR]

Tikhonov regularization on the integral-type nonlocal plasticity model is proposed to obtain a mesh-independent solution of strain localization. A detailed parametric study on the Tikhonov-regularized model is carried out for a one-dimensional and a two-dimensional problem. The influence of the regularization parameter, the tolerance of the nonlocal yield criterion, and the internal length scale on the finite-element solutions are examined. The width of the localization zone was found to be six times the internal length scale for a Gaussian-type weighting function. The solutions of the two-dimensional shear banding problem are compared with those of the one-dimensional strain localization. With the proposed model, no additional boundary conditions have to be introduced in the constitutive level, and only C0 continuity is needed at element interfaces. [ABSTRACT FROM AUTHOR]

To experimentally validate a recently developed theory for predicting the stability of cut slopes under unsaturated conditions, the authors measured increasing strain localization in unsaturated slope cuts prior to abrupt failure. Cut slope width and moisture content were controlled and varied in a laboratory, and a sliding door that extended the height of the free face of the slope was lowered until the cut slope failed. A particle image velocimetry tool was used to quantify soil displacement in the x-y (horizontal) and x-z (vertical) planes, and strain was calculated from the displacement. Areas of maximum strain localization prior to failure were shown to coincide with the location of the eventual failure plane. Experimental failure heights agreed with the recently developed stability theory for unsaturated cut slopes (within 14.3% relative error) for a range of saturation and cut slope widths. A theoretical threshold for sidewall influence on cut slope failures was also proposed to quantify the relationship between normalized sidewall width and critical height. The proposed relationship was consistent with the cut slope experiment results, and is intended for consideration in future geotechnical experiment design. The experimental data of evolution of strain localization presented herein provide a physical basis from which future numerical models of strain localization can be validated. [ABSTRACT FROM AUTHOR]

Strain localization refers to the formation of narrow zones of intense deformation in materials as a result of bifurcation in the stress-strain response during loading. Bifurcation occurs before the theoretical peak strength is reached and is then followed by strain softening. Theories and criteria have been developed to predict the point of this bifurcation in stress-strain relations. Two bifurcation criteria have been proposed for geomaterials: the complex Rudnicki-Rice criterion and the simple Vermeer criterion. The Rudnicki-Rice criterion is for strain-controlled loading, whereas the Vermeer criterion is for stress-controlled loading. This paper reviews and presents a rigorous and theoretical comparison of the two bifurcation criteria in the context of the flow theory of strain hardening elastoplasticity and shows that the simple Vermeer’s criterion is equivalent to the more complicated Rudnicki-Rice criterion for two-dimensional (2D) loading conditions. However, important differences between the two criteria exist for three-dimensional (3D) loading conditions. This paper also shows that the Rudnicki-Rice criterion provides a more realistic prediction of strain localization in geomaterials during 3D loading than does the Vermeer criterion. The paper is envisioned to offer an improved understanding of strain localization in geomaterials. [ABSTRACT FROM AUTHOR]

The constitutive behavior of sheared sand is highly influenced by particle morphology, gradation, mineralogy, specimen density, loading condition, stress path, and boundary conditions. The current literature lacks a three-dimensional (3D) systematic experimental study that investigates the influence of particle morphology, confining pressure, and specimen density on the failure mode of sheared sand. In this paper, surface texture, roundness, and sphericity of three uniform sands and glass beads with similar grain size were quantified by using 3D images of particles. In situ nondestructive 3D synchrotron microcomputed tomography (SMT) was used to monitor the deformation of medium-dense and very dense dry sand specimens that were tested under axisymmetric triaxial loading condition at 15 and 400 kPa confining pressures. The particles were identified and tracked in 3D as shearing progressed within the specimens, and maps of incremental particle translation and rotation were developed and used to uncover the relationship between particle morphology, specimen density, and confining pressure on the deformation and failure mode of sheared sand. This paper discusses the relationship between the failure mode and particle morphology, specimen density, and confining pressure. [ABSTRACT FROM AUTHOR]

The emergence of possible instability modes under undrained biaxial shear of sand was investigated to develop better understanding about the onset of localized and liquefaction-type solid-fluid instability modes using a generalized three-dimensional (3D)materialmodel. These two modes are the primary instability modes that can exist in most cases while conducting undrained biaxial testing of sand at different densities, confining pressures, and boundary conditions. Using a 3D rate-independent and nonassociative constitutive model, the instability analysis was performed as a plane-strain bifurcation problem from a uniform stress-strain state. Large deformation formulation was used to simulate the biaxial test configuration with both rigid and flexible boundaries in the lateral direction. The existing theoretical framework of solid-fluid instability analysis under rigid boundaries was extended to the flexible lateral boundary condition. Interestingly, the onset of solid-fluid instability modes is significantly influenced by the choice of boundary conditions. The trends for the onset of various undrained instability modes were assessed as a function of material state variables. [ABSTRACT FROM AUTHOR]

The strength and failure behaviors of geomaterials, such as soils and rocks, are commonly anisotropic because of lamination and sedimentation. The main purpose of this study is to investigate the effect of anisotropy on the localization pattern and bearing capacity of geostructures by finite-element simulation. To this aim, an extended Drucker-Prager yield criterion is developed for transversely isotropic geomaterials based on the Cosserat continuum. In this criterion, the internal frictional angle is related to the material principal direction and the mixed invariant of the stress tensor and the microstructure tensor. The corresponding stress update and consistent elastoplastic tangent modulus matrix are presented. Numerical results show that the localization pattern and the bearing capacity of the geostructures are very sensitive to the material principal direction as well as the anisotropic degree. [ABSTRACT FROM AUTHOR]

Conventional deformation measurement techniques, such as utilizing a LVDT, a demountable mechanical strain gauge (demec gauge), and an electrical strain gauge, despite their vast usage in experimental studies, suffer several disadvantages, including high cost, time-consuming specimen preparation, and the inability to obtain the whole displacement or strain fields. The aforementioned drawbacks on one hand and the importance of deformation measurements in all civil engineering laboratory tests on the other hand have led researchers to develop other measurement techniques, especially image-based techniques, capable of evaluating whole deformation fields. Among all of these recently developed methods, particle image velocimetry (PIV) has attracted much interest in all branches of civil engineering experimental investigations; PIV is a powerful image-based technique for evaluating both displacement and strain fields by analyzing successive digital images of a field undergoing deformation. Despite its great potential, however, few studies have been reported that use PIV for obtaining deformations for structural tests, especially for evaluating displacement and strain fields in a conventional bending test. Consequently, the intention of the current paper is to show the performance of the PIV technique for displacement and strain field measurement in bending tests of steel and RC beams subjected to four-point flexural loading. Based on different validation experiments of the current study, the PIV technique can be widely used as an alternative to conventional displacement and strain measurement techniques in bending tests. Moreover, the PIV technique demonstrated a great potential for investigating the fracture process in RC beams during the test process. [ABSTRACT FROM AUTHOR]

Analytical solutions have been derived for the onset of strain localization in a broad class of unsaturated elastic-plastic porous materials based on Bishop's definition of effective stress. Critical hardening moduli for constant water content and drained loadings were found to be further gradual simplifications of the critical hardening modulus for an undrained loading. In addition, the solutions were found to reduce to the previously found solutions for fully saturated and monophasic porous materials by adequately adjusting bulk moduli of the pore fluids. This finding demonstrates that the mechanics of fully saturated and monophasic soils is the special simpler case of the mechanics of unsaturated soils. A diagnostic tool for detection of the inception of strain localization was developed by implementing the aforementioned solutions into a constitutive driver for a bounding surface plasticity model. The tool was used to further illustrate the strain localization behavior of unsaturated Bourke silt from the Bourke region of New South Wales, Australia, subjected to undrained, constant water content and drained loadings. [ABSTRACT FROM AUTHOR]

Tension cracking is a very important phenomenon in the case of compacted fine grained soils, which are commonly used in earth dams, embankments, and waste containment systems. The strength and permeability of earthen structures can be seriously affected by the formation of tensile cracks. The purpose of this paper is to evaluate the effect of discrete and randomly distributed fibers (DRDF) in improving the tensile strength-strain characteristics of bentonite amended natural silty soil. The authors conducted a series of direct tensile tests on unreinforced and fiber-reinforced soil by using a specially developed tensile test set up in the laboratory. They conducted tests by varying the fiber content and fiber length and studying their effect on tensile strength-strain characteristics and crack formation. The present paper indicates that the blending of fibers improved the tensile strength-strain characteristics and ductility of the soil. The authors carried out a digital image cross-correlation (DIC) analysis of images of top view of the soil captured during tensile tests to obtain the displacement vectors and strain field distribution. As the fiber content and fiber length increased while keeping other parameters constant, there was an increase in the strain at crack initiation and energy absorption capacity of fiber-reinforced soil and improvement in postcracking behavior. Further, they found longer fibers to be more effective in restraining cracks. The results of DIC analysis were found to be effective in reflecting the distinct strain field development at the onset of tensile loading with fiber inclusions of appropriate length and dosage. [ABSTRACT FROM AUTHOR]

This paper presents the derivation of a mechanical model to estimate the effects of damage on the response of ropes. Damage can be represented through a degradation of the properties of individual rope elements, and it can also include the complete rupture of one or more elements. The general assumptions made to estimate the length over which damage propagates along the length of a rope and how this length is considered in modeling damaged rope behavior are explained. Consistent with tests on damaged polyester (PET) mooring ropes, numerical simulations demonstrate the existence of strain localization around the failure region and, due to degradation of rope element properties, damage localization as well. This damage localization causes the premature failure of rope elements, reducing the maximum load capacity and maximum failure strain that a damaged rope is capable of resisting relative to that of an intact rope. The proposed model suggests that some of the variables that affect damaged rope behavior are the degree of damage present at a given cross-section, the location of broken rope elements, and the length over which damage propagates along the rope length. Experimental data are used to validate the model. [ABSTRACT FROM AUTHOR]

In computational mechanics, strain softening generates ill-posed boundary value problems, which cannot be solved without being regularized, e.g., through the introduction of an internal length scale. This paper investigates how the internal length scale that is introduced by regularization may interact with the external length scale arising from boundary conditions in the particular case of a strain-softening bar of varying cross section and a nonlocal averaging regularization. The interaction of internal and external length scales is examined using an analytical closed-form solution for overnonlocal softening plasticity that derives from a Fredholm equation of the second kind. In the absence of external length (bars of constant section), the analysis shows that the overnonlocal averaging confines and smoothly distributes plastic strain into a localized band. The localization width, plastic strain distribution inside the band, and load-displacement response are controlled by the internal length of the averaging function and the overnonlocal weighting factor. In the presence of external length (bar of varying section), the analytical solution shows that the localization width is controlled by the interaction of external and internal length scales. This interaction is significant when the external and internal lengths are of comparable magnitude, and decreases when the external length becomes large compared to the internal length. The bandwidth is found to depend on the internal and external lengths and stress level while strain localizes, and to relate only to the internal length when the bar collapses. [ABSTRACT FROM AUTHOR]

An improved method based on pseudostatic and limit-equilibrium analysis is proposed for evaluating seismic (static plus dynamic) active earth pressures induced by backfill behind movable rigid retaining walls. The proposed method can take into account the effects of strain localization and postpeak shear resistance reduction in the dense backfill soil during a strong earthquake, and the main improvement over the existing method is that a simple analytical solution is provided. [ABSTRACT FROM AUTHOR]

Recently, a new plating system was proposed based on a strain localization mechanism for addressing the critical debonding problem in externally bonded reinforcing systems for reinforced concrete (RC) structures. The system delays or inhibits debonding by localizing the large strain of the externally bonded reinforcement in certain areas and leaving other places in a smaller strain condition to ensure that global debonding does not occur. This debonding avoidance strategy is in line with the concept of controlling a flood by channeling water away rather than blocking it. Two techniques have been used to achieve strain localization: (1) a nanotechnology called surface mechanical attrition treatment and (2) variation in the cross-sectional area of bonded reinforcement. To better understand this newly developed system, this paper presents a numerical study of RC beams strengthened with such plating systems. This study leads to a better understanding of the mechanism for inhibiting debonding and the development of a general design strategy for the system. In particular, a critical location is identified for strain localization, which forms the basis for the design of such a system in the future. [ABSTRACT FROM AUTHOR]