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The influence of a keyhole defect on local deformation behaviour in additive manufactured Ti-6Al-4V was investigated by comparing it to a representative bulk region without a defect. High resolution digital image correlation (HRDIC) was used to measure the differences in strain localisation at the microstructural length-scale. A nanoscale speckle pattern was used to allow small changes in strain to be detected and resolved within individual lamella and at pre-existing crack locations around the defect. Strain localisation was observed around the defect and formed well below the macroscopic yield stress. In contrast, minimal deformation was found in the bulk at this stress level. Following further deformation into the plastic regime, the strain localisation around the keyhole became more heterogenous with a distinct strain field. A large amount of strain localisation and slip was observed either side of the defect normal to the loading direction compared to relatively little in the regions close to the defect in line with the loading direction. This HRDIC observation was consistent with finite element analysis of the expected strain fields around the defect both below and above the yield point. Furthermore, micro-cracks were observed in αp/αp and αp/βt interfaces in both regions with the more pronounced strain fields around the defect leading to an increased number of long micro-cracks than in the bulk. The formation mechanisms of micro-cracks have been discussed, emphasising the role of localised strain caused by the defect.

Ultra-high-performance fibre-reinforced concrete (UHPFRC) specimens with and without longitudinal reinforcement were experimentally tested under direct tensile loading. The variables considered were the volume fraction of fibres (1.0% and 2.0%), the type of steel fibres (straight and hooked end) and the longitudinal steel reinforcement ratio (none and 1.2%). All of the specimens were tested using a servo-controlled fatigue testing machine in displacement control mode. The changes in displacement were monitored using linear variable displacement transducers and the digital image correlation technique. The strain profiles at different loading stages were used to identify the crack evolution process. The average localised strain was found to be 0.2–0.36%, with corresponding crack widths of 0.3–0.6 mm. A uniaxial tensile stress–strain model was developed based on the test results and data from the literature. Longitudinally steel-reinforced specimens showed both stiffening and strengthening effects. Tension-stiffened specimens with 1.0% fibres failed at a higher strain due to the formation of multiple macrocracks. In the specimens with 2.0% fibres, the rebar fractured in a brittle manner due to crack localisation. It is concluded that a higher longitudinal reinforcement ratio is needed to utilise UHPFRC effectively under tension-dominant loads. [ABSTRACT FROM AUTHOR]

Oceanic core complexes provide an accessible window into deep processes occurring at slow and ultra-slow-spreading mid-ocean ridges. We analyse samples from IODP ocean drilling of core complexes at the Atlantis Bank, Atlantis Massif, and near the Kane Transform at the South West Indian and Mid-Atlantic ridges. We correlate secondary minerals, including oxides, with sites of melt migration. We interpret changes to mineral assemblage and microchemistry, reaction textures and melt-pseudomorph microstructures as fingerprints of open-system melt-mediated processes. This micro-scale information is combined with a macro-scale review of legacy mineral chemistry data to show that melt-fluxed rocks share remarkably similar characteristics across the three core complexes investigated. These are rich in oxides and have olivine, orthopyroxene and clinopyroxene grains that are chemically distinct from oxide-poor gabbros. We propose that oceanic crust fluxed with external melt can be recognised by the following key features: (1) high modes of secondary minerals, such as oxides and olivine, (2) microstructural evidence for the former presence of melt, and (3) mineral chemistry differences between primary and secondary olivine, orthopyroxene, clinopyroxene and plagioclase. Importantly, olivine has previously only been reported as primary, that is, having crystallised from magma. However, our results show that gabbros with secondary olivine are reliable indictors of melt–rock interaction during deformation-assisted diffuse melt migration through the gabbroic oceanic crust. Finally, we propose a new model for the formation of oceanic core complexes where deformation-assisted melt migration plays a critical role in strain localisation, exhumation and evolution of the core complex. Secondary mineral microstructures indicate the former presence of melt. Olivine, plagioclase and pyroxene chemistry fingerprint melt-fluxed oceanic crust. Evidence of multiple fluxes of external melt associated with strain localisation. High oxide mode and secondary minerals are fingerprints of melt-fluxed zones in oceanic core complexes. [ABSTRACT FROM AUTHOR]

Granular materials are made up of smaller particles, manifestation of microstructure results in a macroscopic response of granular material. Understanding the overall mechanical behaviour from microscopic parameters is one of the main challenges in many engineering fields including civil engineering. When modelling this kind of material by Discrete Element Model (DEM) using idealized circular grains, the effects of appropriate sample size and microscopic parameter changes have been a crucial subject. Previous research has primarily relied on the case of purely frictional granular materials. In this paper, we use DEM to investigate the appropriate sample size and the relationship between microscopic parameters and the macroscopic responses of cohesive-frictional granular assemblies by performing a series of biaxial tests. Our findings indicate that a minimum number of particles is required to balance between mechanical behaviour and computing time. In addition, through extensive parametric studies, the paper explores the impact of factors such as interparticle bonds, intergranular friction coefficients, and initial void index on the overall shear behaviour of granular assemblies. Also, the result reveals a strong correlation between shear band formation and the break field of cohesive contact (static variable) and the translations and rotations of grains (kinematic variable).

This paper discusses continuum models for simulating earthquake sequences on faults governed by rate-and-state dependent friction. Through detailed numerical analysis of a conventional strike-slip fault, new observations regarding the use of various continuum earthquake models are presented. We update a recently proposed plasticity-based model using a consistently linearized formulation, show its agreement with discrete fault models for fault thicknesses of hundreds of meters, and demonstrate mesh objectivity for slip-related variables. To obtain a fully regularized fault width description with an internal length scale, we study the performance and mesh convergence of a plasticity-based model complemented by a Kelvin viscosity term and the phase-field approach to cohesive fracture. The Kelvin viscoplasticity-based model can introduce an internal length scale and a mesh-objective response. However, on grid sizes down to meters, this only holds for very high Kelvin viscosities that inhibit seismic slip rates, which renders this approach impractical for simulating earthquake sequences. On the other hand, our phase-field implementation for earthquake sequences provides a numerically robust framework that agrees with a discrete reference solution, is mesh objective, and reaches seismic slip rates. The model, unsurprisingly, requires highly refined grids around the fault zones to reproduce results close to a discrete model. Following this line, the effect of an internal length scale parameter on the phase-field predictions and mesh convergence are discussed. [ABSTRACT FROM AUTHOR]

The temperature increase induced by radioactive waste decay generates the thermal pressurisation around the excavation damage zone (EDZ), and the excess pore pressure could induce fracture re-opening and propagation. Shear strain localisation in band mode leading to the onset of micro-/macro-cracks can be always evidenced before the fracturing process from the lab experiments using advanced experimental devices. Hence, the thermal effects on the rock behaviour around the EDZ could be modelled with the consideration of development of shear bands. A coupled local 2nd gradient model with regularisation technique is implemented, considering the thermo-hydro-mechanical (THM) couplings in order to well reproduce the shear bands. Furthermore, the thermo-poro-elasticity framework is summarized to validate the implemented model. The discrepancy of thermal dilation coefficient between solid and fluid phases is proved to be the significant parameter leading to the excess pore pressure. Finally, an application of a heating test based on Eurad Hitec benchmark exercise with a drift supported by a liner is studied. The strain localisation induced by thermal effects is properly reproduced. The plasticity and shear bands evolutions are highlighted during the heating, and the shear bands are preferential to develop in the minor horizontal principal stress direction. Different shear band patterns are obtained with changing gap values between the drift wall and the liner. A smaller gap between the wall and the liner can limit the development of shear bands. Highlights: The formulation of a coupled local 2nd gradient model considering the thermo-hydro-mechanical (THM) couplings. Validation of the model with comparison with analytical solution of thermo-elastic problem. The prediction of strain localisation pattern induced by thermal effects around a large scale drift. The analysis of the gap distance (between the drift wall and the liner) on the strain localisation process under the thermal loading. [ABSTRACT FROM AUTHOR]

Granular materials are made up of smaller particles, manifestation of microstructure results in a macroscopic response of granular material. Understanding the overall mechanical behaviour from microscopic parameters is one of the main challenges in many engineering fields including civil engineering. When modelling this kind of material by Discrete Element Model (DEM) using idealized circular grains, the effects of appropriate sample size and microscopic parameter changes have been a crucial subject. Previous research has primarily relied on the case of purely frictional granular materials. In this paper, we use DEM to investigate the appropriate sample size and the relationship between microscopic parameters and the macroscopic responses of cohesive-frictional granular assemblies by performing a series of biaxial tests. Our findings indicate that a minimum number of particles is required to balance between mechanical behaviour and computing time. In addition, through extensive parametric studies, the paper explores the impact of factors such as interparticle bonds, intergranular friction coefficients, and initial void index on the overall shear behaviour of granular assemblies. Also, the result reveals a strong correlation between shear band formation and the break field of cohesive contact (static variable) and the translations and rotations of grains (kinematic variable). [ABSTRACT FROM AUTHOR]

The deformation patterns and failure mechanisms of pressurised cavities at shallow depth are relevant to many geotechnical applications, including tunnelling and horizontal directional drilling. In this paper, an experimental study of a reduced-scale pressurised cavity under geostatic stress is presented, in order to measure the effect of cavity length, vertical stress and soil density on soil deformation and failure. X-ray computed tomography is used to acquire images of the system at key stages of the cavity inflation process. A closed-shaped failure region developed around the cavities, beyond which shear planes of elliptic paraboloid shape formed, extending from the bottom of the cavities all the way to the free surface. The plane-strain assumption did not hold beyond the central portion of the longest cavity tested (L = 6D). The volumetric strain and porosity changes inside the shear bands showed significant dilation in dense specimens, but contraction in loose specimens. The average orientation and the thickness of the shear bands were in agreement with those found in the literature for passive arching mechanisms (anchoring). The orientation of the principal strains around the cavity follows catenary shapes, similar to those displayed in active trapdoor mechanisms. [ABSTRACT FROM AUTHOR]

The presence of defects produced by additive manufactured (AM) processes in structural Ti alloys such as Ti-6Al-4V is known to have serious implications on the deformation and fatigue behaviour of engineering components. However, there is little understanding about the localised plastic deformation patterns that develop around AM defects, and the associated local conditions that could lead to the nucleation of micro-cracks under creep loading conditions. In this work, the effects of the morphology and volume fraction of AM defects and temperature on the strain localisation behaviour around such defects in Ti-6Al-4V will be addressed. To that purpose, a novel rate-dependent crystal plasticity formulation is proposed to describe the mechanical behaviour of the alloy's predominant α ′ (HCP)-phase. Representative volume elements (RVEs) of the AM produced microstructures are digitally reconstructed from EBSD orientation maps obtained on planes perpendicular and transversal to the microstructure's AM growth direction. Calibration of the single crystal model for the α ′ -phase is carried out from macroscopic uniaxial tensile data from polycrystalline AM specimens at different strain rates and temperatures and published creep data. Furthermore, RVEs containing AM defects of different morphologies and volume fractions are relied upon to investigate the strain localisation behaviour around the defects under uniaxial loading at ambient and high temperatures. It is found that the extent of the localised accumulated plastic strain around defects depends greatly on whether the voids surface are smooth or have sharp corners, with the latter being associated with more severe localisation patterns. Moreover, a numerical investigation into the crack initiation behaviour of AM Ti-6Al-4V under uniaxial creep loading at 450 ° C revealed that the development of the local conditions suitable for the nucleation of creep damage/micro-cracks is accelerated in the presence of typical AM defects, and the extent of that acceleration depends strongly on their morphology. An AM defect shape parameter is introduced to quantify the way their morphology affects the time for creep crack initiation/damage. • A novel crystal plasticity model for α ′ - phase AM Ti-6Al-4V was proposed. • The severity of the predicted localised deformation patterns around AM defects was studied. • Gradients of plastic deformation in grains found at AM defects' surface were determined. • Two micro-crack indicators were explored to predict the onset of creep damage at both 450 and 600°C. • An AM defect shape parameter was introduced to study the influence of defect morphology on failure. [ABSTRACT FROM AUTHOR]

Heterogeneous deformation occurs between grains in polycrystalline α-titanium. Understanding the role of temperature in local deformation is essential for its applications in extreme environments such as cryo- or high-temperature, but the underlying mechanism still remains elusive. Here we report a study of grain-scale deformation behaviour in CP-Ti plate at the temperature range from −60 °C to 280 °C. The full-field strain measurements were conducted on the tensile samples loaded parallel (RD) and transverse (TD) to the rolling direction, using in-situ optical microscopy and digital image correlation (OM-DIC). The DIC local strain maps were coupled with scanning electron microscopy and electron backscatter diffraction analysis. The grain boundary sliding and slip transfer occurred depending on the geometric relationship (i.e., deformation compatibility) between adjacent grains at 20 °C, and a micro-crack was observed at the { 10 1 ‾ 1 } twist boundary. The strain was recovered in the grains in the RD sample favourable for slip, whilst more accumulated in the grains in TD sample unfavourable for slip at 280 °C. The plasticity of grains differs with decreasing temperature to −40 °C, resulting in the presence of soft/hard grain pairs. The strong strain localisation between the soft and hard grains led to the cracking along the GBs (RD) and cross the grains (TD). Interestingly, the cracking was significantly reduced with decreasing temperature to −60 °C due probably to the temperature dependence of the plasticity of grains. The strain-hardening behaviour of α-Ti polycrystals was significantly affected by the temperature and crystal orientation dependence of grain-scale deformation mechanism. [ABSTRACT FROM AUTHOR]

A sensitivity study is presented to evaluate the influence of different parameters on the simulation of an underground excavation in the Callovo-Oxfordian (COx) argillaceous formation performed in the Meuse/Haute-Marne underground research laboratory. An elasto-viscoplastic constitutive law representing the characteristic behaviour of indurated mudrocks and stiff clays has been employed. It incorporates anisotropy, strain-softening, creep deformations and dependence of permeability on damage. In addition, a non-local formulation, able to simulate localised deformations objectively, has been incorporated in the analyses. The following features affecting the excavation have been studied: initial stress, strength and stiffness anisotropy, strength parameters, hydraulic and hydromechanical parameters, and scale effects. A simulation reported in a companion paper provides the base case for benchmarking. The results are compared in terms of extent and configuration of the excavation fractured zone, vertical and horizontal tunnel convergences, and the development and evolution of pore pressures in the rock. From the comparisons, an enhanced understanding of the hydromechanical mechanisms associated with underground excavations in COx claystone, and other similar argillaceous materials, has been achieved. [ABSTRACT FROM AUTHOR]

Subjected to external loads, granular materials experience severe deformation in a narrow zone before their failure. This phenomenon, which is called strain localisation or shear band, is of vital importance in assessing the stability of the geotechnical structure, studying the stress-strain behaviour of soil and rock materials, and analysing the interaction of soil and structure. The present study is aimed to investigate the effect of various factors on the pattern and inclination of shear band in a general threedimensional condition of stress using the Discrete Element Method (DEM). Several tests were simulated using a developed version of the TRUBAL program called GRANULE. The GRANULE code was further developed to add the capability of carrying out simulations with different intermediate principal stresses and modelling specimens containing non-spherical particles. The shear band was detected by tracking the motion of the particles and plotting the rotation distribution of particles within the sample. The results prove that the shear band inclination and its pattern, are greatly affected by intermediate principal stress, particle shape, and confining stress. Moreover, it was observed that the change in the b value plays a key role in the alteration of the 3D configuration of the shear band. [ABSTRACT FROM AUTHOR]

Carbonate sediments play a prominent role on the global geological stage as they store more than 60 % of world's oil and 40 % of world's gas reserves. Prediction of the deformation and failure of porous carbonates is, therefore, essential to minimise reservoir compaction, fault reactivation, or wellbore instability. This relies on our understanding of the mechanisms underlying the observed inelastic response to fluid injection or deviatoric stress perturbations. Understanding the impact of deformation/failure on the hydraulic properties of the rock is also essential as injection/production rates will be affected. In this work, we present new experimental results from triaxial deformation experiments carried out to elucidate the behaviour of a porous limestone reservoir analogue (Savonnières limestone). Drained triaxial and isotropic compression tests were conducted at five different confining pressures in dry and water-saturated conditions. Stress–strain data and X-ray tomography images of the rock indicate two distinct types of deformation and failure regimes: at low confinement (10 MPa) brittle failure in the form of dilatant shear banding was dominant; whereas at higher confinement compaction bands orthogonal to the maximum principal stress formed. In addition to the pore pressure effect, the presence of water in the pore space significantly weakened the rock, thereby shrinking the yield envelope compared to the dry conditions, and shifted the brittle–ductile transition to lower effective confining pressures (from 35 MPa to 29 MPa). Finally, permeability measurements during deformation show a reduction of an order of magnitude in the ductile regime due to the formation of the compaction bands. These results highlight the importance of considering the role of the saturating fluid in the brittle–ductile response of porous rocks and elucidate some of the microstructural processes taking place during this transition. Highlights: Triaxial testing and petrophysical characterisation of the Savonnières limestone, an oolithic carbonate reservoir analogue Saturation of the pore space with water instead of air reduces the mechanical strength and shrinks the yield envelope Compaction bands are observed in the brittle-ductile transition zone using X-ray Computed Tomography Compaction bands reduce the permeability of the rock [ABSTRACT FROM AUTHOR]

Ductile failure by the onset of strain localisation after non-proportional load paths is investigated herein by using the imperfection version of the strain localisation theory. A computational framework assuming a planar, porous imperfection band inside a homogeneous solid was used to investigate ductile failure as caused by void nucleation, growth, and coalescence. The localisation analysis framework was calibrated based on a single uniaxial tension test and finite element simulations thereof. Despite the somewhat frugal calibration, the localisation analyses successfully reproduced experimentally measured macroscopic fracture strains from notched tension tests and notched compression–tension tests. The method was subsequently applied to a structural problem involving large deformations and complex load paths, and the results show great promise for future work. • Imperfection-based strain localisation theory is used to study ductile failure. • A single tension test is used for calibration of the localisation framework. • Failure from both proportional and non-proportional loads is well captured. • The approach is applied to a pipe denting case with reversed loading. • The results correspond well with experimental observations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel computational formulation capable of solving the problem of material softening and the emerging localisation of strains in spatial frame-like structure, a common phenomenon for brittle heterogeneous materials. This study adopts the embedded strong discontinuity approach within our original velocity-based framework. The velocity-based formulation is thus enhanced with additional capabilities of detection of critical load level and critical cross-section and introduction of the jump-like variables at the level of velocities and angular velocities to enable more realistic description of strain localisation. A modified consistency condition is derived using the method of weighted residuals in complete accordance with the theoretical concept of strong discontinuity. One of the key advantages of the proposed method is its computational efficiency, which is preserved even after detecting cross-sectional singularities and handling post-critical localised strains. The numerical examples show the effectiveness and robustness of the proposed approach. • The problem of material softening and strain localization is addressed. • The primary unknowns are velocities and angular velocities. • The field of unknowns is enriched with additional shape functions. • The solution procedure enables possible discontinuities and localisms. • The updated strains are obtained using kinematic compatibility equations. • We surpass the singularity of cross-sectional constitutive equations. [ABSTRACT FROM AUTHOR]

When modelling the phenomenon of strain localisation in strain-softening soils with the finite element (FE) method, nonlocal approaches have been commonly employed to avoid mesh dependency and numerical instability. This paper first presents the FE formulation of a critical state model for highly overconsolidated clays incorporating a nonlocal method. The performance of the nonlocal strain regularisation is subsequently assessed through a series of coupled hydro-mechanical (HM) analyses of undrained and drained triaxial compression tests on London clay. The mechanism behind the evolution of strain localisation in triaxial tests is investigated and a comparison with equivalent plane strain analyses is discussed. Finally, a comprehensive sensitivity study is presented, investigating the influence of the two nonlocal parameters, in the adopted nonlocal algorithm, on the predicted stress–strain responses. A key outcome is the derived linear relationship between the two parameters, which enables a unique stress–strain response to be achieved in either axisymmetric or plane strain analyses with multiple combinations of the two parameters. Such a modelling capability is essential in applications of the proposed nonlocal strain regularisation in large scale boundary value problems in which restrictions on element size exist. [ABSTRACT FROM AUTHOR]

The objective of this technical note is to illustrate twofold. The first issue is devoted to the ability of the recently developed smoothing gradient-enhanced damage model (SGDM), which is associated with the modified von Mises equivalent strain in modelling mixed-mode fracture problems, in particular the common Nooru–Mohamed's test. We show that the developed approach works pretty well for this test, yielding appropriate structural damage response and crack paths for all three specimen sizes, i.e. 200 × 200 , 100 × 100 and 50 × 50. The second issue is, in a similar manner, to discuss the less accuracy of another damage model, the localising gradient damage scheme recently studied by Shedbale et al. Int. J. Mech Sci 2021, 199:106410, in reproducing crack paths and structural responses for the same mixed-mode problem. [ABSTRACT FROM AUTHOR]

Continuum Damage Mechanics provides a framework for the description of the mechanical response of concrete and rocks which encompasses distributed micro-cracking, macro-crack initiation, and then its propagation. In order to achieve a consistent setting, an internal length needs to be introduced to circumvent the difficulties inherent to strain softening and to avoid failure without dissipation of energy. Upon inserting this internal length, structural size effect is captured too. This paper reviews some the progresses achieved by the author since the introduction of the nonlocal damage model in 1987. Among them, the early proposals exhibited a proper description of the inception of failure but a poor one for complete failure since it is not straightforward to model a discrete cracking with a continuum approach. Candidate solutions, e.g. by considering a variable internal length are outlined. Then, the coupled effects between material damage and material permeability are considered. Is is recalled that the permeability of the material should be indexed on the damage growth in the regime of distributed cracking. Upon macro-cracking, there is a change of regime and it is the crack opening that controls the fluid flow in the cracked material. Both regimes may be captured with a continuum damage approach, however.

Localised corrosion may considerably impair the load‐bearing and deformation capacity of reinforced concrete structures. The Corroded Tension Chord Model allows investigating the related effects. The model combines the effects of tension stiffening and strain localisation due to a local cross‐section loss to calculate the load‐deformation behaviour of tension members and entire structural elements containing locally corroded reinforcing bars on a sound mechanical basis. Based on simple equilibrium considerations, the critical loss of cross‐sectional area is introduced, beyond which most of a reinforcing bar's ductility or a structure's deformation capacity, respectively, is lost. For conventional European reinforcing steel, even small cross‐section losses may be sufficient to impair ductility drastically. Illustrative calculations on structural elements with various spatial corrosion distributions but identical mean cross‐section loss reveal that the load‐deformation behaviour strongly depends on the specific corrosion parameters: Structures with few heavily corroded reinforcing bars seem to be less critical regarding strength and deformation capacity than structures with many slightly corroded reinforcing bars. [ABSTRACT FROM AUTHOR]

[Display omitted] • The magnitude of the crustal shear stress dictates the tectonic style. • Modern style tectonics occurs for a maximum crustal shear stress >300 MPa. • Shear heating is a key factor for strain localisation in modern style tectonics. Orogens are traditionally classified according to their tectonic style. Paleoproterozoic tectonics is referred to as "ancient-style tectonics" while Proterozoic tectonics is referred to as "modern-style tectonics". Ancient-style tectonics is characterised by distributed vertical structures and low topography gradients, often associated with diapirism and partial melting. In contrast, modern-style tectonics involve prominent strain localisation and the formation of thrusts, nappes and high topographic gradients. However, the parameters controlling the transition from ancient to modern-style tectonics are poorly understood. To quantify this transition, a combination of 1D and 2D high resolution lithospheric-scale thermo-mechanical models was conducted. The parameters controlling the strength of the lithosphere (i.e., Moho temperature, strain rate, crustal rheology, crustal radiogenic heat production and role of shear heating) were investigated in detail. Our results show that tectonic style is controlled by the maximum of crustal strength (shear stress). Modern-style tectonics is observed to occur when the maximum of crustal strength is greater than 300 MPa. At the opposite, a maximum crustal strength lower than 300 MPa leads to ancient style tectonic structures. Therefore, crustal rheology, temperature and background strain rate significantly influence the transition from ancient to modern-style tectonics. Shear heating remains a key factor in promoting strain localisation in modern-style tectonics. Crustal radiogenic heat production has a moderate influence by increasing/decreasing the tendency for faulting within the crust. This crustal strength criterion also provides an excellent fit for a second potential proxy: a localisation criterion of ca. 225°C. These two proposed proxies can be used interchangeably to predict the transition from ancient to modern-style tectonics. [ABSTRACT FROM AUTHOR]

The microstructure and mineralogy of volcanic rocks is varied and complex, and their mechanical behaviour is similarly varied and complex. This review summarises recent developments in our understanding of the mechanical behaviour and failure modes of volcanic rocks. Compiled data show that, although porosity exerts a first-order influence on the uniaxial compressive strength of volcanic rocks, parameters such as the partitioning of the void space (pores and microcracks), pore and crystal size and shape, and alteration also play a role. The presence of water, strain rate, and temperature can also influence uniaxial compressive strength. We also discuss the merits of micromechanical models in understanding the mechanical behaviour of volcanic rocks (which includes a review of the available fracture toughness data). Compiled data show that the effective pressure required for the onset of hydrostatic inelastic compaction in volcanic rocks decreases as a function of increasing porosity, and represents the pressure required for cataclastic pore collapse. Differences between brittle and ductile mechanical behaviour (stress-strain curves and the evolution of porosity and acoustic emission activity) from triaxial deformation experiments are outlined. Brittle behaviour is typically characterised by shear fracture formation, and an increase in porosity and permeability. Ductile deformation can either be distributed (cataclastic pore collapse) or localised (compaction bands) and is characterised by a decrease in porosity and permeability. The available data show that tuffs deform by delocalised cataclasis and extrusive volcanic rocks develop compaction bands (planes of collapsed pores connected by microcracks). Brittle failure envelopes and compactive yield caps for volcanic rocks are compared, highlighting that porosity exerts a first-order control on the stresses required for the brittle-ductile transition and shear-enhanced compaction. However, these data cannot be explained by porosity alone and other microstructural parameters, such as pore size, must also play a role. Compactive yield caps for tuffs are elliptical, similar to data for sedimentary rocks, but are linear for extrusive volcanic rocks. Linear yield caps are considered to be a result of a high pre-existing microcrack density and/or a heterogeneous distribution of porosity. However, it is still unclear, with the available data, why compaction bands develop in some volcanic rocks but not others, which microstructural attributes influence the stresses required for the brittle-ductile transition and shear-enhanced compaction, and why the compactive yield caps of extrusive volcanic rocks are linear. We also review the Young's modulus, tensile strength, and frictional properties of volcanic rocks. Finally, we review how laboratory data have and can be used to improve our understanding of volcanic systems and highlight directions for future research. A deep understanding of the mechanical behaviour and failure modes of volcanic rock can help refine and develop tools to routinely monitor the hazards posed by active volcanoes. [ABSTRACT FROM AUTHOR]

In the present study we elucidate the nature of local strain statistics evolution during tensile deformation in polycrystalline materials. A rate-independent formulation was implemented within a crystal plasticity framework by the means of representative volume element (RVE) analysis. Local elastic strain, as well as stress, were found to obey a normal distribution, whereas the statistics of local plastic strain conforms to a lognormal distribution. In line with experimental observations, the plastic strain becomes progressively localised and the local regions of large strains make significant contribution to the overall average strain increase. The results reveal the nature of strain inhomogeneity at the microscale and emphasize the fact that in metallic materials the elastic strain accumulation represents an additive process, whereas plastic deformation is a multiplicative process.

The ductility is an important parameter in the seismic design process of reinforced concrete structures. Under seismic loadings, ductility is required to allow a significant deformation and energy dissipation before the collapse. The plastic design of RC elements under bending loads is based on the formation of plastic hinges. The dissipation is characterised by the rotational capacity of these zones. The non-linearity of these dissipative zones is described by the moment-curvature laws (or moment-rotation curves). The Eurocode 8 (EC8) design code gives empirical formulas to evaluate the moment-rotation curves. The main disadvantage of using this practical design code is that the size effect is not taken into account in evaluating the plastic rotational capacity. In the present paper, a critical review of EC8 regarding the size dependency of the plastic rotational capacity is firstly presented. Furthermore, a performance simplified model is developed to assess the phenomena of size effects and its influence on the ductility behaviour of RC elements under simple bending (without interaction). A comparison with the experimental results from literature shows the ability of the proposed model to describe the size dependency phenomenon. Based on the new developments, news formulas are proposed to improve the EC 8. Finally, a real-life engineering application is carried out in order to highlight the benefits of the EC8 improvements proposed. [ABSTRACT FROM AUTHOR]

Continuum Damage Mechanics provides a framework for the description of the mechanical response of concrete and rocks which encompasses distributed micro-cracking, macro-crack initiation, and then its propagation. In order to achieve a consistent setting, an internal length needs to be introduced to circumvent the difficulties inherent to strain softening and to avoid failure without dissipation of energy. Upon inserting this internal length, structural size effect is captured too. This paper reviews some the progresses achieved by the author since the introduction of the nonlocal damage model in 1987. Among them, the early proposals exhibited a proper description of the inception of failure but a poor one for complete failure since it is not straightforward to model a discrete cracking with a continuumapproach. Candidate solutions, e.g. by considering a variable internal length are outlined. Then, the coupled effects between material damage and material permeability are considered. Is is recalled that the permeability of thematerial should be indexed on the damage growth in the regime of distributed cracking. Upon macro-cracking, there is a change of regime and it is the crack opening that controls the fluid flow in the cracked material. Both regimes may be captured with a continuum damage approach, however. [ABSTRACT FROM AUTHOR]

A severe, spurious dependence of numerical simulations on the mesh size and orientation can be observed in elasto-plastic models with a non-associated flow rule. This is due to the loss of ellipticity and may also cause a divergence in the incremental-iterative solution procedure. This paper first analyses the dependence of the shear band inclination in a biaxial test on the mesh size as well as on the mesh orientation. Next, a Cosserat continuum model, which has been employed successfully for strain-softening plasticity, is proposed to prevent loss of ellipticity. Now, numerical solutions result for shear band formation which are independent of the size and the orientation of the discretisation. [ABSTRACT FROM AUTHOR]

The forty-year history of the Journal of Structural Geology has recorded an enormous increase in the description, interpretation and modelling of deformation structures. Amongst factors that control deformation and the resulting structures, mechanical anisotropy has proven difficult to tackle. Using a Fast Fourier Transform-based numerical solver for viscoplastic deformation of crystalline materials, we illustrate how mechanical anisotropy has a profound effect on developing structures, such as crenulation cleavages, porphyroclast geometry and the initiation of shear bands and shear zones. Image 1 • Mechanical anisotropy strongly enhances strain localisation. • VPFFT + ELLE simulations illustrate effect of mechanical anisotropy. • Axial planar crenulation cleavages can be simulated with the VPFFT + ELLE code. • Mechanical anisotropy reduces rotation of objects, forming σ instead of δ-clasts. • Even small amounts of anisotropic minerals lead to C/C′ shear bands in shear zones. [ABSTRACT FROM AUTHOR]

Localisation of ductile deformation in rocks is commonly found at all scales from crustal shear zones down to grain scale shear bands. Of the various mechanisms for localisation, mechanical anisotropy has received relatively little attention, especially in numerical modelling. Mechanical anisotropy can be due to dislocation creep of minerals (e.g. ice or mica) and/or layering in rocks (e.g. bedding, cleavage). We simulated simple-shear deformation of a locally anisotropic, single-phase power-law rheology material up to shear strain of five. Localisation of shear rate in narrow shear bands occurs, depending on the magnitude of anisotropy and the stress exponent. At high anisotropy values, strain-rate frequency distributions become approximately log-normal with heavy, exponential tails. Localisation due to anisotropy is scale-independent and thus provides a single mechanism for a self-organised hierarchy of shear bands and zones from mm-to km-scales. The numerical simulations are compared with the natural example of the Northern Shear Belt at Cap de Creus, NE Spain. • Anisotropy and power-law rheology lead to shear localisation. • VPFFT-ELLE simulations show extent of localisation due to anisotropy. • Localisation leads to approximately exponential strain-rate distributions. • Patterns of localisation are self-similar. • Localisation patterns are comparable with shear zones at Cap de Creus, Spain. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free‐surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto‐plastic computations of geomaterials, a robust numerical procedure to implement Mohr‐Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr‐Coulomb model. The proposed approach was first validated against two‐dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three‐dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions. [ABSTRACT FROM AUTHOR]

Shearing of magma during ascent can promote strain localisation near the conduit margins. Any mechanical and thermal discontinuities associated with such events may alter the chemical, physical and rheological stability of the magma and thus its propensity to erupt. Lava spines can record such processes, preserving a range of macroscopic and microscopic deformation textures, attributed to shearing and friction, as magma ascends through the viscous-brittle transition. Here, we use a multidisciplinary approach combining petrology, microstructures, crystallography, magnetics and experimentation to assess the evidence, role and extent of shearing across a marginal shear zone of the 1994–1995 lava spine at Unzen volcano, Japan. Our results show that crystals can effectively monitor stress conditions during magma ascent, with viscous remobilisation, crystal plasticity and comminution all systematically increasing towards the spine margin. Accompanying this, we find an increase in mineral destabilisation in the form of pargasitic amphibole breakdown displaying textural variations across the shear zone, from symplectitic to granular rims towards the spine margin. In addition, the compaction of pores, chemical and textural alteration of interstitial glass and magnetic variations all change systematically with shear intensity. The strong correlation between the degree of shearing, crystal deformation and disequilibrium features, together with distinct magnetic properties, implies a localised thermal input due to shear and frictional processes near the conduit margin during magma ascent. This was accompanied by late-stage or post-emplacement fluid- and gas-induced alteration of the gouge, as well as oxidation and glass devitrification. Understanding and recognising evidence for strain localisation during magma ascent may, therefore, be vital when assessing factors that regulate the style of volcanic eruptions, which may provide insights into the cryptic shifts from effusive to explosive activity as observed at many active lava domes. [ABSTRACT FROM AUTHOR]

To examine the impact of preexisting weaknesses on fracture coalescence during volcanic edifice deformation, we triaxially compressed Mount Etna basalt while acquiring in situ dynamic X‐ray microtomograms and calculated the internal strain tensor fields using image correlation. Contraction localization preceded dilation and shear strain localization into the protofault zone. This onset of strain localization preceded macroscopic yielding and coincided with increases in the magnitude and volume of rock experiencing dilation, and spatial clustering of the strain populations. The exploitation of weaknesses by propagating fractures enabled the dominant shear strain to switch senses as propagating fractures lengthened along 30–60° from σ1. Scanning electron microscopy images reveal pore‐emanated fractures, and fractures linking pores. These experiments provide evidence of internal contraction preceding dilation and shear, consistent with inferences from field and laboratory observations. The transition from contraction to dilation may provide a precursory signal of volcanic flank eruption. Plain language summary: Directly observing how rocks break at seismogenic depths in natural settings is at present impossible. Here we used X‐ray imaging techniques to view deforming, and then breaking, basaltic rocks at stress conditions equivalent to the flanks of the upper part of the Mount Etna volcano. We tracked how preexisting weaknesses, including pores and fractures produced during the fast cooling of the lava, controlled the growth and coalescence of new fractures and faults. At 50% of the stress at failure, shear and dilative strains began to concentrate in the volume that eventually developed the largest connected fracture network. The localization of contractive strains preceded this shear and dilation localization. These data sets provide observations of fracture growth within Etna basalt that previous studies could only infer, and thus constraints on how the volcanic edifice deforms under magmatic and tectonic stresses and eventually ruptures in flank eruptions. Key Points: Failure in Etna basalt occurred through contraction localization, and then shear and dilation localization, consistent with geophysical observationsShear and volumetric strain localized into a protofault zone preceding 50% failure stress, and macroscopic yieldingThe precursors to volcanic flank eruptions may include a transition from contraction to dilation [ABSTRACT FROM AUTHOR]

Abstract The progressive non-linear mode of deformation known as steady-state kink band broadening is analysed for fibre composites and layered materials. The mode of deformation is investigated using an analytical, a semi-analytical model and a finite-element model. The semi-analytical model is based on a constitutive model, where independent material behaviour can be given for two constituents. The analytical model assumes rigid fibres and results in a transcendental equation for the kink band broadening state. Both the analytical and semi-analytical model use a Maxwell construction to determine the steady-state, which is done by equating the internal and external work. The influence of size-effects are explored and two case studies are performed; in the first case study the finite element model and semi-analytical model are used upon a carbon fibre-reinforced PEEK composite. The second case study is on a layered composite made from ultra high molecular-weight polyethylene fibres with a kink band developing on ply level. [ABSTRACT FROM AUTHOR]

Summary: This paper reappraises Perzyna‐type viscoplasticity for the constitutive modelling of granular geomaterials, with emphasis on the simulation of rate/time effects of different magnitude. An existing elasto‐plastic model for sands is first recast into a Perzyna viscoplastic formulation and then calibrated/validated against laboratory test results on Hostun sand from the literature. Notable model features include (1) enhanced definition of the viscous nucleus function and (2) void ratio dependence of stiffness and viscous parameters, to model the pycnotropic behaviour of granular materials with a single set of parameters, uniquely identified against standard creep and triaxial test results. The comparison between experimental data and numerical simulations points out the predicative capability of the developed model and the complexity of defining a unique viscous nucleus function to capture sand behaviour under different loading/initial/boundary and drainage conditions. It is concluded that the unified viscoplastic simulation of both drained and undrained response is particularly challenging within Perzyna's framework and opens to future research in the area. The discussion presented is relevant, for instance, to the simulation of multiphase strain localisation phenomena, such as those associated to slope stability problems in variably saturated soils. [ABSTRACT FROM AUTHOR]

Conventional finite element analyses generally suffer from mesh dependency when considering softening effects. Non-local strain regularisation techniques have been developed to address this issue, which are generally complex to implement. In view of this, this paper introduces an more efficient procedure for implementation of a non-local method in Abaqus for Coupled Eulerian-Lagrangian (CEL) large deformation finite element undrained analyses. Results from a series of biaxial compression simulations demonstrate that the non-local method with a strain-softening Tresca model in CEL avoids mesh dependency. Owing to the stationary Eulerian element and the built-in mapping algorithm in CEL, high computational efficiency is achieved, adding no more than 12% to the computational cost. Guidance is provided on selection of internal length scales, element sizes and the search radius to ensure efficient non-local calculations, and it is shown that a softening scaling rule can also be used to allow use of practical mesh densities for some boundary value problems. Simulations of a number of classical geotechnical problems demonstrate the type of boundary value problems where the non-local method can effectively mitigate the mesh dependency, whilst also highlighting that the method fails to control the strain localisation that develops at soil-structure interfaces due to geometrical issues. [ABSTRACT FROM AUTHOR]

[Display omitted] • Triaxial stress state occurs pronouncedly for short pit lengths at corroded rebars. • Apparent uniaxial peak stress increases up to 35% for axisymmetric damage. • Ductility of pit region is higher than predicted by strain localisation models. • Yield behaviour of steel at corrosion pit is significantly altered. • Pit geometry strongly influences intensity of triaxial stresses. Local corrosion damage reduces the load-bearing capacity of reinforcing bars and, even more severely, their deformation capacity. These effects are mainly attributed to the reduced cross-sectional area and the accompanying strain localisation. However, several experimental studies found an altered load-deformation behaviour of naturally corroded as well as artificially damaged reinforcing bars, including an apparently increased tensile strength, which cannot be explained solely by strain localisation. Accordingly, in an experimental campaign carried out by the authors on locally axisymmetrically damaged reinforcing bars, the observed peak load increased with decreasing damage length, and the deformation capacity was much less impaired than predicted by established strain localisation models. A series of nonlinear FE analyses was carried out to investigate a potential effect of the local stress state in the vicinity of the local corrosion damage. The results indeed revealed a triaxial stress state in this region, caused by the local deviation of the stress trajectories, explaining the experimental observations on a mechanical basis, and indicating a pronounced influence of the triaxial stresses on the uniaxial stress–strain behaviour of the bar in the vicinity of the corrosion pit. A parametric study was conducted to investigate a broader range of corrosion damage geometries and the corresponding triaxial stresses. The results indicate that the transverse stresses strongly affect the apparent uniaxial mechanical steel properties (yield stress, tensile strength, deformation capacity, loss of yield plateau) for short damage lengths typically found for pitting corrosion. A simplified modelling approach is proposed to capture the governing effects on the apparent uniaxial stress–strain curve of locally corroded reinforcing bars. [ABSTRACT FROM AUTHOR]

Better understanding of stress perturbations, strain propagation and fluid flow in the upper crust require characterisation of fault damage zone evolution. Outcrop studies help understand the different processes operating during fault movement; but capture little about the evolution through time. In this study, we investigate damage zone evolution using high-resolution analogue modelling; simulating the growth of a normal fault population. The incremental strain reveals that early deformation stages occur by strain localisation into corridors of distributed deformation. Active deformation within these corridors becomes narrower as segment linkage occurs, leading to the formation of master faults, encouraging further localisation of incremental strain. This results in wide zones of cumulative strain around the fault, accommodated by different types of fault damage geometry, which formed at very different stages of the fault system growth. We also highlight the new concept of "fault system damage", that shows similarities with observations in nature. These first descriptions of the fault damage evolution allow an understanding of the composite content of damage zones. This gives support to assess zones of permeability enhancement in naturally fractured reservoirs, and proposes a view of damage distribution for targeting fluid flow, geothermal resources, leaks, micro/macro seismicity and mechanical properties of fault zones. • Fault damage zones evolution is described and grow by fault segment linkage. • Damage zone types are described in out-of-plane dimension. • Damage at fault system scale occurs by the interaction of several master faults. • A new concept of fault system damages is described and compared to nature. [ABSTRACT FROM AUTHOR]