Pure Shear Deformation Research Articles

Superposed shear and compression of strong colloidal gels

Although the rheology of strong colloidal gels is predominantly concerned with either pure shear or pure compressive deformation, the vast majority of practical applications involves an arbitrary combination of shear and compressive stresses and strains. This situation demands a tensorial rheology of colloidal suspensions, where the multidimensional response of these complex materials to arbitrary superposed stress states needs to be characterized and constitutive models developed. In this study, we use 2D discrete element modelling simulations in the absence of hydrodynamic interactions to probe the behavior of a model strong colloidal gel under combined shear and compressive deformation. We consider the deformation and failure of these gels under strain-controlled conditions that range from pure compression to shear-dominated consolidation. Particle-scale observations uncover how shear stresses act to stimulate nonaffine buckling and rupture of force chains during consolidation, leading to augmented failure and collapse of the particle network. At the macroscopic level, we find that the energy required to consolidate a colloidal suspension from the gel point to close packing passes through a minimum that corresponds to weak shear strain, indicating that small amounts of shear play a critical role in destabilizing the colloidal network. These results represent an important step toward a complete understanding of the tensorial rheology of strong colloidal gels.

Unravelling the development of regional-scale shear zones by a multidisciplinary approach: The case study of the Ferriere-Mollières Shear Zone (Argentera Massif, Western Alps)

Shear zone behavior is mainly controlled by deformation regime (brittle versus ductile), deformation temperature, strain rate and magnitude, and rheology of the deformed rocks. If a gradient of strain is established across a shear zone, softening phenomena can produce progressive localization of deformation in its core, resulting in the shear zone maintaining a constant thickness with increasing strain. In contrast, strain hardening processes may induce migration of deformation into the wall-rocks, causing an increase in shear zone thickness. In the Western Alps we have studied a NW-SE striking steeply dipping km-scale shear zone, the Ferriere-Mollières Shear Zone (FMSZ), that cross-cuts Variscan migmatites in the Argentera External Crystalline Massif. The shear zone is characterized by a deformation gradient, with strain increasing toward the center of the shear zone which we interpret to be associated with strain softening during Variscan retrograde metamorphism.In this study, by combining structural and microstructural analyses with quartz fabric analysis, quartz palaeopiezometry and petrochronology, we have identified three main stages of shear zone development, with each stage characterized by specific age, temperature and deformation regime. Stage I occurred between ~340 Ma and ~330 Ma under a temperature range of ~610 - 590 °C with a prevalent (76%–65%) component of pure shear deformation; stage II occurred between ~ 330 and 320 Ma at temperatures between ~ 530 and 480 °C with a decrease in the component of pure shear (73%–49%); stage III developed from ~320 to 300 Ma under temperature conditions between ~ 500 and 420 °C with a prevalent component of simple shear (pure shear of 39%–31%).The FMSZ is a new example of a strain-softening and long-lasting regional-scale shear zone, that may prove to be a useful natural study area for future research on processes operating in large-scale shear zones. We argue that the integration of multiple analytical techniques is essential in the study of such regional-scale shear zones and should be regarded as a standard approach.

New tectonic configuration in NW Iran: Intracontinental dextral shear between NW Iran and SE Anatolia

The Main Recent Fault (MRF) is a major active strike-slip fault system at the NE border of the Arabian platform and Central Iran. Both geometry and kinematics of the fault system is rather well known along its central part and at its SE termination, while its possible continuation to the northwest is ambiguous. Moreover, less regard has been paid to possible relationships between this major intracontinental fault system and other strike-slip faults in NW Iran – SE Anatolia. This paper investigates both the structural pattern and kinematics of deformation in the region to the north of latitude 37°N, between the North Tabriz Fault and the MRF. We followed this goal through detailed fault mapping, structural field measurements, and fault-slip analyses, complemented by the reconstruction of cumulative geomorphic offsets along the main fault segments. The collected data sets have led us to propose a new tectonic model for the northwest corner of the Arabia – Central Iran collision zone. Our results reveal that the intracontinental dextral shear between Arabia-Central Iran, which is mainly localized along the MRF, continues to the north of latitude 37°N along a branch of the Neotethyan suture penetrating into SE Anatolia. The dextral fault system abruptly dies out at latitude 37.5° N joining two NNW-striking normal fault zones, which accommodate the dextral translation of Central Iran relative to Arabia through ESE-trending extension. The region in NW Iran and SE Anatolia is affected by a heterogeneous active stress field due to different tectonic processes such as tectonic escape, block translation, and localized extension. The dynamics of these processes is either directly governed by the Arabia – Eurasia oblique convergence or indirectly controlled by frontal collision and pure shear deformation in central Anatolia.

Experimental and numerical studies of an axial tension-compression corrugated steel plate damper

Metallic dampers are widely used due to their satisfactory plastic energy dissipation, low price and convenient installation. In this study, an axial tension and compression corrugated steel plate damper (ATCCSPD) was proposed. According to the mechanical properties of the ATCCSPD, low-frequency cyclic loading tests and numerical verification of seven ATCCSPD specimens were designed and performed. Additionally, the test phenomena and failure modes of the ATCCSPD specimens were analysed, and seismic performance indices such as the hysteretic curve, skeleton curve, ductility and energy dissipation were obtained. Then, the impacts of the thickness of the corrugated web, the aspect ratio and the thickness of the flange on the seismic behaviour of the ATCCSPD specimens were investigated. The results demonstrated that the seven ATCCSPD specimens exhibited satisfactory ductility and energy dissipation capacity, and the hysteretic curves were stable and full. Overall, the ATCCSPD specimens exhibited axial tension and compression deformation, while the internal corrugated web exhibited pure shear deformation during the loading process. The web thickness and aspect ratio were the main factors affecting the bearing capacity and energy dissipation of the ATCCSPD specimens. The finite element software ABAQUS was used to simulate the ATCCSPD specimens, and shear damage was added to the nonlinear kinematic hardening constitutive model of steel, which could effectively simulate the failure process of the corresponding part after cracks formed in the ATCCSPD specimens. Finally, combined with the test results and the numerical results, the shear bearing capacity formula of the corrugated webs was fitted; then, the formula for calculating the tensile (compressive) bearing capacity of the ATCCSPD specimens was obtained by the superposition principle. By comparing the calculation results with the test results, it was found that the proposed formula was conservative and, hence, suitable for engineering applications.

Crystal rotations and alignment in spatially varying magma flows: 2-D examples of common subvolcanic flow geometries

Summary Elongate inclusions immersed in a viscous fluid generally rotate at a rate that is different from the local angular velocity of the flow. Often, a net alignment of the inclusions develops, and the resulting shape preferred orientation of the particle ensemble can then be used as a strain marker that allows reconstruction of the fluid’s velocity field. Much of the previous work on the dynamics of flow-induced particle rotations has focused on spatially homogeneous flows with large-scale tectonic deformations as the main application. Recently, the theory has been extended to spatially varying flows, such as magma with embedded crystals moving through a volcanic plumbing system. Additionally, an evolution equation has been introduced for the probability density function of crystal orientations. Here, we apply this new theory to a number of simple, 2-D flow geometries commonly encountered in magmatic intrusions, such as flow from a dyke into a reservoir or from a reservoir into a dyke, flow inside an inflating or deflating reservoir, flow in a dyke with a sharp bend, and thermal convection in a magma chamber. The main purpose is to provide a guide for interpreting field observations and for setting up more complex flow models with embedded crystals. As a general rule, we find that a larger aspect ratio of the embedded crystals causes a more coherent alignment of the crystals, while it has only a minor effect on the geometry of the alignment pattern. Due to various perturbations in the crystal rotation equations that are expected in natural systems, we show that the time-periodic behaviour found in idealized systems is probably short-lived in nature, and the crystal alignment is well described by the time-averaged solution. We also confirm some earlier findings. For example, near channel walls, fluid flow often follows the bounding surface and the resulting simple shear flow causes preferred crystal orientations that are approximately parallel to the boundary. Where pure shear deformation dominates, there is a tendency for crystals to orient themselves in the direction of the greatest tensile strain rate. Where flow impinges on a boundary, for example in an inflating magma chamber or as part of a thermal convection pattern, the stretching component of pure shear aligns with the boundary, and the crystals orient themselves in that direction. In the field, this local pattern may be difficult to distinguish from a boundary-parallel simple shear flow. Pure shear also dominates along the walls of a deflating magma chamber and in places where the flow turns away from the reservoir walls, but in these locations, the preferred crystal orientation is perpendicular to the wall. Overall, we find that our calculated patterns of crystal orientations agree well with results from analogue experiments where similar geometries are available.

Theoretical Considerations for Transitioning the Grid Method Technique to the Microscale

As new applications demand the synthesis and validation of materials with specific mechanical performance targets, there is a need for improved characterization and understanding of reduced length-scale deformation processes which govern mechanical behavior (i.e., dislocation slip and twinning). The heterogeneous nature of deformation in polycrystalline materials makes it essential to employ length-scale-independent and material agnostic full-field measurement techniques during mechanics of materials studies. The intention of the current work is to demonstrate the fundamental steps of transitioning the Grid Method (GM), a macro-scale full-field measurement technique used in mechanics of materials studies, to the microscale. Two obstacles overcame when transitioning the technique are reported. The first is the deposition of ultra-fine grids with a pitch of 500nm using a focused ion beam. The second is the characterization and correction of equipment-dependent raster-based image distortions inherent to scanning electron microscope (SEM) image acquisition. The SEM-induced distortions are simulated using a closed-form model which more accurately represents the Fast Fourier Transform modulus obtained from SEM micrographs. The proposed model is validated against synthetic deformation cases, specifically uniaxial tension, uniaxial compression, pure shear, simple shear, and heterogeneous deformation. A two-step filtering procedure informed by the newly introduced closed-form model, consisting of a notch and frame filter is proposed in order to remove distortions observed in SEM micrographs. After correcting the SEM-induced distortions on the stationary microgrid micrographs using the proposed two-step filtering, the extracted strain distortion level is reduced from 0.02 to 0.005 strain. Combined, the efforts presented in the current work demonstrate the initial development and promise of the microscale scanning electron microscope grid method (SEM-GM) to capture distortion corrected strain maps in reduced length-scale.

Subduction characteristics of the ordovician erlangping back-arc basin in the east qinling mountains, china: implications for the tectonic evolution of the northern margin of the proto-tethys ocean

ABSTRACT A relatively complete trench–arc–basin system developed on the northern margin of the Proto-Tethys Ocean, and its subduction mode is key in reconstructing the tectonic evolution of the northern Proto-Tethyan margin. The Erlangping Group in the East Qinling Mountains is thought to be the product of subduction in the back-arc basin. Analysis of the metamorphism and deformation recorded by the group may elucidate the subduction mode of the back-arc basin. In this study, the tectonites in the southern and northern parts of Erlangping Group are taken as the research object, and their dynamic parameters such as geometry, kinematics and vorticity are determined by field observation and indoor tectonic deformation analysis. Deformed rocks in the northern part of the Erlangping Group are mainly feldspathic schists, primary mylonite, and mylonite, and the deformed rocks in the southern part of the Erlangping Group are mainly schists. The geometric characteristics of Erlangping group show that the foliation (30°–60°∠ 42°–70°) and dip lineation (5°–62°∠ 33°–51°) in the north of Erlangping group incline to NE, while the foliation (174°–234°∠ 50°–80°) and dip lineation (195°–230°∠ 45°–65°) in the South incline to SW; the kinematic characteristics show that both sides of Erlangping Group move under Qinling Group and Kuanping Group, respectively. Kinematic vorticity calculation shows that the vorticity values of the northern and southern parts of Erlangping Group are 0.79 and 0.78, respectively, both of which are more than 0.75, indicating that the shear type is dominated by simple shear and supplemented by pure shear. The average values of kinematic vorticity on the northern and southern parts of Erlangping Group are 0.78 and 0.79, respectively, both more than 0.75, indicating that subduction was dominated by simple shear, with minor pure shear deformation. The subduction deformation temperature range of Erlangping Group is estimated to be 380 ~ 500°C by the degree of quartz dynamic recrystallization. There is a positive correlation between the differential stress value σ (southern parts of Erlangping Group: 17.84–46.50; northern parts of Erlangping Group: 17.87–71.66) and strain rate ε (southern parts of Erlangping Group: 2.09 × 10–14 – 2.51 × 10–13; northern parts of Erlangping Group: 2.08 × 10–14 – 8.23 × 10–13) during subduction, while the grain size of dynamically recrystallized quartz is negatively correlated with strain rate. The specific performance is that in the northern part of Erlangping Group, from the Waxuezi–Qiaoduan shear zone to the Damiao–Dongjie shear zone, with the increase of the particle size of dynamically recrystallized quartz particles, the values of differential stress and strain rate gradually decrease, and have the same performance in the southern part of Erlangping Group. Through the above structural deformation analysis, combined with the previous research results on the material composition, sedimentary formation, magmatism, metamorphism and deformation of the Erlangping back-arc basin, it is considered that the Erlangping back-arc basin has the characteristics of bidirectional subduction during the late Palaeozoic subduction.*

On the Performance of Isotropic Hyperelastic Constitutive Models for Rubber-Like Materials: A State of the Art Review

Abstract Besides the well-known landmark models for the hyperelastic response of rubberlike materials, many new hyperelastic constitutive models have emerged over the last decade. Despite many reviews on constitutive modeling or elastomers, it is still a challenging endeavor for engineers to decide for a constitutive model for the specific rubber compound and application. In this work, we have reviewed 44 hyperelastic constitutive models for elastomers and assessed their strength and weaknesses under uniaxial, pure shear, and (equi)biaxial deformations. To this end, we first present a novel parameter identification methodology based on various multi-objective optimization strategies for the selection of the best constitutive models from a given set of uniaxial tension, pure shear, and (equi)biaxial tension experiments. We utilize a hybrid multi-objective optimization procedure using a genetic algorithm to generate multiple initial points for gradient-based search algorithm, Fmincon utility in matlab. The novelty of the approach is (i) simultaneous fitting with variable weight factors for uniaxial, equibiaxial, and pure shear data, and (ii) the sorting of the models based on objective normalized quality of fit metric. For the models incapable of simultaneously fitting the three distinct deformation data, the validity range is assessed through a threshold value for the quality of fit measure. Accordingly, 44 hyperelastic models are sorted with respect to their simultaneous fitting performance to the experimental dataset of Treloar and Kawabata. Based on the number of material parameters, and their fitting performance to experimental data, a detailed discussion is carried out.

Experimental determination of deformation homogeneity and shear states using the digital image correlation method

One of the great challenges in the pure shear and simple shear tests is to maintain the deformation state and deformation homogeneity of a specimen under large deformations. For this reason, the aim of this work is to investigate the state of shear deformation and degree of deformation homogeneity of three different shear specimens. A simple and easily replicable methodology was proposed to estimate the degree of deformation homogeneity of specimens, while a time-independent kinematic vorticity parameter was employed to identify pure shear and simple shear deformation states. All data were obtained from full-field displacements that were extracted with the two-dimensional digital image correlation (2D-DIC) method. Specimens of polytetrafluoroethylene (PTFE) were tested using the modified slotted shear test and the V-notched rail shear test, which are used to induce a simple shear state. The planar tensile test was used to produce a pure shear state in a thin sheet of rubber-like material. For small deformations, both slotted and V-notched shear tests induced a good degree of deformation homogeneity along the shear path between the notches of specimens, mainly in the central region. However, the V-notched specimens buckled at large deformation, producing a decrease in the degree of deformation homogeneity. In this case, the results were qualitatively assessed due to the errors associated with out-of-plane motions. High degree of deformation homogeneity was also observed in pure shear specimens. All tests demonstrated to be effective for inducing a state of pure shear or simple shear. Results show that the two approaches can be used as supplementary tools for determining the state of shear deformation and degree of deformation homogeneity.

Adiabatic shearing mechanism on Al-4.2%Cu alloy bars subjected to electromagnetic loading

This paper proposed an electromagnetic loading process with the high-speed impact. Al-4.2% Cu alloy bars were used to employ electromagnetic impact (EI) experiments. Deformation mechanism and microstructure evolution of EI samples were revealed by theoretical model and microstructure characterizations. The EI process had impact force (peak value 40 kN) and impact velocity (peak value 6.7 m/s) during a short time period (1.25 ms). Adiabatic shearing mechanism dominated the whole deformation process, causing that significant microstructure characteristic was adiabatic shear bands (ASBs). The theoretical analysis implied that the formation of ASBs was accounted for the radial velocity gradient. Most plastic deformations concentrated in ASBs, and approximately pure shear deformations resulted in adiabatic temperature rise of 0.33–0.42 Tm inside ASBs. The width of ASBs was about 135 μm, in which original equiaxial grains were elongated into laminated sub-structures. TEM observations showed multi-slip systems were simultaneously actuated due to severe shear deformations. High dislocation density and dislocation tangles distributed with the ASBs. Adiabatic temperature rise and distorted energies drove sub-grains rotate into recrystallization grains (70–280 nm) with large angle grain boundaries. The needed maximum time (45 μs) for rotational dynamic recrystallization was far less than that of plastic deformation, indicating that rotational dynamic recrystallization mechanism contributed to the formation of recrystallization grains.

Effect of stretching angle on the stress plateau behavior of main-chain liquid crystal elastomers.

The equilibrium nonlinear stress-stretch relationships for a monodomain main-chain nematic elastomer (MNE) are investigated by varying the angle between the stretching and initial director axes (θ0). Angle θ0 has pronounced effects on the ultimate elongation as well as on the width of the low stress plateau regime (Λp) during director rotation, whereas θ0 has no appreciable effect on the plateau stress (σp). In the stretching normal to the initial director (θ0 = 90°), the plateau end exceeds 200% strain. At oblique angles of 90° > θ0≥ 35°, Λp decreases with decreasing θ0, whereas the definite plateau regime vanishes at θ0 < 24°. Wide-angle X-ray scattering and polarized optical microscopy measurements reveal that the director rotates uniformly in the biased direction for the MNE of θ0°≪ 90°, whereas directors rotating clockwise and counterclockwise are coexistent for θ0 = 90°. Over the entire plateau regime, the MNEs exhibit pure shear deformation characterized by a Poisson's ratio of zero in the direction of the rotation axis. The Λp for the corresponding polydomain NE (PNE) undergoing a transition to the monodomain alignment is smaller than that of the MNE of θ0 = 90°, while the σp values for both NEs are almost similar. The semi-soft elasticity concept satisfactorily explains the effects of θ0 on Λp, and the Λp value of the PNE, using a single anisotropy parameter which is evaluated from the degree of thermally induced deformation of MNEs.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids.

We investigate the non-affine displacement fields that occur in two-dimensional Lennard-Jones models of metallic glasses subjected to athermal, quasistatic simple shear (AQS). During AQS, the shear stress versus strain displays continuous quasi-elastic segments punctuated by rapid drops in shear stress, which correspond to atomic rearrangement events. We capture all information concerning the atomic motion during the quasi-elastic segments and shear stress drops by performing Delaunay triangularizations and tracking the deformation gradient tensor Fα associated with each triangle α. To understand the spatio-temporal evolution of the displacement fields during shear stress drops, we calculate Fα along minimal energy paths from the mechanically stable configuration immediately before to that after the stress drop. We find that quadrupolar displacement fields form and dissipate both during the quasi-elastic segments and shear stress drops. We then perform local perturbations (rotation, dilation, simple and pure shear) to single triangles and measure the resulting displacement fields. We find that local pure shear deformations of single triangles give rise to mostly quadrupolar displacement fields, and thus pure shear strain is the primary type of local strain that is activated by bulk, athermal quasistatic simple shear. Other local perturbations, e.g. rotations, dilations, and simple shear of single triangles, give rise to vortex-like and dipolar displacement fields that are not frequently activated by bulk AQS. These results provide fundamental insights into the non-affine atomic motion that occurs in driven, glassy materials.

Shear strain bandgap tuning of monolayer MoS2

Bandgap tuning is an attractive property of two-dimensional semiconductors and monolayer MoS2, in particular. We report here the bandgap tuning of monolayer MoS2. This was achieved by growing monolayer MoS2 on optical fibers that were then subjected to torsion, such that pure shear was transferred to MoS2. The effect of shear was inferred from the observed photoluminescence spectrum, after which a blue shift of ∼10 meV/% emerged. Detailed analysis revealed that this shift is mainly due to the trion luminescence and less due to the excitons. This observation experimentally uncovers the behavior of MoS2 under a yet uncharted pure shear deformation, which may enable the development of devices, such as tunable electronic components and high-precision sensors.

A generalised neo-Hookean strain energy function for application to the finite deformation of elastomers

We present a new model within the class of generalised neo-Hookean strain energy functions for application to the finite deformation of incompressible elastomers. The model has a simple form with only two parameters, namely μ and N with structural roots, and is derived within the classical framework of statistical mechanics for freely jointed molecular chains in rubber elasticity Using existing experimental datasets of uniaxial, biaxial, and pure shear deformations, including Treloar’s canonical data, we show that the proposed model captures the deformation behaviours of each elastomer specimen with a single set of μ and N values (with only a narrow variation range). We conduct qualitative and quantitative comparative analyses to highlight the advantages of the proposed model, and demonstrate improved fits versus the celebrated Gent model. Given its structural molecular basis, simplicity, small number of parameters, and its capability to describe many deformation modes of a specimen using a single set of parameter values, we propose this model for application to finite deformation of elastomers.

Vacancy-driven shear localization in silicon nitride

Vacancies play an essential role on mechanical properties of ceramics, while it is a challenge to reveal the atomistic process of vacancy-driven failure mechanism due to difficulty in characterizing the atomic defects. Here, we used hexagonal silicon nitride as a prototype ceramic and report the shear localization as a main failure mechanism, which is characterized by combining nanoindentation and scanning transmission electron microscopy. It is revealed that the intrinsic point defects in silicon nitride triggers the nanoscale shear bands on the prismatic slip plane when subjected to high stresses. The quantum mechanics simulations ascertained that the shear bands are mediated by nitrogen defects in tetragon sites during the pure shear deformation.

An isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

In the modelling of fibre-reinforced composites, it is well established to consider the fibre direction in the stored energy in order to account for the transverse isotropy of the overall material, induced by a single family of fibres. However, this approach does not include any length scale and therefore lacks in the prediction of size effects that may occur from the fibre diameter or spacing. By making use of a generalised continuum model including non-symmetric stresses and couple-stresses, the gradient of the fibre direction vector can be taken into account as an additional parameter of the stored energy density function. As a consequence, the enhanced model considers the bending stiffness of the fibres and includes information on the material length scale. Along with additional material parameters, increased continuity requirements on the basis functions follow in the finite element analysis. The isogeometric finite element method provides a framework which can fulfil these requirements of the corresponding weak formulation. In the present contribution, the method is applied to two representative numerical examples. At first, the bending deformation of a cantilever beam is studied in order to analyse the influence of the fibre properties. An increasingly stiff response is observed as the fibre bending stiffness increases and as the fibre orientation aligns with the beam’s axis. Secondly, a fibre-reinforced cylindrical tube under a pure azimuthal shear deformation is considered. The corresponding simulation results are compared against a semi-analytical solution. It is shown that the isogeometric analysis yields highly accurate results for the boundary value problem under consideration.

Increase in Total Elongation Caused by Pure Shear Deformation in Ultra-Fine-Grained Cu Processed by Equal-Channel Angular Pressing

Ultra-fine-grained (UFG) Cu shows little total elongation in tensile tests because simple shear deformation is concentrated in narrow regions during the initial stage of plastic deformation. Here, we attempted to improve the total elongation of UFG Cu obtained by equal-channel angular pressing. By making shallow dents on the side surfaces of the plate-like specimens, this induced pure shear deformation and increased their total elongation. During the tensile tests, we observed the overall and local deformation of the dented and undented UFG Cu specimens. Using three-dimensional digital image correlation, we found that the dented specimens showed suppression of thickness reduction and delay in fracture by enhancement of pure shear deformation. However, the dented and undented specimens had the same ultimate tensile strength. These results provide us a new concept to increase total elongation of UFG materials.

Structure-strength relations of distinct MoN phases from first-principles calculations

Molybdenum mononitrides (MoN) exhibit superior strength and hardness among the large class of transition-metal light-element compounds, but the underlying atomistic mechanisms for their outstanding mechanical properties and the variations of those properties among various MoN phases adopting different crystal structures remain largely unexplored and require further investigation. Here we report first-principles calculations that examine the stress-strain relations of these materials, and systematically compare results under pure and indentation shear deformations. In particular, we examine the distinct bonding structures and the associated mechanical properties in four different crystal phases of MoN that have been experimentally synthesized and stabilized under various physical conditions. Our results reveal evolution patterns of bonding configurations and the resulting structural deformation modes in these MoN phases, which produce diverse stress responses and unexpected strength variations. These findings elucidate the structural and bonding characters that are responsible for the rich and distinct mechanical properties in various MoN structures, providing insights for understanding the experimentally observed phenomena and further exploring advanced superhard materials among the promising transition-metal nitrides, borides, and carbides.

Plastic instabilities and yielding in amorphous solids under pure shear

The nature of mechanical yielding in amorphous materials under external loading is investigated using computer simulation. We study the plastic instabilities and yielding transition in a model amorphous solid of a binary Lennard-Jones mixture under pure shear deformation. We carefully examine the plastic instabilities in the pre- and post-yield regime and find that these occur via the so-called saddle-node bifurcation mechanism in the athermal quasistatic limit. To quantify the yielding transition, we use the overlap order parameter Q12, which has been successfully used in various glassy models. Our results show that the yielding transition is accompanied by a dramatic change in the structure of the material. We identify this as a first-order phase transition with a significant difference in the yielding transition point compared to the simple shear protocol.

Formation of tube-pumice structure under pure shear: Insights from extension tests of solidifying foam

Tube pumice, the bubbles of which are highly elongated in one direction, is a common product of explosive silicic eruptions, especially caldera-forming eruptions. To understand the conditions necessary to generate tube-like bubbles, we performed extensional experiments on polyurethane foam, which experiences vesiculation, deformation, and solidification at room temperature. The strain and strain rate of pure shear deformation were controlled by the pull length and pull rate of the extension, respectively. The shapes of bubbles in the solidified polyurethane foam were analyzed in three dimensions by X-ray computed tomography. The experimental results demonstrate that strain and capillary number control the degree of bubble deformation. Highly deformed (tube-like) bubbles were found in the experiments with large strain and large capillary number. In each experimental sample, there is scatter in the relation between the degrees of bubble deformation and expected capillary numbers, which we interpret to be the result of the inhomogeneous shear field around individual bubbles and bubble coalescence. Despite the large scatter, the average deformation degree is predicted well by the dynamics of a single bubble, where the viscous stress acting on the bubble surface is taken as the product of bulk strain rate and effective viscosity. Using this approach, the average deformation degree of experimental bubbles in each sample was approximately calculated from the deformation model of a single bubble at least in the range of pure shear strain smaller than 1.5. Small bubbles in the samples extended at low viscosities tend to be less elongated than those calculated from the deformation model, due to shape relaxation. The effect of shape relaxation is quantified by a new dimensionless number, i.e., the quench number, which represents the ratio of the timescale of increasing viscosity and shape relaxation. Our experiment suggests that bubble shapes in highly vesicular pumice can be used to analyze their viscosity and strain rate during the elongation process. An analysis of the published data was presented as a test case.