Small Deformation Research Articles

Shear and shear-induced normal responses of origami cylinders relate to their structural asymmetries

Origami cylinders have been studied extensively under compression, however, their normal force response under shear deformation is still ill-understood. We experimentally studied the shear-induced normal force of these systems and provided a simple model to predict this response in Yoshimura and Kresling origami cylinders in the range of small deformations. Besides that, the effect of disorder is little understood in those origami patterns. Therefore, we investigate the disorder effect and show it can lead to diverse normal responses perpendicular to shear deformation in crumpled Yoshimura, with slopes of the force perpendicular to torsion that can be positive, zero, or negative depending on the disordered pattern of folds. The disorder leads to an asymmetry concerning the shearing direction, which we quantified via an asymmetry index from the 2D Fast Fourier transform spectrum of the crease pattern images. This asymmetry index is found to be linearly related to the slope of the normal force-torsion relationship.

Theoretical analysis of the interaction between blasting stress wave and linear interface crack under high in-situ stress in deep rock mass

This study theoretically investigates the scattering characteristics of blasting stress waves, treaded as elastic waves, at a linear interface crack in a deep rock mass with an even compressive in-situ stress field. First, the basic equations of the deep rock mass theoretically treaded as a homogeneous isotropic medium with an initial stress field are derived based on the linear elastic, finite deformation, plane strain, isotropic, and small deformation hypotheses, and incremental stress theory. The linear interface crack is theoretically treaded as two displacement-free boundaries, of which the interpolation displacements are described by introducing two dislocation density functions. Next, the mathematical model of the blasting stress wave scattering at the linear interface crack is established through a set of singular integral equations of the first type for these two dislocation density functions with Cauchy kernels. Finally, the dislocating and opening displacements of the linear interface crack and the displacement and effective stress fields of the scattered stress wave are numerically calculated. The principal stress field of the scattered stress wave is compared with the experimental data to qualitatively verify the rationality and correctness of the mathematical model. Theoretically, it is found that even compressive in-situ stress with an amplitude of tens of megapascals significantly affects the displacement and effective stress fields of the scattered stress wave near the linear interface crack. In conclusion, considering even compressive in-situ stress is greatly significant when studying the wave and scattering behaviors of deep rock masses. This mathematical model provides a theoretical guidance for the study of stress wave energy transformation and crack propagation in the process of rock blasting and mineral mining.

Preparation of Na3V2(PO4)3 Cathode Materials by Hydrothermal Assisted Sol-Gel Method for Sodium -Ion Batteries

Na3V2(PO4)3 (NVP) cathode material of the sodium ion battery (1 C=117 mAh g-1) has a NASICON-type structure, which not only facilitates the rapid migration of sodium ions, but also has a small volume deformation during sodium ion de-intercalation and the main frame mechanism remains unchanged, and thus is seen as an energy storage material for a wide range of applications, but has a limited electronic conductivity due to its structure. In this paper, NVP cathode materials with finer primary particles are successfully prepared using a simple hydrothermal treatment-assisted sol-gel method. The increased pore size of the NVP materials prepared under the hydrothermal process allows for more active sites and more effective resistance to the volume deformation of sodium ions during insertion/extraction processes, effectively facilitating the diffusion of ions and electrons. The Na3V2(PO4)3 material obtained by the optimized process exhibited good crystallinity in XRD characterization, as well as superior electrochemical properties in a series of electrochemical tests. A specific capacitance of 106.3 mAh g-1 at 0.2 C is demonstrated, compared to 96.5 mAh g-1 for Na3V2(PO4)3 without hydrothermal treatment, and cycling performance is also improved with 93% capacity retention. The calculated sodium ion diffusion coefficient (DNa = 5.68 × 10-14) obtained after EIS curve fitting of the improved sample illustrates that the pore structure is beneficial to the performance of the Na3V2(PO4)3 cathode material.

An improved analysis of small punch deformation for evaluating tensile properties

Small punch (SP) method is a promising technique for evaluating tensile properties using small volumes of test material, yet its applicability is bound by large errors in estimation of tensile yield strength (YS) using the yield force (FY) determined by the existing two tangent, offset or bilinear function fitting methods. In this study, a yield force (FY) based on the occurrence of yielding across the specimen thickness is identified through finite element analysis and a methodology is formulated for determination of FY from experimental data, supported with acoustic emission (AE) technique. The YS-FY correlation for various structural steels, Inconel and Aluminium exhibit excellent linearity and standard errors within ±7 %. Based on the onset of plastic instability in SP deformation at an inflection point (Fs, us) of force-deflection curve, the specimen deflection us is shown to correlate with tensile uniform strain better than parameter um (deflection at peak load). The tensile properties of neutron irradiated SS 316 evaluated from SP tests using the methodologies and SP-tensile correlations formulated in this work, are found to be within 6–8 % of the uniaxial tensile test results.

A novel metamaterial with instantaneously sign-switchable coefficient of thermal expansion and Poisson's ratio

Most materials expand when heated and contract when cooled. In contrast, negative thermal expansion materials exhibit the opposite behavior. In this paper, we present a metamaterial that expands both when heated and cooled. The unit cell configuration is crafted by embedding two isosceles triangular structures composed of high thermal expansion materials within a re-entrant hexagonal honeycomb framework. Initially, the bases of the two isosceles triangles are in contact. The metamaterial exhibits two deformation states under different external loads. Analytical formulas for the equivalent parameters were derived based on classical beam theory within the regime of small deformation. Finite element simulations were conducted to validate the accuracy of these analytical formulas. The influence of geometric parameters on the metamaterial is discussed in detail. The results demonstrate that the metamaterial can exhibit excellent multi-functional properties within a small range of deformation, including instantaneous sign-variable coefficients of thermal expansion and Poisson's ratios, along with significantly distinct tensile and compressive stiffnesses. This metamaterial consistently exhibits expansive characteristics regardless of variations in ambient temperature. Additionally, the material always expands laterally regardless of the sign of uniaxial loads. Based on these properties, the metamaterial can be applied to fasteners in the aerospace industry that require permanent locking, ensuring stability in various temperature and mechanical load conditions.

Progressive collapse resistance of precast concrete beam–column assemblies using dry connections under uniformly distributed loading condition

Improving the integrity of precast concrete (PC) frame structures using dry connections is essential for enhancing their robustness against progressive collapse. Therefore, three PC beam–column assemblies using different dry connections specially designed to ensure the connectivity were experimentally examined under progressive collapse scenarios. And a seven-point loading tree device was adopted to simulate the uniformly distributed loading conditions in practical engineering. The connection details were classified as follows: normal top-and-seat angle connection in TSA, strengthened top-and-seat angle connection in STSA, and strengthened top-and-seat angle with high ductility longitudinal reinforcements in the plastic regions in DSTSA. Under small deformations, STSA had the highest first peak load attributable to its strengthened joint connection. TSA obtained a lower load than that of STSA because of the low joint connection stiffness. Meanwhile, DSTSA achieved the lowest load among the three specimens because the smoother surface of the high-ductility reinforcements (compared with that of normal ones) weakened its bond to the concrete. However, under large deformations, the high ductility of the reinforcements ensured the specimen integrity; consequently, the largest final load was achieved in DSTSA. On the contrary, the high joint stiffness and normal reinforcements in STSA hindered the beam end rotation, and the steel angle failed early in TSA. As a result, the two connections failed to ensure the specimen integrity. To further shed light on the resistance mechanisms of beam–column assemblies under the uniformly distributed loading condition, an iteration-based model was developed to calculate the first peak load under the beam and compressive arch actions. The maximum prediction error achieved was 12%. Based on the model, the load contribution from the friction effect of the loading device was identified as 27%. And it was found that during the collapse, increasing reinforcement deformation region that might be induced by slippage between the concrete and reinforcements could lead to a continuous increase in the horizontal reaction force after the specimen reaching the first peak load.

Bending creep behaviour of various polymer films analysed by surface strain measurement.

Understanding the temporal bending deformation of polymer films is key to designing mechanically durable flexible electronic devices. However, such creep behaviour under persistent bending remains unclear due to a lack of precise and accurate bending strain analysis methods. Herein, we quantitatively analysed the bending creep behaviour of various polymeric films using our developed strain measurement method that can precisely measure surface strain from optical diffraction. The surface strain measurement reveals that bending creep deformation differs depending on the polymer structure. The four-element Burgers model was employed to model the temporal strain increase on the bending surface successfully. By fitting the four-element model to the time course of the measured surface strain, we found that each polymer film has a different threshold surface strain for the appearance of bending creep deformation. Such disparity in the bending creep behaviour can be explained by the difference in strain energy density between the polymer films and their elastic model; polymer films with a small strain energy density difference show small bending creep deformation. The results obtained in this study contribute to the elucidation of the bending creep behaviour of polymer films and the development of flexible electronic devices operated under persistent bending.

Subduction intraslab-interface fault interactions in the 2022 Mw 6.4 Ferndale, California, earthquake sequence.

The Mendocino triple junction-the intersection of the Pacific, North American, and Gorda plates-activates a collection of disparate faults that reconcile Cascadia subduction with San Andreas transform motion. The 20 December 2022 Mw 6.4 Ferndale, California, earthquake occurred within this complex zone as strike-slip faulting within the subducting Gorda slab. Here, we analyze the seismic and geodetic signatures of the mainshock and aftershock sequence to illuminate its role within complex tectonic surroundings. We find aftershocks on varied fault structures within the uppermost Gorda slab, yet seismicity on the subduction interface itself was notably absent. Nevertheless, we identify small but coherent postseismic deformation that is well modeled by aseismic slip on this interface, likely triggered by stresses generated at the updip limit of coseismic rupture. This sequence demonstrates the potential for interactions between intra-slab earthquakes and slip on the subduction megathrust, highlighting the need to consider this and other subduction zones as coupled systems of interacting faults.

Interpreting correlations in stress‐dependent permeability, porosity, and compressibility of rocks: A viewpoint from finite strain theory

AbstractCharacteristics of stress‐dependent properties of rocks are commonly described by empirical laws. It is crucial to establish a universal law that connects rock properties with stress. The present study focuses on exploring the correlations among permeability, porosity, and compressibility observed in experiments. To achieve this, we propose a novel finite strain‐based dual‐component (FS‐DC) model, grounded in the finite strain theory within the framework of continuum mechanics. The FS‐DC model decomposes the original problem into the rock matrix and micro‐pores/cracks components. The deformation gradient tensor is utilized to derive the constitutive relations. One of the novelties is that the stress‐dependent variables are calculated in the current configuration, in contrast to the reference configuration used in small deformation theory. The model has only a few number of parameters, each with specific physical interpretations. It can be reduced to existing models with appropriate simplifications. Then, model performance is examined against experimental data, including permeability, porosity, compressibility, volumetric strain and specific storage. It proves that the variations of these properties are effectively described by the proposed model. Further analysis reveals the effect of pores/cracks parameters. The validity of the FS‐DC model is examined across a broad range of pressures. The results show that rock properties at high confining pressures (300 MPa) differ from those observed under relatively low pressures (200 MPa). This disparity can be attributed to inelastic behaviors of micro‐structure, wherein the rock skeleton undergoes permanent deformation and breakage.

Deformation and breakup of a ferrofluid droplet in shear flow under magnetic field

Effects of magnetic field applied perpendicular to a shear plane in shear flow on the deformation of a ferrofluid droplet are numerically investigated. The boundary integral method is employed to solve the two-phase Stokes flow under a uniform magnetic field. When the magnetic field is applied perpendicular to the shear plane, the deformation of the droplet in the shear plane decreases. The magnetic field causes the droplet to elongate in the y-direction, and its cross-sectional radius in shear plane decreases. Consequently, the apparent capillary number in the shear plane decreases, thereby suppressing the droplet deformation. Droplet breakup is also suppressed by imposing a magnetic field perpendicular to the shear plane, thereby increasing the critical capillary numbers. The critical capillary numbers for the magnetic Bond numbers Bo = 2.0 and 4.0 increase to approximately 110% and 130%, respectively, than those without magnetic field. Furthermore, an equation for the theoretical prediction of the droplet deformation under a magnetic field in shear flow is presented, which is based on the small deformation theory, the decrease in the cross-sectional radius, and the boundary conditions at the droplet interface. The theoretical prediction agrees well with the numerical results for the variation in the magnetic susceptibility of the droplet as well as the viscosity ratio between the external fluid and the ferrofluid droplet under a small deformation. The critical capillary numbers under a magnetic field can also be predicted by using the numerical results without a magnetic field.

Analytical solutions and classification of vesicle motion and deformation in shear flow: Uncovering new tank-treading modes.

Using a small deformation approach, a fractional ordinary differential system is proposed to investigate the motion and deformation of a vesicle in shear flow. Closed analytical expressions of the orientation angle and the ellipticity of the vesicle contour (shape deformation) are provided. Three different motions are identified, the classical tank-treading state, and two new types of motions, namely, the over-damped tank-treading mode, in which the vesicle's orientation angle ψ and its shape deformation R tend more slowly toward equilibrium, and the under-damped tank-treading mode, in which ψ oscillates all the time along the flow direction with decreasing amplitude, while R starts making a breathing motion and then tends to an attractive amplitude. The implications of our findings extend widely within the field of fluid dynamics, revealing the potential for further advancements and applications in understanding complex fluid systems.

Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries

We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries. The algebra of the symmetry operators is realized projectively on the Hilbert space, signaling anomalies on the lattice, and constraining the long-distance behavior. In the special case of the free Hamiltonian (and small deformations thereof), the continuum limit is the 1+1d free Majorana CFT. Its continuum chiral fermion parity (-1)^{F_L}(−1)FL emanates from the lattice translation symmetry. We find a lattice precursor of its mod 8 ’t Hooft anomaly. Using a Jordan-Wigner transformation, we sum over the spin structures of the lattice model (a procedure known as the GSO projection), while carefully tracking the global symmetries. In the resulting bosonic model of Ising spins, the Majorana translation operator leads to a non-invertible lattice translation symmetry at the critical point. The non-invertible Kramers-Wannier duality operator of the continuum Ising CFT emanates from this non-invertible lattice translation of the transverse-field Ising model.

Understanding structure/rheology relationships of amidated low-methoxyl citrus and apple pectin gels: Implications of sucrose, pectin types and characteristics

In this study, the relationships between structure and rheology (at small and large deformations) of amidated low-methoxyl (LMA) citrus and apple pectin gels were investigated considering how does these relationships can be modulated by soluble solids (sucrose), pectin types and characteristics. For that purpose, various LMA pectins with varying degrees of methyl esterification (DE) and amidation (DA), processed from citrus peels and apple pomace, were used. Scaling models of biopolymer gels have been critically discussed in respect to pectin critical gelling concentration (C0) and their structural variabilities. It was demonstrated that, whatever the types of LMA pectins and their structural variabilities, scalar percolation and quadratic models can be efficiently used for the prediction of the storage modulus G′ and C0 as other biopolymer gels. Fractal approach reveals that the origin of the LMA pectin gel elasticity is more in harmony with an enthalpic network of rod-like filaments with bending rigidity ruling the network's elasticity. The addition of sucrose induced an anticipation of the gelation temperature and an important improvement of the viscoelastic properties of the resulting gels. It was also shown that the most tough gels are obtained for citrus pectins due to the higher level of neutral sugar side chains in apple pectins that can hinder preponderant ca-bridging sites unlike citrus pectins. Finally, it was shown that unlike the firmness and hardness of the gels which appear to be more driven by the amide groups, the deformability of the gels is rather governed by the methyl ester groups.

Conductive Metal-Organic Framework with Superior Redox Activity as a Stable High-Capacity Anode for High-Temperature K-Ion Batteries.

High-temperature rechargeable batteries are essential for energy storage in elevated-temperature situations. Due to the resource abundance of potassium, high-temperature K-ion batteries are drawing increasing research interest. However, raising the working temperature would aggravate the chemical and mechanical instability of the KIB anode, resulting in very fast capacity fading, especially when high capacity is pursued. Here, we demonstrated that a porous conductive metal-organic framework (MOF), which is constructed by N-rich aromatic molecules and CuO4 units via π-d conjugation, could provide multiple accessible redox-active sites and promised robust structure stability for efficient potassium storage at high temperatures. Even working at 60 °C, this MOF anode could deliver high initial capacity (455 mAh g-1), impressive rate, and extraordinary cyclability (96.7% capacity retention for 1600 cycles), which is much better than those of reported high-temperature KIB anodes. The mechanistic study revealed that C═N groups and CuO4 units contributed abundant redox-active sites; the synergistic effect of π-d conjugated character and reticular porous architecture facilitated the K+/e- transport and ensured an insoluble electrode with small volume deformation, thus achieving stable high-capacity potassium storage.

Deciphering non-elastic deformation in amorphous alloy: Simultaneous aging-induced ordering and rejuvenation-induced disordering

The mechanical and physical properties of amorphous alloys depend on their time, temperature, and stress history. Due to their out-of-thermodynamic-equilibrium nature, describing the nonelastic deformation while considering the evolution of the structural state poses a significant challenge. We address this challenge by incorporating a parameter for structural state changes into a conventional deformation theory. This allows us to account for aging-induced ordering and deformation-induced disordering in the description of the mechanical deformation. In the apparent elastic regime (small strain), aging dominates while disorder caused by deformation can be disregarded. In this context, we have also made modifications to the widely used stretched exponential function, incorporating in-situ aging during deformation. This modification successfully describes the stress relaxation behavior under small deformation conditions and provides insights into parameter evolution in this process. Under large deformation conditions, both aging and deformation induced rejuvenation effects on the structural state must be considered simultaneously. By analyzing the evolution of defect concentration during this process, we describe relevant experimental results within the framework of the free volume theory, effectively separating the contributions of aging and rejuvenation to the structural state during the deformation process.

Comparative gelation characteristics of carrageenan via rheological and optical techniques: Glazing gels with different sweeteners

Glazing gels used as decorative gels are most often applied by hot spraying of solutions based on fast-setting hydrocolloids. The formation of a non-sticky gel at room conditions is crucial for their use. Gel formation and gel melting of carrageenan-based glazing gels (CGGs) with various sweeteners (trehalose, erythritol with stevia, maltitol, oligofructose, and nutriose with sucralose and acesulfame) were monitored during cooling-heating cycles using both the oscillatory rheology and the multispeckle diffusing wave spectroscopy (MS-DWS). In addition, rheological properties (shear viscosity of sols, the viscoelastic properties of gels, gel breaking strain) and texture properties (gel strength, elasticity and rupture force) were evaluated. The 12% addition of sweeteners resulted in a significant increase in gelling and melting temperatures by 2–6 °C compared to the sugar-free control sample (42 °C and 57 °C, resp.). MS-DWS, as opposed to oscillatory rheology, allowed determining of the characteristic temperatures at the beginning, middle and end of the phase transitions. The rheology gelling temperatures correlated best with the end of the gelation process, while the melting temperatures corresponded to the middle point temperature of the MS-DWS. Mechanical properties showed CGGs create a continuous gel structure characterized by a viscoelastic solid with comparable hardness and strength at small deformation, and greater elasticity compared to the sugar-free control sample. CGGs containing small molecule sweeteners formed stronger gels against rupture at large deformation than those ones with macromolecular structure. Sols of all CGGs were clear dispersions at 70 °C with Newtonian fluids characteristics and low viscosity (in the range of 9.3–10.9 mPas). These findings prove CGGs with various sugar-replaced sweeteners could be applied by hot spraying method and indicate how MS-DWS can be used to monitor gelation processes.

Study of longitudinal deformation profiles in high-ground-stress mega-section tunnels based on the Hoek–Brown criterion

In rock tunnel construction, the analysis of rock deformation characteristics is an essential aspect of the overall safety evaluation. In this study, the high-ground-stress section of the Tongzi tunnel was taken as the research object and the longitudinal wave velocities of the disturbed and undisturbed areas of the surrounding rock were measured using on-site drilling to determine the disturbance range of the surrounding rock excavation. The uniaxial and triaxial compressive strengths of the rocks sampled in the field were measured through indoor tests. Through a combination of the field acoustic test and indoor test results, the Hoek–Brown (H-B) failure criterion parameters of the surrounding rock were quantitatively obtained. A numerical model was developed for the analysis, and the following conclusions were drawn: At the pre-deformation stage, the influence of the crown settlement, horizontal displacement, and the tunnel face extrusion deformation were all within the range of one times the tunnel diameter. The location and area of the first tunnel face influenced the extent of the surrounding rock’s pre-deformation. A more pronounced effect on the pre-deformation of the tunnel crown settlement was obtained the closer the first tunnel face was to the tunnel crown. In addition, the closer the first tunnel face was to the arch waist, the more pronounced the impact was on the pre-deformation of the horizontal displacement, and the pre-deformation increased exponentially with the increase in the significance of the excavation area of the first tunnel face. The deformation varied in tunnels that had been excavated using different construction methods. The three-step method employed in this study resulted in the most considerable deformation, followed by the CD method, and the double-side heading method resulted in the smallest deformation. The results show that increasing the number of working faces and using small cross-sectional staggered slot excavation are beneficial to tunnel stability. The field monitoring data are generally consistent with the numerical simulation results, providing a degree of validation for the numerical simulation results. The intrinsic model used in the numerical simulation influences the simulation results. When compared with the Hoek–Brown principal structure model, using the Mohr–Coulomb central structure to simulate the high-ground-stress rock tunneling may result in more considerable elevation arch uplift and tunnel face extrusion deformation. Therefore, it is more reasonable to use the Hoek–Brown principal structure model.

Morphological evolution and property changes of acrylate rubber/polyacetal thermoplastic vulcanizates during dynamic vulcanization process

AbstractA new type of thermoplastic vulcanizates (TPV) that is resistant to hot oil, high temperature, and aging was prepared using acrylate elastomer (ACM) and polyoxymethylene (POM) as raw materials. The phase transition process and micromorphology development of the blends with the change of dynamic vulcanization (DV) time, and to illustrate the effects of the phase transition and the degree of elastomer phase crosslinking on the macroscopic properties of TPV were investigated. It was shown that ACM crosslinking occurs continuously during 0–8 min of DV, whereas the phase inversion process occurs predominantly during 0–3 min. In contrast, the cross‐section of the blends after phase inversion is flat, The constant elongation stress under small deformation, hardness, and permanent deformation after break are reduced, and the elongation at break, nonrelaxable modulus, and aging resistance are improved. The increase in the degree of vulcanization of the ACM phase resulted in a significant increase in the modulus of the blends under large deformation, an increase in the nonrelaxable modulus and relaxable modulus, an increase in the aging resistance, and a decrease in the elongation at tear were observed.

Degree growth of lattice equations defined on a 3x3 stencil

We study complexity in terms of degree growth of one-component lattice equations defined on a $3\times 3$ stencil. The equations include two in Hirota bilinear form and the Boussinesq equations of regular, modified and Schwarzian type. Initial values are given on a staircase or on a corner configuration and depend linearly or rationally on a special variable, for example $f_{n,m}=\alpha_{n,m}z+\beta_{n,m}$, in which case we count the degree in $z$ of the iterates. Known integrable cases have linear growth if only one initial values contains $z$, and quadratic growth if all initial values contain $z$. Even a small deformation of an integrable equation changes the degree growth from polynomial to exponential, because the deformation will change factorization properties and thereby prevent cancellations.

A parametric study on the elastic limit stresses of rotating variable thickness orthotropic disk

This paper investigates the stress fields at the onset of plastic yield of variable thickness rotating orthotropic disk, which is rigidly fixed on an inclusion. In the analytical modeling of the problem, two different analytical solution methods have been displayed where small deformations have been considered with the application of plane stress conditions. Well-known power law is considered for the disk's thickness variation, and Hill’s yield criterion is applied to obtain the elastic limits. Four parameters have been utilized while analyzing the limit fields: geometric parameter to manipulate the disk thickness, orthotropy parameter from the ratio between Young's modulus in radial and tangential directions, and two parameters owing to the applied yield criteria. The effects of these parameters on the limit fields have been comprehensively examined in the numerical examples, and possible outcomes have been discussed. Additionally, using Autodesk Inventor Nastran, finite element solution of the disk is generated, analytical and numerical results have been compared, and consequently, closely matching results have been achieved.