Linear Elastic Deformation Research Articles

Damage characteristics and constitutive model of magnesium slag-based cemented backfill based on energy dissipation

Uniaxial compression tests were conducted on magnesium slag-based backfill with different curing ages (3, 7, and 28 d) and different magnesium slag grinding time (0, 40, 60, and 80 min) to investigate the energy damage characteristics and the constitutive model of ground magnesium slag-based cemented backfill in depth. The effects of curing age and magnesium slag grinding time on the energy evolution and distribution characteristics, as well as energy indexes at characteristic points of magnesium slag-based backfills, were examined. From the perspective of energy dissipation, damage variables and modified damage constitutive models were proposed to address the shortcomings of existing damage constitutive studies. The results of the study show that extending the curing age can effectively increase the energy storage limit of backfill and exhibit higher linear elastic deformation capacity. The elastic energy ratio curves of the backfill show an upward and then a downward trend, while the dissipated energy ratio curves show the opposite trend. The relationship between the total energy at the peak stress and the curing age and magnesium slag grinding time can be characterized by linear and quadratic polynomial functions, respectively. The pre-peak energy consumption, post-peak energy consumption, total energy consumption, and energy storage limit of magnesium slag-based backfill all show a linear increase with increasing curing age. The modified energy damage constitutive of magnesium slag-based backfill considering the compaction stage and residual strength shows higher consistency with the test constitutive, which can more realistically reflect the deformation process of the backfill. These results can provide a theoretical basis for investigating the stability of magnesium slag-based backfills in mine filling applications.

Wind-induced collapse mode and mechanism of super-large hyperbolic steel reticulated shell cooling tower with stiffening rings

With advancement of dry-air cooling technology, it has become feasible to use steel reticulated shell structures in design and construction of industrial cooling towers. Steel reticulated shell cooling towers (SRSCTs) with light weight, high strength, and rapid construction have development potential. Wind-induced collapse accidents in cooling towers frequently occur, characterized by pronounced nonlinear behavior involving significant deformation and material failure. Nevertheless, current stability and collapse analyses of cooling towers based on linear theory and elastic deformation are inadequate and unsafe. Thus, the wind-resistant stability of SRSCTs must be evaluated considering their inherent high flexibility and low damping levels. Considering a 220 m high hyperbolic SRSCT as a case study, a wind-induced collapse FEM simulation and analysis were performed. The average and fluctuating wind loads were measured in a reduced-scale model during wind tunnel tests and used as the time-variant wind pressure in a structural finite-element model. The dynamic performance and buckling collapse analyses of the cooling tower were conducted considering geometric and material nonlinearities. The entire wind-induced failure process of the SRSCT in extreme winds was systematically investigated. The weaknesses in the structural stiffness and the failure process were quantified, with five failure stages and four failure modes. The failure stages included linear elasticity, local member failure, local regional failure, overall structural failure, and collapse. The failure modes included circumferential plastic buckling zone failure, windward buckling failure of the shell, crosswind failure of the stiffening ring (hinged curved-beam mechanism), and windward failure of the stiffening ring (triangular arch-like mechanism). This study confirms that development of plastic buckling zones and formation of plastic hinges, considering geometric and material nonlinearity, are the dominant factor in wind-induced failure and collapse of SRSCTs.

In-situ CT scan-based analysis of damage evolution of coral reef limestone under cyclic loads

The subtropical hurricane, ocean circulation, and excavation disturbance by deep engineering of island reefs bring many challenges for the insight into the mechanical behaviors of coral reef limestone (CRL) under cyclic loads. This paper investigated the damage characteristics of coral gravel limestone (CGL) under triaxial cyclic loads based on the in-situ computed tomography (CT) technique and digital volume correlation method (DVC). The results suggested that the plastic strain of CGL still existed after unloading in the stage of linear elastic deformation. Crack initiation within the specimen occurred at the stress level of about 0.72, and accelerated damage occurred when the stress level exceeded 0.86. Subsequently, we utilized DVC technique to visualize the evolution process of 3-D strain field under cyclic loads. The strain field of the specimen generated strain release in the locality of crack initiation, and the heterogeneous degree of strain field firstly increase and then decrease with the increase of upper limit pressure. Moreover, the secant modulus exhibits a trend consistent with the heterogeneous degree of strain field. Therefore, we introduced the concept of self-information entropy to characterized the heterogeneous degree of strain field, attempting to describe the process of compression and damage of sample. The evolving relationship between secant modulus and axial strain of CGL under cyclic loads was established based on the heterogeneity of strain field. The proposed model provides promising way to predict secant modulus of porous rock materials based on-site CT testing and in-situ measurement in practical engineering.

Effects of foliation angle on mechanical characteristics of carbonaceous slate using uniaxial compression tests

Carbonaceous slate is one kind of metamorphic rocks with developed foliation, which is frequently encountered during tunnel construction in Western China. The foliation plays a crucial role in the stability of tunnels. For this, we conducted uniaxial compression tests, acoustic emission (AE) monitoring and scanning electron microscope (SEM) tests on carbonaceous slate. The results show that the strength, failure mode, and AE characteristics exhibit marked anisotropy with the angle between the axial and the foliation (β). As β increases, the ultrasonic wave velocity decreases monotonically, whereas the uniaxial compressive strength (UCS) displays a distinctive U-shaped trend. The elastic modulus initially decreases and then increases. The cumulative AE counts curve and energy curve show a stepped growth when β ≤ 45°. The AE events are active during the crack compaction phase and remain calm during the linear elastic deformation phase when β > 45°. Upon failure, the energy release accounts for the highest proportion (67%) when β = 45°, while the proportions in other cases are less than 37%. The maximum percentage (31%) of shear cracks is reported when β = 60°, which is six times greater than that at β = 0°. Moreover, Kernel density estimation analysis reveals that the high concentration area with low AF (AE counts / duration time) and high RA (rise time / amplitude) increases initially, and then decreases when β > 60°. In addition, nine types of cracks and seven modes of failure were identified. The foliation angle has a pronounced impact on shear failure modes in comparison with tensile failure modes. The supports could suffer larger deformation when β ≥ 60° compared to other cases. The failure behaviors correspond well with field observations.

Experimental and Meshless Numerical Simulations on the Crack Propagation of Semi-Circular Bending Specimens Containing X-Shaped Fissures Under Three-Point Bending.

Cracks in rock and concrete have a great adverse effect on the stability of engineering structures; however, there are few studies on X-shaped fissures which widely exist in rock and concrete structures. Based on this background, three-point bending fracture tests of SCB specimens containing X-shaped fissures are carried out. The momentum equations in the SPH method are improved, and the crack propagations of SCB specimens under three-point bending are simulated. The results show that cracks grow simply along the vertical direction in the sample with no X-shaped fissures, and the existence of an X-shaped fissure changes the crack growth path and final failure modes of the SCB samples. The crack propagation simulation results are consistent with the experimental results, which verifies the rationality of the improved SPH method. The load-displacement curves mainly present three typical stages: the initial compaction stage, linear elastic deformation stage, and failure stage. The peak load decreases first then increases with an increase in eccentricity. With an increase in X-shaped fissure length and decrease in X-shaped fissure angle, the peak load decreases. The damage counts remain at 0 at the initial loading stage, corresponding to the initial compaction stage and the linear elastic deformation stage, and increase sharply at the later loading stage, corresponding to the failure stage, which is consistent with the experimental results. The influence mechanisms of X-shaped fissures on the crack propagation paths are discussed; the existence of different X-shaped fissure morphologies aggravate the tensile stress concentration at specific positions, leading to different crack propagation modes in the experiments. The research results can provide a certain reference for understanding the failure mechanisms of engineering structures containing X-shaped fissures and promote the applications of the SPH method into the simulations of cross-fissure crack propagations.

Strain-dependent work function of metal surfaces: Insights from first-principles investigation

Establishing a fundamental understanding of the relationship between electronic work function (WF) and applied strain is crucial for the development flexible electrodes of and enhancement of metal corrosion resistance. The underlying mechanisms of this relationship have remained unknown, largely due to inconsistencies from previous studies caused by different strain states and the complex impact of anisotropic surface effects. In this study, we employ first-principles methods to investigate the work functions of strained metal surfaces. Our research findings suggest that lateral strain states significantly affect the WF, while strain perpendicular to the surface has minimal influence. Through subjecting the metal surface to linear elastic deformation, we establish a canonical relationship between the work function and strain. Further comparison of work functions under biaxial strain indicates that surfaces with high atom packing density exhibit greater susceptibility to strain. The mechanism behind the strain-dependent WF is attributed to the interplay of bulk electronic structure and surface dipole effects, which. These effects are influenced by volume changes and the redistributedion of charge density. To this end, we propose an effective strain-induced approach for engineering the WF of metal electrode is proposeds, with potential applications in other various materials.

Damage evolution in asphalt mixtures based on in-situ CT scanning

A novel approach utilizing in-situ Computed Tomography (CT) scanning and digital image processing techniques was developed to overcome the limitations of traditional CT image analysis in studying microcrack evolution in asphalt mixtures. Two types of graded asphalt mixtures (continuous gradation/AC and intermittent gradation/SMA) were scanned in-situ to capture internal structural changes. Digital image processing distinguished primary voids from cracks and extracted crack evolution. Multivariate regression analysis linked crack parameters to compressive strain. The study found that crack evolution during uniaxial compression in asphalt mixtures can be divided into densification, linear elastic deformation, and nonlinear failure stages. As load increases, the number, volume, and void percentage occupied by cracks rise, peak, and then decrease due to merging and engulfing after the ultimate load. The skeletal structure of cracks was obtained, and a damage evolution equation was established, linking crack parameters to damage evolution. Crack tortuosity was used to characterize the resistance effect of different gradations on crack propagation. This methodology provides new insights and technical support for studying damage evolution and understanding the failure mechanisms of asphalt mixtures.

Soft rock rheological similarity criterion under thermal-mechanical effects—a research and its application

The similarity criterion of soft rock in both the linear elastic deformation range and the rheological process are systematically studied in this paper by using the equation derivation method and the dimensional analysis method under the effects of temperature and pressure. A brief analysis is performed and COMSOL is used to verify the deduced similarity criterion numerically. A shale-like material with paraffin wax as the binder and river sand as the main aggregate is then prepared by following the similarity criterion, including compressive strength, tensile strength, elastic modulus, Poisson’s ratio, and thermal conductivity. The mechanical parameters and thermal conductivity of the fabricated shale-like material are measured, and the result shows that the shale-like material has a high similarity with the shale prototype material by comparing the experimental data with the calculated data based on the similarity criterion. This reveals the significance of the similarity criterion for developing model experiments. Thus, this research has enriched the rheological similarity principle system of soft rock and has an important practical value in deep soft rock excavation and support engineering.

Получение и обработка акустических откликов волн Лэмба в датчиках водных растворов базовых вкусов

In this work, the total acoustic wave losses in 128°Y-LiNbO3 wafers during liquid application due to radiation emission of waves into the liquid medium, as well as its viscosity, conductivity, density and dielectric constant of the liquid analyte are measured. Solutions with 5 basic flavors, widely used for calibration and reference creation in liquid media testing, were selected as test liquids. The measurements were performed in the range of 30...60 MHz. After the measurements, the experimental data were presented in the form of polar histograms, from the comparison of areas and shapes of which the flavor of a particular liquid was determined. Then, a principal component analysis (PCA) method was applied to the same experimental results to describe linear elastic wave deformation processes based on experimental data containing known values of physical wave measurements for different types of liquid media, which was previously used to identify gases and predict the properties of various substances from the linear response of a normal acoustic-electronic wave. In this paper, a comparative analysis of the results obtained using polar histograms and the standard PCA classification method is performed. The advantages of the latter are demonstrated. The results of this study are useful both for the development of acoustic sensors without sensor layers and for the application of machine learning methods to data in other types of sensors.

Experimental Study on the Strength and Damage Characteristics of Cement–Fly Ash–Slag–Gangue Cemented Backfill

In order to achieve the goal of effectively utilizing solid waste resources and improving mining stability, it is necessary to incorporate various types of solid wastes in the production of cemented backfill. For investigating the compressive strength and damage characteristics of Cement–Fly Ash–Slag–Gangue (CFSG) cemented backfill under loading, real-time X-ray Computed Tomography (CT) scanning was employed to capture two-dimensional (2D) grayscale slices and three-dimensional (3D) fracture models during uniaxial compression testing. The study quantitatively assessed the evolution of cracks and microstructural damage in CFSG cemented backfill. The results indicate that the specimens underwent four stages of transformation, including compaction, linear elasticity, yielding, and residual deformation, during the uniaxial compression process. The specimens exhibited a measured compressive strength of 3.44 MPa and a failure strain of 0.95%. As the axial strain increased, there was an increase in 2D porosity observed in the CT images and a greater dispersion of crack distribution. A 3D model constructed from CT slices illustrated the feature of cracking expansion, with the fracture volume gradually increasing during the elastic deformation phase and experiencing rapid growth during the yielding and residual deformation phases. The damage variable, obtained from the volume of 3D cracks, exhibited a slow-growth pattern, characterized by a rapid increase followed by a more gradual rise with the increase in axial strain. This study serves as a significant reference for comprehending the micro-mechanisms involved in the damage process and cracking characteristics of cemented backfill mixed with solid wastes under external loading conditions.

Universal slope-based J-integral methods for characterization of the mode I, mode II and mixed mode I/II fracture behaviour of adhesively bonded interfaces

Universal slope-based J-integral methods have been developed for the determination of the energy release rate for adhesively bonded joints under mode I, mode II and mixed-mode (I/II) loading conditions. The individual J components corresponding to the mode I and mode II loading were separated based on the J-integral decomposition theory. The proposed methods use the slopes of the substrates at various locations to characterize the energy release rate and thus avoid the measurement of crack lengths, which are especially suitable for characterizing the tough interfaces associated with large fracture process zones ahead of crack tips. Under linear elastic deformation, the slope-based J equations were found to be equivalent to classical G equations based on linear elastic fracture mechanics (LEFM). Both experimental and numerical testing of adhesively bonded joints were undertaken to validate the slope-based J equations. The universal slope-based J-integral methods provide a reliable alternative to the measurement of G for adhesive joints or laminated composites undergoing nonlinear or inelastic deformations where conventional LEFM is not valid. It is shown that LEFM, even when coupled with an effective crack length approach, can be inaccurate when damage occurs in a test specimen away from the fracture process zone, as was seen here in mode II. Slope-based J equations can avoid these inaccuracies with a careful selection of contour paths. Slope based methods are therefore strong candidates for selection in future test standards for mode II fracture characterisation of structural adhesive joints.

Phase transformation in the palladium hydrogen system: Effects of boundary conditions on phase stabilities

Different elastic constraint conditions affect the phase stabilities of metal-hydrogen systems. This is studied considering the free energy density within a chemo-mechanically coupled approach with linear elastic deformations and homogeneous concentrations. Utilizing the palladium-hydrogen alloy as a model system, the effects of various mechanical constraints in 1D, 2D and 3D are investigated. These constraints change occurring mechanical deformations and strongly influence the systems chemical potential compared to the unconstrained system. With increasing dimensionality of the constraints, large compressive mechanical stresses occur, which destabilize the hydride phase. This yields a reduced critical temperature of hydride formation. Spinodal and equilibrium miscibility gaps of the system are deduced as a function of the boundary conditions. Notably, the critical temperature of the ideal palladium-hydrogen system with 2D constraints is predicted to be ▪, revealing a driving force for hydride formation at room temperature even under these constraints.

Strength, Deformation and Fracture Properties of Hard Rocks Embedded with Tunnel-Shaped Openings Suffering from Dynamic Loads

In rock engineering, the dynamic loads caused by mechanical action and rock blasting have an extremely significant influence on the stableness of surrounding rock masses. To examine the impact of dynamic load on the mechanical properties and fracturing characteristics of hard rocks as well as the failure responses of underground openings, a number of prismatic samples with holes of different numbers and configurations were prepared for dynamic tests employing an SHPB loading device. The experimental results demonstrate that the order of dynamic compressive strength of each group of samples under the impact nitrogen pressure of 0.45 MPa is: G3 > G2 > G5 > G4 > G7 > G6, and the dynamic deformation process of the samples is parted into three phases: linear elastic deformation, plastic deformation and post-peak deformation. A total of three categories of cracks, i.e., spalling cracks, shear cracks and tensile cracks, occur in the specimens. The failure mode of the samples having one or two holes arranged in a vertical direction is controlled by shear cracks, whilst that of the rest groups of pre-holed specimens belongs to tensile-shear failure. The existence of the fabricated holes in the samples significantly weakens the mechanical properties and affects the fracture evolution characteristics, which rely on the quantity and layout of the cavities in the specimens. The interesting results are also discussed and explained, and could supply some insight in the mechanisms of tunnel surrounding rock failure and rock dynamic hazards such as rock burst.

Nonlinear Deformation of Cylinders from Materials with Different Behavior in Tension and Compression

A new numerical-analytical method for solving physically nonlinear deformation problems of axisymmetrically loaded cylinders made of materials with different behavior in tension and compression has been developed. To linearize the problem, the uninterrupted parameter continuation method was used. For the variational formulation of the linearized problem, a functional in the Lagrange form, defined on the kinematically possible displacement rates, is constructed. To find the main unknowns of the problem of physically nonlinear cylinder deformation, the Cauchy problem for the system of ordinary differential equations is formulated. The Cauchy problem was solved by the Runge-Kutta-Merson method with automatic step selection. The initial conditions were established by solving the problem of linear elastic deformation. The right-hand sides of the differential equations at fixed values of the load parameter corresponding to the Runge-Kutta-Merson’s scheme are found from the solution of the variational problem for the functional in the Lagrange form. Variational problems are solved using the Ritz method. The test problem for the nonlinear elastic deformation of a thin cylindrical shell is solved. Coincidence of the spatial solution with the shell solution was obtained. Physically nonlinear deformation of a thick-walled cylinder was studied. It is shown that failure to take into account the different behavior of the material under tension and compression leads to significant errors in the calculations of stress-strain state parameters.

The influence of industrial solid waste in conjunction with lepidolite tailings on the mechanical properties and microstructure of cemented backfill materials

The global demand for lithium resources continues to increase, resulting in significant solid waste generation, including tailings, during the process of lithium mining. To maintain a consistent 80% solid content and a cement-to-solid waste ratio of 1:12 in cementitious backfill (CB), an orthogonal experimental design was employed. The curing periods were set at 7 and 14 days respectively. Uniaxial compressive strength tests were conducted on specimens of CB containing varying proportions of desulfurization gypsum (DG), fly ash (FA), steel slag (SS), and lepidolite tailings (LT). Mechanical properties and microstructure were studied and analyzed using scanning electron microscopy (SEM), gray value analysis, as well as other equipment and methods. The results indicate that:(1)The compressive strength of CB specimens cured for 7 days ranged between 1.28 and 3.05 MPa, while those cured for 14 days exhibited compressive strengths ranging from 2.14 to 3.17 MPa, with the optimal solid waste mix ratio being 2:4:4:3. (2) The predominant macroscopic failure modes of the CB specimens are tensile failure and a combination of tensile and shear failure. The entire failure process encompasses four stages: initial pore compaction, linear elastic deformation, micro-crack propagation, and post-peak failure development. (3) Appropriately increasing the content of DG, FA, and LT and appropriately reducing the content of SS can effectively improve the mechanical properties of CB samples and contribute to the formation of hydration products by hydration reaction. The internal hydration products within the CB specimens encompass ettringite AFt (3CaO·Al₂O₃·3CaSO₄·32 H₂O) and C-(A)-S-H gel, with the latter demonstrating superior binding properties compared to AFt. As the curing age increases, the quantity of hydration products correspondingly grows. Furthermore, CB samples prepared with an optimal solid waste ratio exhibit a more compact internal microstructure. This work provides theoretical support for seeking the best proportions of multiple industrial solid wastes, such as lithium mica mine tailings, as backfill materials, while significantly reducing the cement costs associated with conventional filling and the handling burden of tailings generated from lithium mine extraction.

Smoothed Particle Hydrodynamics (SPH) Analysis of Slope Soil–Retaining Wall Interaction and Retaining Wall Motion Response

The occurrence of slope instability disasters seriously endangers the safety of people’s lives and property in China. Therefore, it is essential to study the slope instability process and the interaction between soil and retaining walls. In this paper, the smoothed-particle hydrodynamics (SPH) method, based on the elastoplastic constitutive model of rock and soil, was used to simulate the entire process of slope instability and the interaction between soil and retaining walls. The model, based on the classical elastic–plastic theory, includes linear elastic deformation and plastic deformation following the non-associated flow rule under the Drucker–Prager (DP) yield criterion. By considering the plastic characteristics of geotechnical materials, this method can accurately simulate the slope movement process. The model was established, calculated, and compared with a slope example, thus verifying its feasibility. Furthermore, the motion response of the retaining wall under different conditions was studied, which provides a new numerical simulation platform for the stability checking of the retaining wall and motion analysis after the interaction between the retaining wall and slope soil.

Mechanical properties and energy damage evolution mechanism of fiber-reinforced cemented sulfur tailings backfill under uniaxial compression.

This paper studies mechanical properties and energy damage evolution of fiber-reinforced cemented sulfur tailings (CSTB) backfill. The effects of fiber length and fiber content on the stress, toughness and failure properties of the CSTB were systematically revealed. In addition, the energy index evolution law was studied, and the energy damage evolution mechanism of CSTB was revealed. The results show that the deformation failure of fiber-reinforced CSTB mainly goes through four stages: initial crack compaction, linear elastic deformation, yield failure and post-peak failure. The peak stress and residual stress of the CSTB firstly increase and then decrease with the increase of fiber content and the addition of fiber can promote the change from brittle failure to ductile failure of the CSTB. Adding appropriate amount of fiber can improve the toughness of CSTB, and the influence degree of fiber length on the toughness index of CSTB is 6mm>12mm>3mm. The total strain energy increases linearly along the variation of fiber content, while the elastic strain energy and dissipated energy increase exponentially at the peak stress point. In the process of CSTB deformation and failure, "gentle-linear growth-slow growth-rapid decline" is for elastic strain energy, while "gentle-slow growth-rapid growth-linear growth" is for dissipation energy. The damage and failure of CSTB mainly experienced four stages: initial damage, slow growth of damage, accelerated damage and damage failure, and the damage evolution curve also showed the changing characteristics of "gentle-slow growth-rapid growth-linear growth". The CSTB without added fiber showed obvious "Y-type" and "linear-type" shear failure characteristics and the phenomenon of shear cracks penetrating the backfill appeared. No big shear crack occur when it is damaged, showing that the fiber addition restrain the crack growth and improve the overall crack resistance of the CSTB. Hydration products are obviously distributed on the surface of the fiber, which indicates that the fiber will be evenly dispersed in the CSTB and form a certain bonding force with the cement-tailings matrix, thus improving the overall mechanical properties of the CSTB.

Nonlinear Performance of Steel Tube Tower in Ultra-High Voltage Transmission Lines under Wind Loads

As complex, statically indeterminate structures, transmission towers are subject to complex forces and are usually simplified into truss structures that only consider the effects of axial force. When the load and deformation of a tower are small, it is reasonable to carry out analysis according to the linear elasticity theory. However, the height of an ultra-high voltage (UHV) transmission tower is significantly large, meaning that the calculation result according to the current elastic analysis method often has a large deviation from the actual stress of the structure. With the influence of the bending moment at the end of the member, a numerical model is established considering the influence of geometric nonlinearity and material nonlinearity in this paper. The stress distribution characteristics and development law of UHV transmission towers in linear and nonlinear stress states are analyzed and studied. The real tower test and elastoplastic ultimate bearing capacity analysis show that the elastoplastic analysis is closer to the actual tower. The UHV steel pipe tower designed according to the linear elasticity and small deformation theory has a large safety margin under the design load, resulting in a significant waste of materials. Under the action of heavy load, the tower exhibits strong nonlinearity, and the influence of geometric and material nonlinear factors should be fully considered when designing the structural components in UHV transmission towers.

A soft departure from jamming: the compaction of deformable granular matter under high pressures.

The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follow the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.

Transverse-inertia-induced wave dispersion in plate–shell chains with a variable Poisson ratio

One-dimensional shell chain structures can cause stress wave dispersion, and the dispersion ability is mainly affected by the apparent elastic Poisson ratio of the unit cell composing the chain. In this study, a novel plate–shell chain structure with a variable Poisson ratio is proposed by combining bent plates and arc shells (BPAS). The dispersive wave propagation features in the BPAS chains under striker impact are studied theoretically, numerically, and experimentally. An equivalent continuum model of the unit cell under compression in a linear-elastic deformation regime is established, which contains two material parameters, i.e., the apparent elastic modulus and the apparent elastic Poisson ratio. It is found that the unit cell can reach a relatively large Poisson ratio by adjusting its structural parameters. A continuum-based wave propagation model considering transverse inertia is developed, and an explicit analytical solution is obtained to represent the dispersion wave propagation behavior within a linear-elastic deformation regime. The model can reasonably predict the force and velocity evolution features of the chains and is verified by the numerical/experimental tests. The results show that the BPAS chain with a large Poisson ratio exhibits superior wave dispersion performances. The underlying mechanism is that more impact energy is dispersed by the transverse movement of the cells in the BPAS chain. Increasing the aspect ratio of the unit cell can improve the wave dispersion ability of the BPAS chains, achieving a high attenuation of the stress wave and is helpful for impact mitigation.