Linear Elastic Deformation Research Articles

The Establishment of Segmented Constitutive Relationship of Coal under Triaxial Compression: Take the No. 3 Coal of Xinhe Colliery as an Example

Constitutive relationship of coal under triaxial compression must be determined during solving the theoretical calculation and numerical simulation about coal body failure. This paper carried out the conventional triaxial compression test on No. 3 coal of Xinhe Colliery using the MTS815.03 servo‐controlled rock mechanical test system. The results indicate that the failure process of coal can be divided into 5 stages: densification stage, apparent linear elastic deformation stage, accelerated inelastic deformation stage, fracture and developing stage, and plasticity flow stage. Within the test confining pressure (20 MPa), the peak strain of coal is approximately linearly positively correlated with the confining pressure. The relationship between elastic modulus of coal and confining pressure is quadratic polynomial. The triaxial compressive strength and residual strength of coal are approximately linearly positively correlated with confining pressure. The constitutive relationship model of coal can be simplified as the four segments of straight line model of “elastic–plastic hardening–plastic softening–residual perfectly plastic.” Through fitting calculation of test data, the segmented constitutive equation of coal can be obtained, and the every segment span of strain.

An experimental investigation on the tensile stiffness in layered rock interface using the digital image correlation technique

Tensile stiffness of interfacial layered rock is the basis of studying the law of interlaminar propagation of hydraulic cracks. We used similar materials to make simulated specimens of sand-mud layered rock with prefabricated cracks, and used the digital image correlation (DIC) technique together with the three-point bending (TPB) test to obtain the strain field near the prefabricated crack tip in tensile state. Combined with the tensile stress in the corresponding area calculated by the load of the tester, the tensile stress-displacement curve at the interface of layered rock is obtained, and the tensile stiffness and interfacial fracture law at the interface of layered rock is calculated by the curve. The results show that in the process of tensile failure, before reaching its peak value, the interfacial tension stress of layered rock has a linear elastic deformation stage followed by a short hardening stage. Upon reaching the peak value, it is accompanied by interfacial failure and macro-cracks, and then the load decreases and enters the softening stage, which results in the complete destruction of the interface. The tensile stiffness values of layered rock with different sizes vary greatly, which indicates that the interfacial tensile stiffness values are sensitive to the specimen size and have a size effect. The results are of great significance to the study of the law of hydraulic fracture propagation in the interface of layered rock.

Подъем пылевых частиц при воздействии лазерного излучения на хондритовую мишень и возможность моделирования плазменно-пылевых процессов у поверхности Луны

The results of the first study on experimental modeling of the rise of dust particles by a shock wave above a target surface, performed on the Saturn installation, are presented. The interaction of laser radiation with a porous chondritic target, the surface of which contains fine particles of talc, is investigated. The results of experimental modeling can be used to describe the rise of dust particles from zones of nonlinear and linear elastic deformations of the regolith material, which characterize the impact of the meteoroid on the surface of the Moon.

Experimental investigation on dynamic strength and energy dissipation characteristics of gas outburst‐prone coal

AbstractWe report laboratory experiments to investigate the dynamic failure characteristics of outburst‐prone coal using a split Hopkinson pressure bar (SHPB). For comparison, two groups of experiments are completed on contrasting coals—the first outburst‐prone and the second outburst‐resistant. The dynamic mechanical properties, failure processes, and energy dissipation of both outburst‐prone and outburst‐resistant coals are comparatively analyzed according to the obtained dynamic compressive and tensile stress‐strain curves. Results show that the dynamic stress‐strain response of both outburst‐prone and outburst‐resistant coal specimens comprises stages of compression, linear elastic deformation, then microfracture evolution, followed by unstable fracture propagation culminating in rapid unloading. The mechanical properties of both outburst‐prone and outburst‐resistant coal specimens exhibit similar features: The uniaxial compressive strength and indirect tensile strength increase linearly with the applied strain rate, and the peak strain increases nonlinearly with the strain rate, whereas the elastic modulus does not exhibit any clear strain rate dependency. Differences in the dynamic failure characteristics between outburst‐prone and outburst‐resistant coals also exist. The hardening effect of strain rate on outburst‐prone coal is more apparent than on outburst‐resistant coal, which is reflected in the dynamic increase factor at the same strain rate. However, the dynamic strength of outburst‐prone coals is still lower than that of outburst‐resistant coals due to its low quasi‐static strength. The dissipated energy of outburst‐prone coal is smaller than that of outburst‐resistant coal. Therefore, the outburst‐prone coal, characterized by low strength, high deformability, and small energy dissipation when dynamically loaded to failure, is more favorably disposed to the triggering and propagation of gas outbursts.

Low force, high noise: Isolating indentation forces through autocorrelation analysis

Simple contact models are often used in combination with indentation measurements to determine the elastic moduli of materials in the limits of small strain and linear-elastic deformation. However, for soft biological samples these limits can occur at indentation forces comparable to detection noise from the instrument. Here we describe a data analysis method for determining the moduli of soft materials when the measured forces are comparable to the level of instrumental noise; relationships between the force and displacement autocorrelation functions enable the elastic modulus to be determined from indentation curves with large uncertainties in the measured force. In simulations of force-displacement indentation data using the Hertz and Winkler foundation contact models with added noise, we find the autocorrelation analysis enables the accurate measurement of known elastic moduli, even when the noise-to-signal ratio is large throughout an indentation experiment. We also find that this analysis method is more accurate at measuring the modulus at high noise levels compared to directly fitting the model curve to the data. We further validate this approach experimentally by testing a series of polyacrylamide hydrogel slabs prepared within a wide polymer concentration range, finding the measured modulus to be in agreement with the moduli determined through rheological characterization.

Acoustic emission characteristics of pre-cracked specimens under biaxial compression

AbstractThis paper presents an experimental study in which molded gypsum pre-cracked specimens with two types of flaw (single and X-shaped cross flaws) were tested under biaxial compression. Results show that acoustic emission (AE) energy rate curves can be divided into three different periods during uniaxial compression, which correspond to crack closure, linear elastic and unstable failure stages of specimens. However, only two periods are observed during biaxial compression, which correspond to linear elastic deformation and unstable failure. Furthermore, two proposed AE parameters, namely the AE energy ratio and AE energy release ratio, and a classical AE parameter b-value were used to analyze the influence of biaxial compression loading on AE energy, respectively. With increasing confining pressure, the AE energy release ratio, as well as AE b-value decreases gradually while AE energy ratio increases. Moreover, maximum and average AE energy rate values decrease as confining pressure increases. Data presented herein is useful to study the AE characteristics of pre-cracked specimens under biaxial compression.

Design and fabrication of a (β+α") dual-phase Ti-Nb-Sn alloy with linear deformation behavior for biomedical applications

In this study, a (β+α") dual-phase Ti-33Nb-4Sn alloy was successfully fabricated by a designated severe cold rolling plus pre-deformation (CRP) treatment to display a linear deformation behavior. Upon CRP treatment, a high density of dislocation tangles and grain refinement were induced into the Ti-33Nb-4Sn alloy consisting mainly of α" martensite as well as some retained β parent phase. Due to the retardation effect of dislocations and grain boundaries on martensitic transformation, the slight stress induced martensitic (SIM) transformation from β to α" in CRP Ti-33Nb-4Sn alloy covered a wide stress range during loading, together with the linear elastic deformation behavior of β and α" phases. In such a case, the (β+α") dual-phase Ti-33Nb-4Sn alloy exhibited macroscopically linear deformation behavior before yielding. Our results might shed light on design and development of novel (β+α") dual-phase Ti-based alloy with linear deformation behavior for biomedical applications.

Green’s functions for soft materials containing a hard line inhomogeneity

The linear elastic plane deformation of a soft material containing a rigid line inhomogeneity subjected to a concentrated force, a concentrated moment, and a point heat source was studied. Distinct from the existing rigid line inhomogeneity model which neglects the deformation of the inhomogeneity induced by both the mechanical stresses and thermal expansion, the current model allows for the thermal expansion-induced stretch and rotation of the inhomogeneity. In this context, we derive the closed-form solution for the full stress field in the soft material by solving the corresponding Riemann–Hilbert problem. In particular, our solution can serve as the Green’s function to establish other analytical solutions for more practical and complicated problems in this area. Several numerical examples are presented to illustrate our closed-form solution corresponding to the thermal loading. It is found that the presence of the heat source contributes significantly to the rigid rotation of inhomogeneity, and the thermal expansion-induced stretch of the inhomogeneity has a great impact on the stress intensity factors at the inhomogeneity tips.

Establishment of Coal-rock Constitutive Models for Numerical Simulation of Coal-rock Cutting by Conical Picks

One of the key points in numerical simulation of coal-rock cutting by conical picks is to select a proper coal-rock constitutive model. In order to find a reasonable coal-rock constitutive model, a uniaxial compression test was conducted to obtain the constitutive model. The several stages for linear elastic deformation and creep, plastic yielding, hardening, and finally brittle cracking of the constitutive units were studied, and the coal-rock constitutive model was established. As a result, the coal-rock cutting by one conical pick or two conical picks was simulated and the results were compared with coal-rock cutting experiment on a Coal-rock Cutting Machine. According to the simulation and experimental results, it is believed that the numerical simulation can reveal coal-rock crushing process. And the total error rate of coal-rock cutting by one conical pick between the simulation and experiment is 8.5%. The maximum deviation of coal-rock cutting by two conical picks between the simulation and experiment is 9.8%. All simulation values are within a reasonable range. The comparison indicates that the coal-rock constitutive model should better be defined considering the coal-rock crushing process by conical picks.

Modeling deviation propagation of compliant assembly considering form defects based on basic deviation fields

PurposeA new deviation propagation model considering the form defects in compliant assembly process is proposed. The purpose of this paper is to analyze the deviation propagation by using the basic deviation fields. In particular, each basic deviation field is defined with a generalized compliance matrix of part.Design/methodology/approachFirst, the form defects of parts may be decomposed into a linear combination of basic deviation fields, which are constructed by the eigen-decomposition of the structure stiffness of parts with ideal dimensions. Each basic deviation field is defined with a generalized compliance of part. Moreover, by analyzing the relationship between the basic deviation fields before and after assembling process, a new sensitive matrix is obtained in which each value expresses the correlation of a basic deviation field between the parts and the assembly.FindingsThis model may solve the deviation propagation problems of compliant assembly with considering form defects. Here, one case is used to illustrate the deviation propagation in the assembly process. The results indicate that the proposed method has higher accuracy than the method of influence coefficient when the entire deviation fields of parts are considered. Moreover, the numerical results with the proposed method basically agree with the experimental measurements.Research limitations/implicationsOwing to the hypothesis of linear superposition of basic deviation fields, the research in this paper is limited to the parts with linear elastic deformation. However, the entire form defects of parts are considered rather than the deviations of the local feature points. It may be extended to analyze the three-dimensional deviations of complex thin-walled parts.Originality/valueA deviation propagation model considering parts form defects is developed to achieve more accurate predictions of assembly deviation by using the basic deviation fields.

Assembly Variation Analysis of Aircraft Panels under Part-to-part Locating Scheme

A typical aircraft panel is the assembly consisting of a multitude of thin and lightweight compliant parts. In panel assembly process, part-to-part locating scheme has been widely adopted in order to reduce fixtures. By this locating scheme, a part is located onto the pre-fixed part/subassembly by determinant assembly (DA) holes, and temporary fasteners (e.g., spring pin) are used for joining these DA hole-hole pairs. The temporary fasteners can fasten DA hole-hole pairs in the axial and radial directions of DA holes. The fastening in the radial directions is realized by the expansion of temporary fasteners. Although the usage of temporary fasteners helps reduce the positional differences between hole-hole pairs, their clamping forces thereby may lead to elastic deformation of compliant parts/subassemblies. Limited research has been conducted on such elastic deformation produced by temporary fastener and its influence on assembly dimensional quality. This paper proposes a novel rigid-compliant variation analysis method for aircraft panel assembly, incorporating the deformation in part-to-part locating process. Based on the kinematic theory and linear elasticity deformation assumption, the variation propagation through the locating process, as well as the entire assembly process of an aircraft panel, is formulated. Then, the statistical variation analysis is performed with Monte Carlo (MC) simulation. Finally, the proposed method is validated by a case study. The result shows the deformation in the part-to-part locating process significantly impacts the assembly variations, and our method can provide a more accurate and reliable prediction.

Research on In‐plane Quasi‐Static Mechanical Properties of Gradient Tetra‐Chiral Hyper‐Structures

Chiral hyper‐structure is a family of lightweight structure with negative Poisson's ratio, which leads benefit in mechanical properties and designability. In order to further improve some mechanical properties of chiral hyper‐structures, the concept of gradient is introduced into the structure. Five groups of gradient tetra‐chiral hyper‐structure with different gradient factors are fabricated based on waterjet cutting technology, and the in‐plane quasi‐static lateral compression tests are carried out. Finite element models are developed for the in‐plane linear elastic mechanical properties and plastic deformation modes under lateral compression condition. Theoretical prediction models of elastic modulus in gradient direction and Poisson's ratio of the gradient tetra‐chiral hyper‐structure is derived based on geometric assumptions and inhomogeneous deformation mode which are verified by experiments and finite element analysis. Simultaneously, the effects of gradient factors on the deformation characteristics and mechanical behaviors of the tetra‐chiral hyper‐structure are discussed and analyzed.

Influence of elastoplastic embedment on CSG production enhancement using graded particle injection

A large percentage of coal seam gas (CSG) reservoirs exhibit low permeability and require stimulation to achieve economic production rates. Graded particle injection (GPI) into the natural fracture and cleat system around hydraulically-induced fractures has been proposed and demonstrated by prior laboratory studies as an effective method of enhancing CSG production. However, pore pressure and fracture width decrease with the distance from the wellbore and hydraulic fractures. Previous modelling determined that staging the injected particles with increasing size may sequentially fill the propped cleats and keep them open during production. GPI results in an increase in permeability above the initial value, expands the stimulated zone, and consequently, increases the productivity index. The present work aims to improve our understanding of the GPI process for production enhancement by developing a generalised modelling methodology for GPI into the fracture network. The new model accounts for elastoplastic deformation of fracture surface during particle embedment. This is based on elastoplastic finite element modelling of fracture deformation and flow modelling by the lattice Boltzmann method (LBM). Effects of packing densities, effective stress and material properties are incorporated in the modelling. Results of fracture permeability reduction factor due to particle embedment are then applied to the mathematical model for well productivity prediction. Modelling results indicate that elastoplastic fracture deformation leads to lower permeability and production enhancement using GPI, as compared with linear elastic deformation applied in traditional models. The developed model is applicable to the assessment of potential stimulation outcomes for a range of uncertain reservoir parameters. Better understanding and implementation of GPI schemes can potentially improve post-fracturing results in low-permeability coal intervals substantially.

Microscale interfacial adhesion assessment in a multilayer by a miniaturised four-point bending test

Microscale techniques capable of selectively isolating and delaminating embedded multilayer interfaces in a stable manner have the potential to be powerful characterisation tools for improving the reliability of microelectronic devices. Here we propose an analytical approach to assess the steady-state strain energy release rate during the delamination of an embedded multilayer interface, initiated by our recently developed miniaturised four-point bending technique. Stable delamination of a SiN-GaAs interface was initiated via nanoindentation induced bending of microbridges that had been milled into the surface of an Al-SiN-GaAs multilayer using a focused ion beam. Analytical models quantify the strain energy released within a section of a microbridge using the load-displacement relation obtained during delamination. The models are validated by demonstrating their capacity to approximate the experimentally observed linear-elastic deformation of a reference microbridge under both three- and four-point bending. We find that deformation of the clamped-ends as well as indenter penetration of a microbridge contribute significantly to the total indenter displacement. We then show this can be accounted for through a combination of Euler–Bernoulli beam and Hertzian contact theory. A mean steady-state strain energy release rate of G¯SS=2.20±0.36Jm−2 is obtained for the SiN–GaAs interface.

Compliant assembly analysis including initial deviations and geometric nonlinearity—Part I: Beam structure

In the past decades, several compliant assembly analysis models have been developed to consider structural deformations during assembly progresses. Available methods address the influence of linear elastic deformations, whereas for the case of large-scale flexible structures with complex boundary conditions, the geometric nonlinearity will be a significant factor affecting the accuracy of assembly variation prediction. This paper introduces a refined mechanical model to develop a variation analysis method for beam structures. Based on the Timoshenko theory, governing equations of flexible beam are obtained by using the principle of virtual work with consideration of initial deviations and a von Kármán type of kinematic nonlinearity. Moreover, corresponding finite element formulas are presented, which also can be degenerated into non-initial deviation form or the linearized form. With the nonlinear beam model, an assembly variation analysis method is proposed for beam structures, which takes initial deviations, fixture errors, and matching deviations into account. Case studies of static loading analysis and slender beam assembly springback analysis are demonstrated to verify the feasibility and accuracy of the presented method.

Polarization-induced alignment of azobenzene/fluorinated polyimide for three-dimensional shape-persistent and photo-responsive elastic helixes

Three-dimensional (3D) macroscopic chiral helixes using anisotropic polymer assembly shows a great potential for designing micromechanical systems and soft robotics. However, movement of flexible polymer chains make the fabrication of 3D macroscopic helical ribbons with excellent shape stability under high temperature or multitudes of stretch/strain cycling very problematic. This paper presents the polarization-induced alignment of a non-LC supramolecular azobenzene-polyimide assembly (Azo/f-PI). We prepare 3D left- or right-handed Azo/f-PI helixes with shape-persistence, high-elasticity and photoresponsivity by large-area molecularly oriented assembly films. The Azo/f-PI helix treated at 100 °C for 10 min retains its linear-elastic deformation with 77.16% retention of the elastic potential energy density (0.304 J/g), and an extremely low permanent deformation of 3.68% upon 1000 stretching-relaxation cycles. Moreover, the 3D helix exhibited a light-driven elongation up to about 175.0% of the original length under UV irradiation. This 3D high-elastic helix with excellent shape persistence and photo-responsive actuability opens a gate for micromechanical control.

Additive manufacturing of elastomeric foam with cell unit design for broadening compressive stress plateau

PurposeThe purpose of this paper is to provide additive manufacturing-based solutions for preparation of elastomeric foam with broaden compressive stress plateau.Design/methodology/approachMechanic models are developed for obtaining designs of foam cell units with enhanced elastic buckling. An experimental approach is taken to fabricate the foams based on direct ink writing technique. Experimental and simulation data are collected to assist understanding of our proposals and solutions.FindingsA simple tetragonal structured elastomeric foam is proposed and fabricated by direct ink writing, in which its cell unit is theoretically designed by repeating every four filament layers. The foam exhibits a broader stress plateau, because of the pronounced elastic buckling under compressive loading as predicted by the authors’ mechanic modeling. A two-stage stress plateaus as observed in the foam, being attributed to the dual elastic buckling of the cell units along two lateral directions of the XY plane during compression.Research limitations/implicationsFuture work should incorporate more microscopic parameters to tune the elastomeric foam for mechanic performance testing on linear elastic deformation and densification of polymer matrix.Practical implicationsAdditive manufacturing offers an alternative to fabricate elastomeric foam with controlled cell unit design and therefore mechanics. Our results comment on its broad space for development such superior cushioning or damping material in the fields of vibration and energy absorption.Originality/valueThis work has contributed to new knowledge on preparation of high performance elastomeric foam by providing a better understanding on its cell structure, being printed using direct ink writing machines.

Deformation mechanisms and mechanical properties of porous magnesium/carbon nanofiber composites with different porosities

This study investigated mechanical properties and deformation mechanisms of porous magnesium–carbon nanofiber composites with different porosities manufactured through powder metallurgy. Compressive stress–strain curves of the samples exhibit three phases: Phase I of linear elastic deformation at low stress state, Phase II of a stress plateau, and Phase III of densification. The manufactured porous composites with different porosities show different deformation mechanisms. The composites with low porosity (i.e., 24 and 34%) manifest stretch-dominated deformation with hard (i.e., tension, compression) modes, while the composite with high porosity (i.e., 50%) demonstrates bending-dominated deformation with soft (i.e., bending) modes. The yield strength and the ultimate compressive strength decreased at an increasing rate with the increase in the porosity from 24 to 50%. Theoretical estimations were obtained for the yield strength of dense magnesium composites based on Gibson and Ashby model.

FiloGen: A Model-Based Generator of Synthetic 3-D Time-Lapse Sequences of Single Motile Cells With Growing and Branching Filopodia.

The existence of diverse image datasets accompanied by reference annotations is a crucial prerequisite for an objective benchmarking of bioimage analysis methods. Nevertheless, such a prerequisite is hard to satisfy for time lapse, multidimensional fluorescence microscopy image data, manual annotations of which are laborious and often impracticable. In this paper, we present a simulation system capable of generating 3-D time-lapse sequences of single motile cells with filopodial protrusions of user-controlled structural and temporal attributes, such as the number, thickness, length, level of branching, and lifetime of filopodia, accompanied by inherently generated reference annotations. The proposed simulation system involves three globally synchronized modules, each being responsible for a separate task: the evolution of filopodia on a molecular level, linear elastic deformation of the entire cell with filopodia, and the synthesis of realistic, time-coherent cell texture. Its flexibility is demonstrated by generating multiple synthetic 3-D time-lapse sequences of single lung cancer cells of two different phenotypes, qualitatively and quantitatively resembling their real counterparts acquired using a confocal fluorescence microscope.

Numerical Simulation of the Stress-Strain State of Thin-Layer Rubber-Metal Vibration Absorber Elements Under Nonlinear Deformation

Stress-strain state components of thin-layer rubber-metal elements are investigated. The compression level of a thin rubber layer under the action of vertically applied stress is calculated. For simplified hypotheses the relationship between the rubber layer thickness reduction and its radius-thickness ratio was analytically derived. The problem was solved under linear-elastic deformation of a rubber layer vulcanized onto the metal plates. For numerical calculations, weak rubber compressibility was simulated with the moment finite element scheme for weakly compressible materials, involving the triple approximation of displacement fields, strain components, and a volume variation function. The numerical solution was obtained by the finite element method for different layer radii and thicknesses under geometrically nonlinear elastic and viscoelastic deformation of the rubber material. The geometrical nonlinearity is described by the nonlinear strain tensor. Viscoelastic rubber properties are simulated by the hereditary Boltzmann– Volterra theory with the Rabotnov relaxation kernel. Nonlinear boundary problems are solved by the modified Newton–Kantorovich method. The calculation is effected for the two cases of curing the rubber layer onto the metal elements of the structure. The first case assumes that the rubber layer is vulcanized onto the metal plates, in the second one, it can freely slide over their surface. For the first case, numerical results are compared with the analytical solution. The effect of geometrical nonlinearity and viscoelastic rubber properties on the rubber layer thickness reduction was examined.