Stress-strain Law Research Articles

Geophysics-Inspired Nonlinear Stress-Strain Law for Biological Tissues and Its Applications in Compression Optical Coherence Elastography.

We propose a nonlinear stress-strain law to describe nonlinear elastic properties of biological tissues using an analogy with the derivation of nonlinear constitutive laws for cracked rocks. The derivation of such a constitutive equation has been stimulated by the recently developed experimental technique-quasistatic Compression Optical Coherence Elastography (C-OCE). C-OCE enables obtaining nonlinear stress-strain dependences relating the applied uniaxial compressive stress and the axial component of the resultant strain in the tissue. To adequately describe nonlinear stress-strain dependences obtained with C-OCE for various tissues, the central idea is that, by analogy with geophysics, nonlinear elastic response of tissues is mostly determined by the histologically confirmed presence of interstitial gaps/pores resembling cracks in rocks. For the latter, the nonlinear elastic response is mostly determined by elastic properties of narrow cracks that are highly compliant and can easily be closed by applied compressing stress. The smaller the aspect ratio of such a gap/crack, the smaller the stress required to close it. Upon reaching sufficiently high compressive stress, almost all such gaps become closed, so that with further increase in the compressive stress, the elastic response of the tissue becomes nearly linear and is determined by the Young's modulus of the host tissue. The form of such a nonlinear dependence is determined by the distribution of the cracks/gaps over closing pressures; for describing this process, an analogy with geophysics is also used. After presenting the derivation of the proposed nonlinear law, we demonstrate that it enables surprisingly good fitting of experimental stress-strain curves obtained with C-OCE for a broad range of various tissues. Unlike empirical fitting, each of the fitting parameters in the proposed law has a clear physical meaning. The linear and nonlinear elastic parameters extracted using this law have already demonstrated high diagnostic value, e.g., for differentiating various types of cancerous and noncancerous tissues.

Study of Mechanical Properties of Different Hydrate Reservoirs

Based on the triaxial shear tests of mud sediments in the South China Sea, mud chalk-type sediments in the South China Sea, and sandy sediments in the Nankai Trough, Japan, at different hydrate saturation and enclosing pressures, the stress-strain relationships of hydrate-bearing clays, mud chalk-type soils, and sandy soils were analyzed. The test results show that:(1)The stress-strain curves of the South China Sea clay sediments show three stages of elasticity, plastic deformation and strain hardening, which are significantly different from those of the hydrate-free clays; the stress-strain relationships of the hydrate-containing clays before and after hydrate decomposition are significantly different, and the undrained strength of the clays decreases by up to 50% after hydrate decomposition compared with that before hydrate decomposition; the above results indicate that the presence of hydrate enhances the linkage or cementation between the clay particles. The above results indicate that the presence of hydrate enhances the linkage or cementation between the clay particles.(2)For the mechanical properties of the hydrate specimens of the muddy chalky sand type in the South China Sea, the hydrate endowment, effective stresses and pore pressures all have some influence on the strength and deformation properties. The inclusion of hydrate in the pore space enhances the shear expansion characteristics of the sediments. For the effect of effective stress on the mechanical properties of hydrate sediments, the increase of effective peritectic pressure reduces the strain softening properties of hydrate sediments. The destructive strength of the sediments increases with the increase of effective confining pressure.(3)For the hydrate specimens in the Nankai Trough of Japan under the same effective circumferential pressure conditions, with the increase of hydrate saturation, the stress-strain law of the sediments showed a tendency to transform from strain hardening to strain softening, and the morphology of sandy sediment axial strain-lateral strain curves was controlled by the factors of hydrate saturation, and the absolute value of the slope of the curves expressed the rule of change of the tangent Poisson's ratio.

Mechanical properties and energy evolution mechanism of wheat grain under uniaxial compression

To determine the mechanical properties and energy evolution characteristics of wheat kernels during compression, the mechanical properties and energy evolution of wheat kernels with high-gluten, medium-gluten, and low-gluten were analyzed in uniaxial compression test. Based on the theory of Hertz's formula, the stress-strain laws of the three varieties of wheat kernels in the process of compression damage were investigated; Based on the law of energy conservation, the energy evolution characteristics of the three varieties of wheat kernels under the same compression conditions were analyzed. The results showed that the stress-strain process of wheat kernels with high-gluten, medium-gluten, and low-gluten under compressive stress followed a similar trend overall, with the corresponding minimum failure strengths at the peak being 51.79 MPa, 50.07 MPa, and 46.21 MPa, respectively. The energy evolution patterns of three varieties of wheat kernels under uniaxial compressive loading were approximately the same, indicating that the elastic energy was mainly accumulated before the peak and reached the maximum at the peak. In contrast, the proportion of dissipated energy increases after the peak and rapidly exceeds the elastic energy. In this paper, the damage characteristics of wheat kernels are described from the energy point of view, which is of great significance for the new conceptualization of the evolution of wheat grain damage.

Uniform elastic field inside an elliptical inhomogeneity with Neuber’s nonlinear stress–strain law under generalized plane strain deformations

We prove the uniformity of the in-plane and anti-plane elastic field of stresses and strains inside an incompressible nonlinear elastic elliptical inhomogeneity embedded in an infinite linear isotropic elastic matrix subjected to uniform remote in-plane and anti-plane stresses. The elastic material occupying the elliptical inhomogeneity obeys Neuber’s special nonlinear stress-strain law. The original boundary value problem is finally reduced to a single non-linear equation for the constant effective strain within the inhomogeneity, which is rigorously proved to have a unique solution. Once the non-linear equation is solved numerically, we establish the uniform elastic field within the elliptical inhomogeneity and the non-uniform elastic field in the linear elastic matrix.

Experimental Study on the Mechanical Properties of Disposable Mask Waste-Reinforced Gangue Concrete.

This paper is grounded on the following information: (1) Disposable masks primarily consist of polypropylene fiber, which exhibits excellent flexibility. (2) China has extensive coal gangue deposits that pose a significant environmental hazard. (3) Coal gangue concrete exhibits greater fragility compared to regular concrete and demonstrates reduced resistance to deformation. With the consideration of environmental conservation and resource reutilization, a preliminary concept suggests the conversion of discarded masks into fibers, which can be blended with coal gangue concrete to enhance its mechanical characteristics. In this paper, the stress-strain law of different mask fiber-doped coal gangue concrete (DMGC) under uniaxial compression is studied when the matrix strength is C20 and C30, and the effect of mask fiber content on the mechanical behavior and energy conversion relationship of coal gangue concrete is analyzed. The experimental results show that when the content of mask fiber is less than 1.5%, the strength, elastic modulus, deformation resistance, and energy dissipation of the concrete increase with mask fiber content. When the amount of mask fiber is more than 1.5%, because the tensile capacity and energy dissipation level of concrete produced by the mask fiber cannot compensate for the compression and deformation resistance of concrete of the same quantity and because excess fiber is difficult to evenly mix in the concrete, there are pore defects in concrete, which decreases the concrete strength due to the increase in mask fiber. Therefore, adding less than 1.5% mask fiber helps to improve the ductility, toughness, impermeability, and oxidation and control the cracking of coal gangue concrete. Based on Weibull theory, a constitutive model of DMGC is established, which fits well with the results of a uniaxial test, providing support for understanding the mechanical law of mask fiber-doped concrete.

Carbon Fabric Reinforced Cementitious Mortar confinement of concrete cylinders: the matrix effect for multi-ply wrapping

The confinement of columns is one of the most used strengthening techniques for reinforced concrete (RC) framed structures being able to improve both the axial strength and ductility. In the last decades, technological advances provided different tools/solutions for the achievement of an effective confinement, among all: the RC-jacket, the steel ties, the fibre reinforced polymer (FRP) wrapping, and lastly the fabric reinforced cementitious mortar (FRCM) plastering.The proposed research aims to investigate two open-issues and their combination related to the use of the FRCM, such as the multi-ply confinement and the role of the inorganic matrix with respect to the confinement effectiveness. At this scope, a set of pure compression tests were carried out to evaluate the representative laws of the mechanical behaviour of confined columns, namely the axial stress versus axial/lateral strain. Consequently, the axial strength and ductility gains were computed. In particular, the investigated variables were the grade of the inorganic matrix, by varying its compressive strength (i.e. ∼25 MPa and ∼50 MPa), and the number of plies (i.e. 1, 2 and 3). The results showed that the higher gain in term of axial strength and ductility is met by increasing the mortar’s compressive/tensile strength and, at the same time, the number of plies. Lastly, available design-oriented analytical models were found able to predict the FRCM-confinement effect in terms of strength. In addition, an available analysis-oriented model accurately foreseen the axial stress–strain law when dealing with the high-grade strength matrix confining in both single, double and triple layer of FRCM-system.

Effect of Mineral Grain and Hydrate Layered Distribution Characteristics on the Mechanical Properties of Hydrate-Bearing Sediments

The mechanical characteristics of gas hydrate-bearing sediments (HBS) are important for evaluating reservoir stability. The interbedded formation of HBS is common in target mining reservoirs. Existing studies on the triaxial mechanical properties of HBS are primarily based on homogeneous and isotropic samples. Therefore, the stress–strain law of the target mining reservoirs cannot be predicted accurately. In this study, a series of sediment models with interlayers of coarse and fine mineral grains were established based on the PFC3D code, and the influence of the layered distribution characteristics of sediment particles and hydrates on the macroscopic mechanical behaviour of the reservoir was comprehensively analysed. The triaxial compression simulation results indicate that the peak strength, deformation modulus, and cohesion of the layered HBS are significantly lower than those of the homogeneous model. The deformation modulus of the reservoir is mainly affected by the fine-grained layer without hydrates. When the coarse and fine grains correspond to different mineral components, the two minerals are heterogeneous in terms of their micromechanical parameters, which can further reduce the macroscopic mechanical parameters of the HBS. In addition, the layered distribution of hydrate results in significant anisotropy of the reservoir. This study constitutes a reference regarding the control mechanism of gas hydrate reservoir strength.

Mechanical Characteristics Analysis of Composite Rubber Elements in Elastic Cam of Large Coal Cake Tamper

The phenomenon of coal cake collapse is often caused by the unstable operation of the elastic cam in a large coal cake tamper. Aiming at this problem, the mechanical characteristics of the composite rubber elements during cam rotation are studied. A rubber piecewise-function constitutive model is established based on phenomenological theory, and different rubber constitutive model coefficients are obtained according to rubber test data. A contact simulation model between the elastic cam and the tamping hammer friction plate is established to obtain the stress–strain law of the composite rubber elements and the pressure-displacement curve of the elastic cam. The stiffness test platform of the elastic cam is designed, and the differences in results between the test and the simulation are discussed. The results show that the stress–strain curve of rubber has a nonlinear increasing trend and the error between the proposed piecewise function and the test value is less than 2%. As the cam displacement increases from 1 mm to 10 mm, the cam pressure increases from 7715 N to 40,000 N. The simulation results of the rubber stress–strain relationship using the piecewise-function constitutive model are closer to the test data than the simulation results using the elastic modulus as a constant, and the error is less than 6.18%.

Experimental study on the tensile performance of a large-diameter UHPC grouted sleeve with thread

An ultra-high-performance concrete (UHPC)-grouted sleeve with a large-diameter seamless steel pipe with threads and bolts was designed. To study the mechanical properties of this grouted sleeve, various factors, such as the grouts type, rebar, thread, and bolts, were considered to conduct a uniaxial tensile test on the grouted sleeve specimens. The bonding performance of the grouted sleeve under a combination of various factors was studied, and its working mechanism was discussed. The results showed that the failure modes of the test sleeve specimens included rebar fracture, rebar slip and grouts slip. The G1 (UHPC without basalt fibre) grouted sleeve showed the best bonding performance and bearing capacity. Bolts and inner wall threads of the sleeve improved the grouts–sleeve bond strength. However, the level of improvement was related to the bolt location, thread spacing and depth. The closer the bolt position was to the elastic section of the sleeve port, the more significant the bond performance improved. The thread could provide mechanical bite force. The greater the thread depth were, the greater the mechanical bite force; nevertheless, there was a threshold. Based on the thick-walled cylinder theory, the calculation model for stress on the sleeve surface was obtained; these calculations were used to analyse the stress–strain law on the sleeve surface.

A DEM bonded particle model compatible with stress/strain constitutive relations

The Discrete Element Method (DEM), also known as distinct element method, is mainly used to study divided media such as granular materials. Moreover, DEM is also widely used for modeling non-linear discontinuous phenomena in rock materials and ceramics such as fragmentation, crack initiation, crack propagation or diffuse cracking. These phenomena are often studied with the Bonded Particle Model (BPM) thanks to the ability of the bond to break in order to simulate a discontinuity in the material. Among the literature, many bonded particle models exist and the choice of the most suitable model remains difficult. Furthermore, these models require fastidious calibration steps because the input bond parameters do not correspond to the whole mechanical response of the DEM assembly. This article introduces a new approach that enables the direct usage of stress–strain laws without calibration steps. Here, these laws directly come from already implemented constitutive laws available in a finite element code. The ability of the proposed software architecture to deal with complex material behaviors (anisotropy, damage and plasticity) is investigated. The obtained results are quite close to the expected ones. This work demonstrates the ability of the proposed approach to deal with such complex mechanical problems which are very challenging to tackle with standard DEM-BPM models.

Mechanics of tensegrity cell units incorporating asymmetry and insights into mollitaxis.

The mechanical response of a contractile cell anchored to the substrate through focal adhesions is studied by means of an asymmetric pre-strained tensegrity structure obeying a neo-Hookean stress-strain law. The aim is to assess the influence of overall asymmetric contraction on the cell durotaxis and on the growth of the focal adhesion plaque. The asymmetric kinematics of the system is obtained in two ways, that is by assuming a gradient of the substrate stiffness and through asymmetric buckling. Equivalent springs are purposely considered to represent the stiffness of the ensemble formed by the substrate, the focal adhesion plaque and the integrin ligands. Then, contraction results from elastic strains induced by competing polymerization and actomyosin contraction. The cell mechanical response in terms of durotaxis and its coupling with focal adhesion plaque growth is finally analysed with respect to the effects of asymmetry, gaining some insights into how this asymmetry could participate to redirect cell migration, both in terms of durotaxis and mollitaxis.

Mechanical properties of Q690E/Q960E high-strength steels at low and ultra-low temperatures: Tests and full-range constitutive models

Mechanical properties of high-strength steels (HSSs) at varying temperatures are fundamental information for the design and numerical analysis of cold-region structures and LNG containers using HSSs. Tensile tests on 14 HSS Q690E and 17 Q960E tensile coupons were firstly carried out at six low temperatures of 20, −30, −60, −80, −120 and −165 °C. The required low-temperature environment for the tensile tests was achieved through an insulation chamber with injecting liquid nitrogen (LN) gas. Their results showed that decreasing the low temperature from 20 to −165 °C slightly affected the elastic modulus of both HSS Q690E and Q960E materials, but significantly increased their yield and ultimate strengths. In addition, ductile failure occurred to all the HSS coupons at low temperatures, and the ductility of HSS was not compromised. Finally, this paper developed full-range constitutive models to describe stress–strain laws of HSS Q690E and Q960E at a low-temperature range of −165 ∼ 20 °C. Validations against the reported test results showed that the proposed full-range constitutive model reasonably estimated the stress–strain behaviours of Q690E and Q960E HSSs at low temperatures.

A simplified vertical and horizontal geomechanical model for compaction in sedimentary basins

In the context of mechanical compaction in sedimentary basins, we introduce a simple model including lateral deformations with the goal to improve the results obtained under oedometric conditions (i.e., neglecting horizontal strains) without losing much computational time. The model is based on a modified vertical porosity-stress law where horizontal strains are inserted and on an elastic stress-strain law with stress-dependent Young modulus. Though it is not three-dimensional and does not involve plasticity, we manage to validate the model on a geometrically and lithologically complex test case by comparing our results with those obtained on the same case using a full-dimensional finite-element simulator. We conclude that our model offers a significant improvement in accuracy against an oedometric model, with little loss in computational time, and so provides a useful tool to users who want a quick insight into results before running longer and more accurate simulations.

Stochastic analysis of small-scale beams with internal and external damping

Random flexural vibrations of small-scale Bernoulli–Euler beams with internal and external damping are investigated in the paper. Such a kind of problem occurs in design and optimization of structural components of smart miniaturized electromechanical systems. Internal damping is related to the viscoelastic stress–strain law describing the beam time-dependent behavior while the external damping represents the interaction between the structure and the surrounding viscous environment. In the proposed formulation, Boltzmann superposition integral and fractional-order viscoelasticity are exploited to capture the above mentioned non-conventional phenomena. Size effects caused by long range interactions arising at small-scale are also taken into account and modeled by means of an integral nonlocal formulation based on the stress-driven approach. Moreover, in order to reproduce stochastic vibrations of small-size devices, such as resonators and sensors, the external loading are modeled by taking into account their random nature. The relevant dynamic problem is thus described by a fractional-order stochastic partial differential equation in space and time equipped with standard and non-classical boundary conditions. A proper differential eigenanalysis for the nonlocal viscoelastic bending problem is performed to find the modal shapes and closed-form expressions of power spectral density and stationary variance of displacements are provided. The proposed methodology, accounting for size-effects, hereditariness behaviors, viscous properties of surrounding environment and randomness of external loadings, is suitable to model and capture the effective behavior of miniaturized devices. The presented theoretical findings and numerical outcomes show the influence of size-effects and viscoelastic parameters on the structural response.

A calculation model of TC4 shot peening residual stress based on elastic-plastic theory

Shot peening is widely used in automobile, aviation, and other industries because it can change the fatigue strength of metal structures by introducing residual compressive stress field on the surface and significantly improve the fatigue life of mechanical structures. In order to improve the surface properties of parts after shot peening, an analysis method for rapidly predicting residual stress of parts surface during shot peening is proposed. During the analysis, an elastoplastic impact model of shot was established, and stress–strain laws in three processes of elastic loading, plastic deformation and stress release were studied. The residual stress under different shot peening parameters was predicted by considering the plastic strengthening effect of TC4 (Ti-6Al-4V). A TC4 shot peening test was performed and residual stress was measured, and the results are consistent with the model predictions, which verified correctness of the model.

Mechanical properties of Q235∼Q460 mild steels at low temperatures

Mechanical properties of mild steels (MSs) at varying temperatures are fundamental to structural design and numerical analysis. This paper studied mechanical properties of Q235∼Q460 mild steels used for the cold-region infrastructures and LNG tanks. To investigate the mechanical properties of mild steels at low temperatures, standard tensile tests on 12 Q235, 16 Q355 and 12 Q460 mild steel coupons in a cooling chamber were carried out at low temperatures of 20 ∼ -165℃. Test results showed that the yield and ultimate strength of mild steels increased with the decreasing temperatures. In addition, the ductility of MS was not compromised, and ductile failure occurred to MS at low temperatures. Furthermore, prediction equations on mechanical properties of MS at low temperatures were established by regression analyses. Finally, based on the predicted mechanical indexes, two- and three-stage constitutive models were proposed to describe the true stress–strain laws of Q355, Q460 and Q235 mild steels at 20 ∼ -165℃, respectively. Validations showed that the proposed constitutive model reasonably estimated the stress–strain behaviours of Q235 ∼ Q460 mild steels at low temperatures.

Research on the Structure Design and Mechanical Properties of Performance Optimized Multi-Axial Geogrid.

In order to solve the problem of low transverse tensile strength of triaxial geogrid, a kind of performance-optimized multi-axial geogrid (POMG) that can bear larger transverse loads was designed. Firstly, the forming equipment and process of POMG are designed. Secondly, through the test of formability and mechanical properties, the POMG with good formability and mechanical properties is obtained, and the average tensile strength of POMG with circular and semicircular holes is the highest, reaching more than 16 KN/m. Finally, the feasibility of the process is further verified by numerical simulation, and the shape distribution and stress-strain law of POMG during the forming process are obtained, which provides further guidance for the actual production.

Mechanical behavior and models for porosity-free concrete reinforced with high amounts of steel fiber

• Mechanical properties of porosity free concrete were investigated in several material tests. • Compressive stress–strain curve and tension softening curve were modeled. • Equivalent characteristic length (average crack spacing) was obtained by numerical analysis. • Tensile stress–strain relationship was proposed by using equivalent characteristic length. A new cementitious composite characterized by an extremely high compressive strength (>400 MPa), known as porosity-free concrete (PFC), has been recently developed. Many tests have been conducted to formulate appropriate stress–strain laws for compression and tension. This study clarified that PFC has extremely high compressive strength and post-cracking toughness owing to the reinforcing fibers. In addition, the flexural strength of porosity-free concrete was investigated by combining experimental and numerical analyses. Furthermore, the formulation of the stress–strain law in tension introduced “equivalent characteristic lengths” to convert the crack width into an equivalent strain. (93 words)

Optimized design of high-efficiency lunar soil sampling tube structure based on stress–strain law

Understanding the influence of the sampling apparatus on in-situ lunar soil lamination information during the sampling process of the direct push-through lunar weathering layer is of great importance. This paper develops a discrete element model for direct push-through lunar weathering layer sampling using the CUG-1A simulated lunar soil developed by the China University of Geosciences as a simulation object and determines the stress–strain law of the inner wall of a sampling tube. A method for optimizing the inner wall structure of a sampling tube based on the stress–strain law is proposed. The structural disturbance of the marker layer and the lunar soil disturbance rate evaluation function are used to assess the degree of disturbance of the laminar information during the sampling process. The results show that the proposed method can effectively reduce the structural disturbance of the lunar soil in-situ laminar information. In addition, it can also optimize the structural information disturbance of the marker layer. The proposed method can decrease the simulated lunar soil disturbance rate from 0.31 to 0.251 and effectively reduce the penetration force load by 15–20% in the direct push-through sampling process.

Planar Crack Approach to Evaluate the Flexural Strength of Fiber-Reinforced Concrete Sections.

This article describes a model based on concepts of Fracture Mechanics to evaluate the flexural strength of fiber-reinforced concrete (FRC) sections. The model covers the need by structural engineers to have tools that allow, in a simple way, the designing of FRC sections and avoiding complex calculations through finite elements. It consists of an analytical method that models FRC post-cracking behavior with a cohesive linear softening law (σ − w). We use a compatibility equation based on the planar crack hypothesis, i.e., the assumption that the crack surfaces remain plane throughout the fracture process, which was recently proven true using digital image correlation. Non-cracked concrete bulk follows a stress–strain law (σ − ε) combined with the Bernoulli–Navier assumption. We define a brittleness number derived from non-dimensional analyses, which includes the beam size and the softening characteristics. We show that this parameter is key to determining the FRC flexural strength, characterizing fiber-reinforced concrete, and reproducing the size-effect of sections in flexure. Moreover, we propose an expression to calculate the flexural strength of FRC as a function of the cited brittleness number. The model also gives the ratio between the residual strength in service conditions and the flexural strength. Model results show a good agreement with tests in the scientific literature. Finally, we also analyze the brittle–ductile transition in FRC sections.