Complete Stress-strain Relation Research Articles

A 3D micromechanical model to predict the complete stress-strain relation of microencapsulated self-healing concrete

The research on the concrete structure built with self-healing materials brings inspiration to increase the safety and sustainability of underground structures in the whole life cycle. The utilization of microencapsulated healing agents in self-healing concrete has demonstrated efficacy in the repair of microcracks within concrete structures. Nevertheless, there exists a dearth of effective methodologies for assessing the impact of microcapsule parameters on the mechanical properties of self-healing concrete. This study introduces an innovative three-dimensional micromechanical model that can be utilized to analyze the micromechanical response of microencapsulated self-healing concrete under tensile loading conditions. The 3D micromechanical model is accomplished through the utilization of the elastic secant compliance tensor. Subsequently, a comprehensive examination is undertaken to analyze the progression of damage-healing in self-healing concrete incorporating microcapsules. Finally, a parametric investigation is conducted to elucidate the impact of the micro-parameters on the mechanical behavior of self-healing concrete. The present discovery holds significant implications for the development of microencapsulated self-healing concrete for underground structures, particularly in terms of establishing appropriate parameters.

Complete Stress-Strain Relations of Early-Aged Cementitious Grout under Compression: Experimental Study and Constitutive Model.

The compressive stress–strain behaviors of early-aged cementitious grout specimens were experimentally investigated, and the differences of characteristic parameters of the stress–strain curve and the energy evolution law of each specimen under uniaxial compression were discussed in this study. The results indicate that with an increase in the specimen age, the peak stress, peak strain, ultimate strain, elastic modulus, peak secant modulus, strain ductility coefficient, and energy-dissipation coefficient of the prism specimens gradually improved. Additionally, a comparison of the test results of cementitious grout specimens and concrete specimens with the same age reveals that the peak stress, peak strain, and ultimate strain of cementitious grout specimens were greater than that of concrete specimens, the elastic modulus and peak secant modulus of the specimens were less than that of concrete specimens, and the strain ductility coefficient and energy-dissipation coefficient show no consistent conclusions with respect to the material type. Moreover, comparing the energy evolution curves of specimens with different specimen ages shows that the decrease rate of the elastic strain rate and the increase rate of the dissipated energy rate gradually decreased with the increase in specimen age. The elastic strain rate and dissipated energy rate of the CGM−270 specimen and control specimens were greater than that of other specimens, and the decrease rate of the elastic strain rate was less than that of other specimens. Based on the statistical damage theory, a statistically stochastic damage constitutive model was derived by considering the characteristics of cementitious grout according to the compression test results. A comparison of the proposed models with the experimental results indicated that the proposed stress–strain constitutive models were sufficiently accurate.

Constitutive behavior of hybrid fiber reinforced concrete subject to uniaxial cyclic tension: Experimental study and analytical modeling

A reasonable cyclic tensile model is indispensable in the design and nonlinear analysis of fiber reinforced concrete structural members against repeated loads. This paper presents a systematic study on the constitutive behavior of hybrid steel-polypropylene fiber reinforced concrete material (HFRC) subject to uniaxial cyclic tension. A total of seven groups of cylindrical HFRC specimens were tested with influential factors in terms of fiber type, volume fraction and aspect ratio considered. The results show that HFRC specimens failed in a ductile manner due to the contributions of hybrid fiber on the cracking resistance at multiple length scales. It is noted that increasing the steel fiber (SF) content has a significant effect on the enhancement of the concrete cyclic tensile properties. Further improvements in the post-peak residual strength and toughness can be seen for the cases with a larger SF aspect ratio that also helps alleviate the stiffness degradation of the HFRC. Furthermore, an appropriate volume content of polypropylene fiber addition can improve the deformation and energy dissipation of the matrix. Finally, a semi-empirical constitutive model is proposed to describe the complete stress–strain relation and the damage accumulation of HFRC.

Stress-strain model for confined concrete with corroded transverse reinforcement

This paper presents an experimental study on the stress-strain relation of confined concrete that considers the corrosion effects of transverse reinforcement. The main variables are the corrosion level of transverse reinforcement, cross sectional shape of confined concrete, as well as arrangement and configuration of confining transverse reinforcing bars. The test results revealed that four key parameters of the complete stress-strain relation are significantly affected due to the corrosion of transverse reinforcement, including the maximum concrete strength and corresponding axial concrete strain, maximum concrete strain at the fracture of the first hoops, and descending branch of the stress-strain curve after exceeding the maximum strength. Based on the test data and regression analysis, the empirical equations to estimate these key parameters are proposed, and a complete stress-strain model for confined concrete with corroded transverse reinforcement is developed. The proposed model showed good correlation with the test data of both circular and square specimens with various corrosion levels and subjected to compression axial loading.

A damage model for modeling the complete stress–strain relations of brittle rocks under uniaxial compression

Based on the “elastic modulus method” derived from the hypothesis of strain equivalence and test data of complete stress–strain curves of marble, granite, and sandstone under uniaxial compression, a damage model in the form of Logistic equation is proposed to simulate the stress–strain relation of rocks. This model can describe the complete deformation process of rocks under uniaxial compression satisfactorily. The used mathematical function is simple with just four model parameters, and each parameter has distinct physical meaning. The validity of the model is demonstrated by a mathematical deduction analysis and the model is further verified using laboratory test data. In addition, this model provides a method for estimating the elastic modulus of undamaged rocks using uniaxial compression test results and it presents a reasonable explanation of the chaos phenomenon occurred in uniaxial compression test.

Experimental study and constitutive model on complete stress-strain relations of plain concrete in uniaxial cyclic tension

Due to the difficulties of testing concrete in direct uniaxial tension, only limited data are available. In this paper, the cyclic tensile test on the plain concrete was carried out. Based on the experimental data, the plasticity and damage evolution can be formulated with respect to elastic strain. A constitutive model for cyclic tensile behavior of concrete is proposed. The proposed model can describe the nonlinear post-peak performance of concrete in direct tension including hysteresis loops. Finally, a statistical damage model is derived to describe the microcrack growth of concrete under monotonic and cyclic tension loading. Results demonstrated that the microcracks growth of concrete under cyclic tension loading can be formulated by the Weibull cumulative distribution function.

Tensile Behavior of Steel-Polypropylene Hybrid Fiber-Reinforced Concrete

The present study deals with the uniaxial tensile behavior of steel-polypropylene hybrid fiber-reinforced concrete (HFRC). The tensile strengths and complete stress-strain responses of HFRC were measured in terms of different volume fraction and aspect ratio. It was observed that the uniaxial tensile behavior of plain concrete can be significantly improved upon with the addition of hybrid fibers. The steel fiber primarily increases the peak tensile strength, while the polypropylene fiber mainly contributes to increasing residual strength in post-peak response. Subsequently, predictive equations for both the tensile strength and complete stress-strain relation of HFRC were developed, and the results were found in satisfactory agreement with experimental results. Furthermore, a simple elliptic-cap model in tension region was also proposed for the tensile meridian of HFRC within the framework of elastoplasticity, representing a three-dimensional scenario of strength criterion capable of predicting the multiaxial stress state of HFRC in tension region.

Computational method of large deformation and its application in deep mining tunnel

The characteristics of deep rock mass, such as the elastic resilience, creep, stress release, expansion, dilation and the long-term strength, are of great importance to the rock mass deformation and failure mechanism. However, there is not yet a constitutive model which can describe all these properties of the deep rock mass. The proposed dynamic failure constitutive model in this paper analyzes the elastic resilience and the dilation deformation of the surrounding rock mass during the unloading process, and the pre-peak (elastic and internal frictional hardening stages) and the post-peak(softening and residual failure stages) stages are also taken into account. A computational software has been coded based on the dynamic explicit finite element method. The constitutive model has also been implemented into this software. The complete stress–strain relation using the new model in numerical unloading test was obtained. The sensitivity of the parameters of the dynamic failure constitutive model has also been analyzed. Based on the long-term monitored data for Zhuji coal mine, the parameter inversion of the two different sections of the piebald mudstone has been conducted with the nonlinear least square method. Further, the whole process simulation of the deformation of Zhuji coal mine has been performed with the inversed parameters. A high degree of agreement on the deformation has been achieved by the comparison between the calculated and the measured data in actual engineering project.

Unconstrained vector nonlinear dynamic shell formulation applied to Fluid Structure Interaction

Fluid Structure Interaction (FSI) is a well-developed subject and several authors constantly provide improvements in related solution processes. The aim of this paper is to present an improvement in the shell formulation regarding large displacement analysis applied to FSI problems, i.e., a new curved shell finite element based on positions and unconstrained vector mappings is coupled with a compressible 3D fluid flow Finite Element approach. This improvement is important when an initial simple fluid velocity field cannot replace embedded shell movements, or when the shell closure changes position in a way that large rotations are present. The proposed formulation does not use the concept of rotations, resulting in an algorithm that conserves linear and angular momentum for large rigid body displacements when using the well established Newmark time integrator. Other advantages of this formulation are the use of complete stress–strain relations and the possibility of solving thin or thick shells developing large displacements and small strains. Numerical examples are presented in order to validate the proposed shell formulation regarding FSI applications.

Mechanical properties of L12type Al3X (X = Mg, Sc, Zr) from first‐principles study

AbstractThe mechanical properties of L12type Al3X (X = Mg, Sc, Zr) have been investigated by first‐principles calculations. The calculated elastic properties showed that Al3Sc was the stiffest and intrinsically brittle, while Al3Mg was the softest and exhibited ductility tendency. The obtained stress–strain curves demonstrated that both of the ideal tensile and shear strengths of Al3Zr were the strongest, followed by Al3Sc and Al3Mg, and Al3Zr was also the most ductile among three phases, which disagreed with the prediction from the calculated elastic properties, indicating that the mechanical properties should be measured from the complete stress–strain relations at both small and large strains. The electronic density of states (DOS) especially the variations of the charge density during the strain loading were investigated to unveil the intrinsic mechanism for the mechanical properties of L12type Al3X (X = Mg, Sc, Zr) phases.

Constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects

A micromechanical model is proposed to describe both stable and unstable damage evolution in microcrack-weakened brittle rock material subjected to dynamic uniaxial tensile loads. The basic idea of the present model is to classify the constitution relationship of rock material subjected to dynamic uniaxial tensile loads into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress–strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to consistent with the experimental results.

Techniques for Numerical Simulations of Concrete Slabs for Demolishing by Blasting

The subject of this article is the numerical simulation of concrete under explosive loading using a meshbased and a meshfree discretization technique. The presented techniques are verified by experimental data. Experimental evidence suggests that the complete stress-strain history relation must be considered as a basis for constitutive modeling if concrete is subjected to high loading rates. These dynamic phenomena cause a retardation of damage activation which must be taken into account when constitutive modeling is pursued on mesolevel instead of microlevel. By including a dynamic relaxation formulation within the framework of a general three-dimensional coupled continuum damage-plasticity law, it is shown that the solution of the wave propagation problem in materials with strain-softening becomes independent of mesh size. As the simulation of concrete under contact detonation causes severe numerical problems because of the large deformations, special numerical spatial discretization techniques have to be used. In this article we compare the results of a concrete slab under contact detonation using the finite element method code LS-DYNA with an arbitrary Lagrangian Eulerian coupling and the results obtained by a MLSPH code developed at our institute with experimental data. The same constitutive model for concrete and the same equation of state for the explosive is implemented in the two codes. The results of the different numerical simulations and the experimental data agree with each other well.

Microcrack interaction brittle rock subjected to uniaxial tensile loads

A micromechanics-based model is proposed to describe unstable damage evolution in microcrack-weakened brittle rock material. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress–strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to be consistent with the experimental results.

Upper and lower bounds for constitutive relation of crack-weakened rock masses under dynamic compressive loads

A micro-mechanics-based model is proposed to investigate the rate-dependent constitutive relation for crack-weakened rock masses subjected to dynamic compressive loads. The present micro-mechanical model reveals that the nucleation, growth and coalescence of sliding cracks dominate the failure and macroscopic properties of crack-weakened rock masses subjected to dynamic compressive loads. The interactions among multiple parallel sliding cracks in crack-weakened rock masses subjected to dynamic compressive loads are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the stress–strain relation. Based on the micro-mechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the rate-relation for rock masses containing multiple rows of echelon cracks subjected to dynamic compressive loads. The factors that affect the rate-dependent properties of crack-weakened rock masses have been analyzed. The strain energy density factor approach, which is related to crack growth velocity and dynamic fracture toughness of rock material, is employed in the analysis. The rate-dependent constitutive relation of crack-weakened rock masses is derived from micro-mechanical framework and the asymptotic analysis. The closed-form explicit expression for the rate-dependent constitutive relation of rock masses containing echelon cracks subjected to dynamic compressive loads is obtained. Finally, the present model is used to analyze the complete stress–strain relation and strength for jointed rock masses at shiplock slope of the Three Gorges Dam.

Triaxial compressive behavior of rock with mesoscopic heterogenous behavior: Strain energy density factor approach

The strain energy density factor approach is used in conjunction with a micromechanics model to investigate the condition and direction of shear failure for brittle rock subjected to triaxial compression. Moderate confinement in addition to localized deformation and damage are considered. Quantified are the effects of the various geometric and load parameters that involve the interaction of microcrack, friction and the confining pressure such that the path of the wing crack is taken into account. The influence of all microcracks with different orientations are introduced into the constitutive relation. The closed-form solution for the complete stress–strain relation of rock containing microcracks is obtained. It is shown that the complete stress–strain relationship includes linear, nonlinear hardening, rapid stress drop and strain softening effects. The theoretical results show that deviation of the direction of wing cracks from the line of the pre-existing crack decreases with increasing confinement pressure and friction coefficient. Theoretical predictions and experimental results show good agreement.

Localization of deformation and stress–strain relation for mesoscopic heterogeneous brittle rock materials under unloading

Stress redistribution induced by excavation of underground engineering and slope engineering results in the unloading zone in parts of surrounding rock masses. The mechanical behaviors of crack-weakened rock masses under unloading are different from those of crack-weakened rock masses under loading. A micromechanics-based model has been proposed for brittle rock material undergoing irreversible changes of their microscopic structures due to microcrack growth when axial stress is held constant while lateral confinement is reduced. The basic idea of the present model is to classify the constitution relation of rock material into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The closed-form explicit expression for the complete stress–strain relation of rock materials containing cracks under unloading is obtained. The results show that the complete stress–strain relation and the strength of rock materials under unloading depend on the crack spacing, the fracture toughness of rock materials, orientation of the cracks, the crack half-length and the crack density parameter.

Analysis of the localization of damage and the complete stress-strain relation for mesoscopic heterogeneous brittle rock subjected to compressive loads

A micromechanics-based model is established. The model takes the interaction among sliding cracks into account, and it is able to quantify the effect of various parameters on the localization condition of damage and deformation for brittle rock subjected to compressive loads. The closed-form explicit expression for the complete stress-strain relation of rock containing microcracks subjected to compressive loads was obtained. It is showed that the complete stress-strain relation includes linear elasticity, nonlinear hardening, rapid stress drop and strain softening. The behavior of rapid stress drop and strain softening is due to localization of deformation and damage. Theoretical predictions have shown to be consistent with the experimental results.

Analysis of the localization of damage and the complete stress-strain relation for mesoscopic heterogeneous rock under uniaxial tensile loading

The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results.

Bounds on the complete stress–strain relation for a crack-weakened rock mass under compressive loads

The interactions among multiple parallel sliding cracks in rock materials are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the complete stress–strain relation. Based on the micromechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the complete stress–strain relation for rock masses containing multiple rows of echelon cracks. The present model studies further influence of both the interaction among crack rows and mutual collinear interaction on the constitutive relation and strength for a crack-weakened rock mass. The closed-form explicit expression for the complete stress–strain relation of rock masses containing echelon cracks subjected to compressive loads is obtained. The complete stress–strain relation includes the stages of linear elasticity, nonlinear hardening, strain softening. The results show that the complete stress–strain relation and the strength of a crack-weakened rock mass depend on the crack interface friction coefficient, the sliding crack spacing, the fracture toughness of rock materials, orientation of cracks, the crack half-length and the crack density parameter.

Effect of a fault and weak plane on the stability of a tunnel in rock—a scaled model test and numerical analysis

The characteristics of deep rock mass, such as the elastic resilience, creep, stress release, expansion, dilation and the long-term strength, are of great importance to the rock mass deformation and failure mechanism. However, there is not yet a constitutive model which can describe all these properties of the deep rock mass. The proposed dynamic failure constitutive model in this paper analyzes the elastic resilience and the dilation deformation of the surrounding rock mass during the unloading process, and the pre-peak (elastic and internal frictional hardening stages) and the post-peak(softening and residual failure stages) stages are also taken into account. A computational software has been coded based on the dynamic explicit finite element method. The constitutive model has also been implemented into this software. The complete stress–strain relation using the new model in numerical unloading test was obtained. The sensitivity of the parameters of the dynamic failure constitutive model has also been analyzed. Based on the long-term monitored data for Zhuji coal mine, the parameter inversion of the two different sections of the piebald mudstone has been conducted with the nonlinear least square method. Further, the whole process simulation of the deformation of Zhuji coal mine has been performed with the inversed parameters. A high degree of agreement on the deformation has been achieved by the comparison between the calculated and the measured data in actual engineering project.