scholarly journals Lognormal Distribution Function for Describing Seepage Damage Process of Single-Cracked Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Xinyu Liu ◽  
Zhende Zhu ◽  
Aihua Liu ◽  
Yuan Tian
Keyword(s):  
Constitutive Model ◽  
Lognormal Distribution ◽  
Fractured Rock ◽  
Strain Curve ◽  
Tensile Failure ◽  
Distribution Model ◽  
Deformation Analysis ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Statistical Damage

The precondition of rock stress and deformation analysis is a reasonable rock constitutive model. Most of the previous studies have described the heterogeneous microdamage by Weibull distribution or normal distribution. However, both of them have limitations. Therefore, this paper intends to use the lognormal distribution as the probability distribution model of rock microunit strength. Based on the tensile failure of the single-fractured rock under the hydrodynamic force, the maximum tensile strain failure criterion is used as the distribution parameter of rock microunit strength. And, considering the multiphase properties of the filling fractured rock, the equivalent elastic modulus parameter is adopted in the model. We design a triaxial seepage test for the filled single-fractured rock and analyze the applicability and rationality of the modified lognormal statistical damage model for characterizing the fractured rock by using the test data. According to the comparison of the experimental stress-strain curve and the model stress-strain curve and the analysis of the damage value test curve and the model curve, the rationality of the established statistical damage constitutive model is verified, and the advantages and limitations of the model are proposed.

scholarly journals An Improved Statistical Damage Constitutive Model for Granite under Impact Loading

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Zhenwei Zhao ◽  
Bo Wu ◽  
Xin Yang ◽  
Zhenya Zhang ◽  
Zhantao Li
Keyword(s):  
Constitutive Model ◽  
Elasticity Modulus ◽  
Strain Curve ◽  
Peak Strength ◽  
Peak Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

To study the impact properties of granite, the parameters (including the stress-strain curve, elasticity modulus, peak strength, and peak strain) of the test pieces in each group were determined via standard split-Hopkinson pressure bar tests. The results revealed that the prepeak stress-strain curves are approximately linear; the postpeak stress-strain curve declined sharply and exhibited the characteristics of brittle material failure after the stress exceeded the peak strength. In terms of the specimen form following failure, for increasing strain rate, the granite specimen became increasingly fragmented after failure. In addition, the single-parameter statistical damage constitutive model was improved, and a double-parameter statistical damage constitutive model for describing the total stress-strain curve of granite under the action of impact loading was proposed. The parameters of the statistical damage model, m and a, were obtained via fitting. The results revealed that the parameter m decreases with increasing elasticity modulus, whereas the parameter a increases. Similarly, the peak strength and the peak strain increased (in general) with increasing strain rate.

Experimental Research on the Stress - Strain Curve of Regional Confined Concrete under Single Axial Press

2014 ◽  
Vol 584-586 ◽  
pp. 1289-1292
Author(s):  
Guo Liang Zhu
Keyword(s):  
Mechanical Properties ◽  
Theoretical Analysis ◽  
Constitutive Model ◽  
Theoretical Basis ◽  
Strain Curve ◽  
Confined Concrete ◽  
Constitutive Relationship ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Relationship Of

Regional confined concrete is base on confined concrete. It is the theory and application of a new attempt and development on confined concrete. To apply it to the actual project, we need to research mechanical properties and establish constitutive relationship of regional confined concrete. According to the research, we had carried on a series of tests, founded the stress-strain constitutive model of regional confined concrete under single axial press. The accuracy of theoretical analysis were more fully verified , and a theoretical basis for the application was provided.

scholarly journals Constitutive Model of 30CrMoA Steel with Strain Correction

Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1214
Author(s):  
Song Zhang ◽  
Xuedao Shu ◽  
Jitai Wang ◽  
Yingxiang Xia
Keyword(s):  
Flow Stress ◽  
Constitutive Model ◽  
High Speed ◽  
Strain Curve ◽  
Material Constant ◽  
Test Machine ◽  
Experimental Stress ◽  
High Speed Train ◽  
Stress Strain Curve ◽  
Stress Strain

It is necessary to establish a constitutive model of 30CrMoA steel to optimize the forming shape and mechanical properties of high-speed train axles. The experimental stress–strain curve of 30CrMoA steel was obtained by an isothermal compression test on a Gleeble-3500 thermal simulation test machine under temperature of 1273~1423 K and strain rate of 0.01~10 s−1. Considering the effect of strain on the material constant, an empirical constitutive model was proposed with strain correction for 30CrMoA steel. In addition, the material constant in the constitutive model is determined by linear regression analysis of the experimental stress–strain curve. Comparing the theoretical value and experimental value of flow stress, the correlation R is 0.9828 and the average relative error (ARRE) is 4.652%. The constitutive model of 30CrMoA steel with strain correction can reasonably predict the flow stress under various conditions. The results provide an effective numerical tool for further study on accurate near-net forming of high-speed train axles.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

scholarly journals Damage Model and Experimental Study of a Sand Grouting-Reinforced Body in a Seawater Environment

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2495
Author(s):  
Hongbo Wang ◽  
Quanwei Liu ◽  
Shangqu Sun ◽  
Qingsong Zhang ◽  
Zhipeng Li ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Underground Structure ◽  
Damage Model ◽  
Strain Curve ◽  
Sand Layer ◽  
Stress Strain Curve ◽  
Underground Engineering ◽  
Stress Strain ◽  
Seawater Environment

A water-rich sand layer is a common stratum in marine underground engineering. Grouting is a technology for soil or rock sealing, a method to solve the water seepage problem, and can be used to solve geological challenges in water-rich sand layers. A grouting-reinforced body deteriorates by the long-term erosion of seawater, resulting in attenuation of the performance of the solid. Obtaining the decay law of the performance of the grouting-reinforced body can guarantee the safe operation of the underground structure over a long life cycle. To this end, by describing the solid damage after seawater erosion, the stress–strain curve and the relationship between the damage variable and the internal micro-cracks and pores in the grouting-reinforced body were analyzed. Then, a constitutive model of the solid damage in the seawater environment was established. The stress–strain curve of added solid after deterioration was obtained by designing an indoor grouting reinforcement test and an accelerated deterioration test. Finally, the constitutive model of the sand layer plus solid deterioration in a seawater environment was determined. This research is of great importance for improving the deterioration theory under a seawater environment and ensuring the long term safety of tunnel operations.

The Study of Cemented Sand and Gravel Constitutive Model

2011 ◽  
Vol 243-249 ◽  
pp. 4596-4601
Author(s):  
Ming Quan Sun ◽  
Shi Feng Yang
Keyword(s):  
Constitutive Model ◽  
Axial Strain ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Cemented Sand ◽  
Shearing Strength ◽  
Sand And Gravel ◽  
Strain Increase ◽  
Peak Value

Basing on triaxial experiments, the paper conducts the research to Cemented Sand and Gravel constitutive model. Using virtual rigid spring method, the Cemented Sand and Gravel constitutive model with considering the softening characteristics of material is established, and parameters needed are determined, the model establishes the foundation of non-linear analysis of Cemented Sand and Gravel structure. Mechanical properties and constitutive model study of Cemented Sand and Gravel is key to Cemented Sand and Gravel faced eath-rockfill dam. Basing the Mechanical properties triaxial experiment of the material, the paper gives further discussion on the constitutive model of Cemented Sand and Gravel. From the results of the triaxial test, when the cemented material content is smaller than 20kg/m3, the stress strain curve agrees quite well with hyperbolic law to which the normal gravel test curve also obeys, the exception is the increase of shearing strength. If the cemented material content is more than 30kg/m3, there is a peak value on the stress strain curve, the curve (before peak value) shows that axial strain increase with deviatoric stress with the increment gradually changing slowly, i.e. the stress strain curve has obvious nonlinear feature. the curve peaks value at the axial strain =2％, the stress strain curve present softening pattern that deviatoric stress decreases with the strain increase if continuous applying axial load. When axial strain lies between 2% and 6%, the shearing strength of samples decreases rapidly, after this interval, the shear strength tends to the stable value in the final. It is core problem the paper try to solve that how to describe Cemented Sand and Gravel constitutive model.

scholarly journals A Simplified Uniaxial Stress-strain Curve of Concrete and Its Application in Numerical Simulation

2021 ◽  
Vol 283 ◽  
pp. 01045
Author(s):  
Lou Yafei ◽  
Zou Tao ◽  
Yang Jie ◽  
Jiang Tao ◽  
Zhang Qingfang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Constitutive Model ◽  
Computational Efficiency ◽  
Concrete Beams ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Good Convergence ◽  
High Computational Efficiency

Detennining the constitutive model is a key procedure in numerical simulation of concrete structures. The uniaxial stress-strain curve is important information to determine the concrete constitutive model. This paper provided a simplified stress-strain curve of concrete that can be used in simulation. The comparison between Chinese Code and the simplified curve shows that the simplified curve of uniaxial compression is close to the code value. Numerical simulation of concrete beams show that the simplified curve proposed has high computational efficiency and good convergence.

A modified version of MATLAB application window for predicting the weld bead profile and stress–strain plot of AA5052 CMT weldment using ER4043

SIMULATION ◽  
2021 ◽  
pp. 003754972110315
Author(s):  
B Girinath ◽  
N Siva Shanmugam
Keyword(s):  
Strain Curve ◽  
Weld Bead ◽  
Welding Parameters ◽  
Bead Geometry ◽  
Hybrid Technique ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Weld Bead Geometry ◽  
Inference System ◽  
Engineering Stress

The present study deals with the extended version of our previous research work. In this article, for predicting the entire weld bead geometry and engineering stress–strain curve of the cold metal transfer (CMT) weldment, a MATLAB based application window (second version) is developed with certain modifications. In the first version, for predicting the entire weld bead geometry, apart from weld bead characteristics, x and y coordinates (24 from each) of the extracted points are considered. Finally, in the first version, 53 output values (five for weld bead characteristics and 48 for x and y coordinates) are predicted using both multiple regression analysis (MRA) and adaptive neuro fuzzy inference system (ANFIS) technique to get an idea related to the complete weld bead geometry without performing the actual welding process. The obtained weld bead shapes using both the techniques are compared with the experimentally obtained bead shapes. Based on the results obtained from the first version and the knowledge acquired from literature, the complete shape of weld bead obtained using ANFIS is in good agreement with the experimentally obtained weld bead shape. This motivated us to adopt a hybrid technique known as ANFIS (combined artificial neural network and fuzzy features) alone in this paper for predicting the weld bead shape and engineering stress–strain curve of the welded joint. In the present study, an attempt is made to evaluate the accuracy of the prediction when the number of trials is reduced to half and increasing the number of data points from the macrograph to twice. Complete weld bead geometry and the engineering stress–strain curves were predicted against the input welding parameters (welding current and welding speed), fed by the user in the MATLAB application window. Finally, the entire weld bead geometries were predicted by both the first and the second version are compared and validated with the experimentally obtained weld bead shapes. The similar procedure was followed for predicting the engineering stress–strain curve to compare with experimental outcomes.

scholarly journals Effect of Nanopores on Mechanical Properties of the Shape Memory Alloy

Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 529
Author(s):  
Chunzhi Du ◽  
Zhifan Li ◽  
Bingfei Liu
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Shape Memory ◽  
Young’S Modulus ◽  
Residual Strain ◽  
Surface Effect ◽  
Young's Modulus ◽  
Strain Curve ◽  
Stress Strain ◽  
Strength Limit

Nanoporous Shape Memory Alloys (SMA) are widely used in aerospace, military industry, medical and health and other fields. More and more attention has been paid to its mechanical properties. In particular, when the size of the pores is reduced to the nanometer level, the effect of the surface effect of the nanoporous material on the mechanical properties of the SMA will increase sharply, and the residual strain of the SMA material will change with the nanoporosity. In this work, the expression of Young’s modulus of nanopore SMA considering surface effects is first derived, which is a function of nanoporosity and nanopore size. Based on the obtained Young’s modulus, a constitutive model of nanoporous SMA considering residual strain is established. Then, the stress–strain curve of dense SMA based on the new constitutive model is drawn by numerical method. The results are in good agreement with the simulation results in the published literature. Finally, the stress-strain curves of SMA with different nanoporosities are drawn, and it is concluded that the Young’s modulus and strength limit decrease with the increase of nanoporosity.

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