A Statistical Constitutive Model of Continuous Damage for Fragile Solid Material

2012 ◽  
Vol 557-559 ◽  
pp. 2217-2220 ◽  
Author(s):  
Hua Lin Liao
Keyword(s):  
Experimental Data ◽  
Probability Distribution ◽  
Constitutive Model ◽  
Elastic Strain ◽  
Solid Material ◽  
Constructive Model ◽  
Rock Damage ◽  
Deformation Characteristics ◽  
Fitting Method ◽  
Curve Fitting Method

Based on the probability distribution theory of rock micro-unit strength and taking the Mohr-Coulomb damage criterion as the distribution variable, the theoretical equations for the evolution of damage variables and the statistical constitutive model of rock damage in triaxis test were established. The arbitrary triaxis experimental data w ere used to calculate the parameters in the model by using curve fitting method and extreme value method. The calculated results of the model agree well with the experimental data. This constructive model can reflect effectively the deformation characteristics of rocks under loads and the constructive relation between elastic strain and stress of rock damage.

A Useful Curve Fitting Method for Concrete Uniaxial Compressive Experiment Data

2011 ◽  
Vol 291-294 ◽  
pp. 1015-1020 ◽  
Author(s):  
Chong Jin ◽  
Hong Wang ◽  
Xiao Zhou Xia
Keyword(s):  
Experimental Data ◽  
Orthogonal Polynomial ◽  
Least Square ◽  
Base Function ◽  
Concrete Material ◽  
Fitting Method ◽  
Orthogonal Base ◽  
The Matrix ◽  
Uniform Function ◽  
Curve Fitting Method

Based on the superiority avoiding the matrix equation to be morbid for those fitting functions constructed by orthogonal base, the Legendre orthogonal polynomial is adopted to fit the experimental data of concrete uniaxial compression stress-strain curves under the frame of least-square. With the help of FORTRAN programming, 3 series of experimental data is fitted. And the fitting effect is very satisfactory when the item number of orthogonal base is not less than 5. What’s more, compared with those piecewise fitting functions, the Legendre orthogonal polynomial fitting function obtained can be introduced into the nonlinear harden-soften character of concrete constitute law more convenient because of its uniform function form and continuous derived feature. And the fitting idea by orthogonal base function will provide a widely road for studying the constitute law of concrete material.

Solubility of Sn(IV) Oxide in Dilute NaClO4 Solution at Ambient Temperature

1996 ◽  
Vol 465 ◽  
Author(s):  
Takayuki Amaya ◽  
Tamotsu Chiba ◽  
Kazunori Suzuki ◽  
Chie Oda ◽  
Hideki Yoshikawa ◽  
...  
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Ambient Temperature ◽  
Equilibrium Constants ◽  
Inert Gas ◽  
Fitting Method ◽  
Naclo4 Solution ◽  
Safety Assessments ◽  
Curve Fitting Method ◽  
Image Position

ABSTRACTThe solubility of Sn(IV) oxide was determined in a dilute NaClO4 solution with pH 2 through 12 at ambient temperature. Both oversaturation and undersaturation experiments were carried out in an inert gas glovebox where the concentration of the oxygen and carbon dioxide were less than 1 ppm. The solubility of Sn(IV) oxide was 3×10-8 mol/1 at neutral pH, and increased at pH >7.5. Equilibrium constants of soluble reactions were calculated from the experimental data, using curve fitting method.The study suggests that the solubility of Sn(IV) oxide would be higher than that provisionally used in current safety assessments of HLW disposal sites.

A curve-fitting method for experimental data

1988 ◽  
Vol 65 (4) ◽  
pp. A96
Author(s):  
Fred R. Hilgeman ◽  
Gary H. Richter
Keyword(s):  
Experimental Data ◽  
Curve Fitting ◽  
Fitting Method ◽  
Curve Fitting Method

scholarly journals Study of statistical damage constitutive model of layered composite rock under triaxial compression

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yong-Sheng Liu ◽  
Zhuan-Zhuan Qiu ◽  
Xue-Cai Zhan ◽  
Hui-Nan Liu ◽  
Hai-Nan Gong
Keyword(s):  
Constitutive Model ◽  
Axial Strain ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Layered Composite ◽  
Model Parameters ◽  
Compression Tests ◽  
Fitting Method ◽  
Confining Pressures ◽  
Curve Fitting Method

Abstract The layered composite rock was subjected to triaxial compression tests under constant confining pressure and the stress–strain curves under different confining pressures were obtained. Based on the continuous damage theory and statistical strength theory, it is assumed that the strength of rock microelements obeys Weibull distribution by taking the defects such as random micro-cracks in the rock into account. The statistical constitutive model of layered composite rock with damage correction is established by taking the axial strain of rock as a random distribution variable of microelement strength. The model parameters were determined by the curve fitting method and referring to some test parameters. By comparing the experimental data and the constitutive model curve, the rationality and feasibility of the model are verified.

Effect Of Elevated Temperatures On Complete Concrete Deformation Diagrams

2019 ◽  
pp. 9-14
Keyword(s):  
Experimental Data ◽  
Elastic Modulus ◽  
Elevated Temperatures ◽  
Peak Load ◽  
Relative Deformation ◽  
Deformation Characteristics ◽  
Compression Tests ◽  
Strain Behavior ◽  
Different Temperatures ◽  
Deformation Diagrams

The analysis of the previous results of the study on concrete stress-strain behavior at elevated temperatures has been carried out. Based on the analysis, the main reasons for strength retrogression and elastic modulus reduction of concrete have been identified. Despite a significant amount of research in this area, there is a large spread in experimental data received, both as a result of compression and tension. In addition, the deformation characteristics of concrete are insufficiently studied: the coefficient of transverse deformation, the limiting relative compression deformation corresponding to the peak load and the almost complete absence of studies of complete deformation diagrams at elevated temperatures. The two testing chambers provided creating the necessary temperature conditions for conducting studies under bending compression and tension have been developed. On the basis of the obtained experimental data of physical and mechanical characteristics of concrete at different temperatures under conditions of axial compression and tensile bending, conclusions about the nature of changes in strength and deformation characteristics have been drawn. Compression tests conducted following the method of concrete deformation complete curves provided obtaining diagrams not only at normal temperature, but also at elevated temperature. Based on the experimental results, dependences of changes in prism strength and elastic modulus as well as an equation for determining the relative deformation and stresses at elevated temperatures at all stages of concrete deterioration have been suggested.

Using A Segmented Voltage Sweep Mode and A Gaussian Curve Fitting Method to Improve Heavy Metal Measurement System Performance

2012 ◽  
Vol 19 (2) ◽  
pp. 381-394
Author(s):  
José Pereira ◽  
Octavian Postolache ◽  
Pedro Girão
Keyword(s):  
Heavy Metals ◽  
Heavy Metal ◽  
Measurement System ◽  
Curve Fitting ◽  
System Performance ◽  
Redox Potentials ◽  
Voltage Sweep ◽  
Gaussian Curve ◽  
Fitting Method ◽  
Curve Fitting Method

Using A Segmented Voltage Sweep Mode and A Gaussian Curve Fitting Method to Improve Heavy Metal Measurement System PerformanceThis paper presents a voltammetric segmented voltage sweep mode that can be used to identify and measure heavy metals' concentrations. The proposed sweep mode covers a set of voltage ranges that are centered around the redox potentials of the metals that are under analysis. The heavy metal measurement system can take advantage of the historical database of measurements to identify the metals with higher concentrations in a given geographical area, and perform a segmented sweep around predefined voltage ranges or, alternatively, the system can perform a fast linear voltage sweep to identify the voltammetric current peaks and then perform a segmented voltage sweep around the set of voltages that are associated with the voltammetric current peaks. The paper also includes the presentation of two auto-calibration modes that can be used to improve system's reliability and proposes the usage of a Gaussian curve fitting of voltammetric data to identify heavy metals and to evaluate their concentrations. Several simulation and experimental results, that validate the theoretical expectations, are also presented in the paper.

scholarly journals Analysis on the Return Period of “7.26” Rainstorm and Flood in 2017 in the Wudinghe Basin

2018 ◽  
Vol 246 ◽  
pp. 01105
Author(s):  
Shuang-yan Jin ◽  
Wen-yong Gao ◽  
Si-wu Luo ◽  
Ya-jun Gao
Keyword(s):  
Return Period ◽  
Peak Discharge ◽  
Observation Data ◽  
Historical Survey ◽  
Annual Maximum ◽  
Frequency Curve ◽  
Recurrence Period ◽  
Fitting Method ◽  
Curve Fitting Method ◽  
Hydrological Station

The return period of "7.26" rainstorm flood in 2017 in Wudinghe basin is analyzed by the method of P-III distribution. The Lijiahe and Dingjiagou stations with long rainfall observation data in the rainstorm area are selected, and the frequency curve of the annual maximum 24 hours rainfall are established, and the recurrence period of rainfall stations in rainstorm area are estimated according to the parameters determined by the curve fitting method. The frequency curve of the annual maximum peak discharge of Baijiachuan hydrological stations and so on are established, and the return period are analyzed in combination with the historical survey floods. The results show that the return period of Zhaojiabian of heavy rainfall center is about 100 years, and which of the other stations over than 200mm in Wudinghe basin is about 30~90 years; while the return period of the peak discharge of Baijiachuan and Suide hydrological station is about 30 and 20 years respectively.

An additional branch free algebraic B-spline curve fitting method

2010 ◽  
Vol 26 (6-8) ◽  
pp. 801-811 ◽  
Author(s):  
Mingxiao Hu ◽  
Jieqing Feng ◽  
Jianmin Zheng
Keyword(s):  
Curve Fitting ◽  
B Spline ◽  
Spline Curve ◽  
Fitting Method ◽  
Additional Branch ◽  
Curve Fitting Method

scholarly journals A Mathematical Method for Determining the Parameters of Functional Dependencies Using Multiscale Probability Distribution Functions

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1085
Author(s):  
Ilya E. Tarasov
Keyword(s):  
Experimental Data ◽  
Probability Distribution ◽  
Integrated Circuits ◽  
Distribution Functions ◽  
Independent Parameter ◽  
Functional Dependencies ◽  
Computing Device ◽  
System On A Chip ◽  
Error Probability Distribution ◽  
Special Case

This article discusses the application of the method of approximation of experimental data by functional dependencies, which uses a probabilistic assessment of the deviation of the assumed dependence from experimental data. The application of this method involves the introduction of an independent parameter “scale of the error probability distribution function” and allows one to synthesize the deviation functions, forming spaces with a nonlinear metric, based on the existing assumptions about the sources of errors and noise. The existing method of regression analysis can be obtained from the considered method as a special case. The article examines examples of analysis of experimental data and shows the high resistance of the method to the appearance of single outliers in the sample under study. Since the introduction of an independent parameter increases the number of computations, for the practical application of the method in measuring and information systems, the architecture of a specialized computing device of the “system on a chip” class and practical approaches to its implementation based on programmable logic integrated circuits are considered.

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