Formulation of a constitutive equation and a damage evolution equation of cortical bone with rate dependency

2004 ◽  
Vol 2004.5 (0) ◽  
pp. 63-64
Author(s):  
Masami IWAMOTO ◽  
Eiichi TANAKA ◽  
Kohei DENDA ◽  
Sota YAMAMOTO
Keyword(s):  
Constitutive Equation ◽  
Evolution Equation ◽  
Cortical Bone ◽  
Damage Evolution ◽  
Rate Dependency ◽  
Damage Evolution Equation

Damage Analysis of Concrete Subjected to Freeze-Thaw Cycles and Chloride Ion Erosion

2011 ◽  
Vol 488-489 ◽  
pp. 464-467
Author(s):  
Ji Ze Mao ◽  
Zhi Yuan Zhang ◽  
Zong Min Liu ◽  
Chao Sun
Keyword(s):  
Constitutive Equation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Damage Mechanics ◽  
Chloride Ion ◽  
Offshore Structures ◽  
Damage Evolution Equation ◽  
Freeze Thaw ◽  
Concrete Materials ◽  
Ion Erosion

With the development of damage mechanics, many researchers have used it to analyze the constitutive equation of concrete. Since the special environment in the cold marine regions, the offshore structures are common to subject to the comprehensive effects of freeze-thaw action and chloride erosion. This might cause concrete materials degradation and reduce the mechanical performance of concrete seriously. In this paper, based on the analysis and mechanical experiments of concrete materials under the comprehensive effects of freeze-thaw action and chloride ion erosion, the damage evolution equation of concrete elastic modulus along with the freeze-thaw cycles and chloride ion contents was established. The effects of chloride ion were investigated during the process of concrete degradation. According to the damage evolution equation, a new constitutive equation of concrete under freeze-thaw action and chloride erosion was established. And then, by means of the element simulation analysis of concrete beams when subjected to the comprehensive actions, the feasibility and applicability of the equation was examined and discussed. In this equation, both the freeze-thaw action and chloride ion erosion were considered together. It will be more suitable for analyzing the durability of concrete structures in the real cold marine regions. It will also provide some references for concrete constitutive theory.

A Multiaxial Damage Statistic Constitutive Model for Concrete

2012 ◽  
Vol 166-169 ◽  
pp. 56-59
Author(s):  
Shan Suo Zheng ◽  
Wen Yong Li ◽  
Qing Lin Tao ◽  
Yu Fan
Keyword(s):  
Numerical Simulation ◽  
Quantitative Analysis ◽  
Stress State ◽  
Constitutive Equation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Equivalent Strain ◽  
Triaxial Stress State ◽  
Decoupling Method ◽  
Damage Evolution Equation

In order to apply the uniaxial damage evolution equation that established with the variable of strain to the multiaxial damage quantitative analysis, this paper bases on the Hsieh-Tang-Chen four-parameter failure criterion and adopts the way of making the triaxial equivalent strain combining with the uniaxial damage evolution equation to analyze and deduce the uniaxial damage evolution equation of SRHSHPC, and which is expanded to multiaxial condition as well. A function considered triaxial stress state and a related correction value are suggested, then, improving the damage evolution equation from triaxial to multiaxial form, finally proposing the multiaxial damage statistic constitutive equation for concrete, taking numerical simulation with the complete decoupling method and the result shows that the model is effective.

Rock Damage Constitutive Equation Based on Weibull Distribution of Intensity

2011 ◽  
Vol 90-93 ◽  
pp. 565-569 ◽  
Author(s):  
Xiao Wei Li ◽  
Cheng Lin Jiang ◽  
Wen Peng Liu ◽  
Ming Ji
Keyword(s):  
Constitutive Equation ◽  
Evolution Equation ◽  
Weibull Distribution ◽  
Damage Evolution ◽  
Yield Criterion ◽  
Evolutionary Process ◽  
Uniaxial Stress ◽  
Characteristic Parameter ◽  
Rock Damage ◽  
Damage Evolution Equation

the evolution of rock microdefect is a random variation, and we can consider evolutionary process of microdefect system as nonequilibrium statistic processes. The microbit’s intensity distribution obey Weibull distribution, therefore, this paper adopts Druckr-Prager yield criterion, establishes the damage evolution equation using strain as characteristic parameter under the uniaxial stress, and derives relevant damage constitutive equation. Experiments prove that this equation, to some extent, reflect damage evolution processes under the uniaxial stress.

Study on Damage Constitutive Model of Cemented Tailings Backfill under Uniaxial Compression

2013 ◽  
Vol 353-356 ◽  
pp. 379-383 ◽  
Author(s):  
Gen Bo Yu ◽  
Peng Yang ◽  
Ying Zhou Chen
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Constitutive Model ◽  
Evolution Equation ◽  
Uniaxial Compression ◽  
Damage Evolution ◽  
Damage Evolution Equation ◽  
Damage Constitutive Model

Under the premise of isotropic and continuum cemented tailings and damage proportional to the external doing work, the damage evolution equation and damage evolution constitutive equation were derived by using the strain equivalent principle. Under the consideration of the damage also transferring stress when uniaxial compression, the damage corrected parameter was introduced to obtain the damage evolution constitutive equation containing corrected parameter. Based on the experimental data from the uniaxial compression of cemented tailing, this article validates the theoretical curves consist with the experimental ones under certain damage corrected parameter.

Study On the Damage Evolution Equation of Rockburst

2008 ◽  
Vol 33-37 ◽  
pp. 663-668
Author(s):  
Quan Sheng Liu ◽  
Bin Liu ◽  
Wei Gao
Keyword(s):  
Energy Dissipation ◽  
Evolution Equation ◽  
Damage Evolution ◽  
Minimum Energy ◽  
Strength Criterion ◽  
Internal Variable ◽  
Total Strength ◽  
Damage Evolution Equation ◽  
Traditional Research ◽  
Minimum Energy Dissipation

This paper introduces the principle of minimum energy dissipation and its general procedures to establish development equation of internal variable. With the accepted viewpoint that the damage is only mechanics of energy dissipation during the rockburst and utilizing the total strength criterion based on released strain energy, the general damage evolution equation is deduced. Compared with the traditional research method of damage evolution equation, this method has universal and objective characteristics.

Damage Evolution Equation of AZ31B Magnesium Alloy during Superplastic Deformation

2009 ◽  
Vol 610-613 ◽  
pp. 831-837
Author(s):  
Mei Juan Song ◽  
Ling Yun Wang ◽  
Rao Chuan Liu ◽  
Zhi Xiang Wang
Keyword(s):  
Quantitative Analysis ◽  
Evolution Equation ◽  
Superplastic Deformation ◽  
Damage Evolution ◽  
Volume Fraction ◽  
Tensile Tests ◽  
Critical Value ◽  
Cavity Volume ◽  
Characteristic Parameters ◽  
Damage Evolution Equation

After superplastic tensile tests and quantitative analysis of cavity volume fraction, the damage evolution equation based on the law of the micro-damage evolution and statistical mechanics was derived out. The characteristic parameters of damage evolvement and critical value of damage variables are achieved from the experiments.

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