Papers by Keyword: Damage Evolution Equation

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Authors: Xiao Jing Li, Wei Min Yang, Wei Shen Zhu, Shu Cai Li, Ai Hua Sun
Abstract: The jointed rock mass distributed in the nature widely and its mechanical characteristic influenced the stability of the rock engineering badly. The cracks propagated and coalesced each other and macroscopic failure happened. Bolts were a kind of effective reinforcement instrument and they could prevent the cracks from propagating. However, the anchoring mechanism of bolts was not realized clearly and their reinforcement could not be reflected effectively in the numerical simulation yet. Based on the damage mechanics, a constitutive relation and damage equation of anchored jointed rock mass were presented in this paper. With a project application, the model was proved to be feasible one.
Authors: Zhan Hong Qiu, Wo Hua Zhang, He Long Chen
Abstract: The model of Helmholtz free energy serves as the constitutive functional expression for a damaged material, and was expanded into Taylor's series with respect to some state variables εij and Ω, the generalized expressions of isotropic elastic damage constitutive equations and the damage strain energy release rate with a configuration of isotropic damage scale were derived directly from the second law of thermodynamics. From the aspect of relationship between the porosity and damage variable, the different influence to damage effective functions were discussed theoretically and some valuable conclusions were carried out from the variation of material properties. The limitations of the classical damage constitutive equation based on the well-known strain equivalence hypothesis were overcome, and the method developed in this article can be applied to study different damage problems. It is shown that the applied method and obtained conclusions are useful to study the damage mechanics problems further.
Authors: Ding Han, Bing Gen Zhan, Xiao Ming Huang
Abstract: Damage evolution equations of asphalt mixture specimen beams were analyzed using the fracture toughness index and the ultimate tension strain index, respectively. The fracture toughness of the asphalt mixture was calculated by FEM. Damage evolution equations controlled apart by the stress and the strain were given. Their coefficients were back-calculated using partial fatigue tests data. The fully coupled stress-damage method and the fully coupled strain-damage method were used. The life prediction precision of each equation was verified by residual fatigue tests data. The results show that FEM is effective to calculate the fracture toughness of the asphalt mixture. Two damage evolution equations have better life prediction abilities comparing with the S-N equation used usually.
Authors: Bin Liu, Quan Sheng Liu, Yue Xiu Wu
Abstract: It is common to use the damage mechanics to study the deformation of fractured rock mass. The geometric damage tensor is always used to describe the effect of distributed joints on mechanical properties of rock mass. The disadvantages of the traditional determination method about geometric damage is that the natural section of rock mass, mining section and the measurement section are not perpendicular to each other. In this paper, a method combining with the probability theory and field scale line method is adopted to determine the geometric damage tensor. This method is convenient and fast. The solution of initial damage in damage evolution equation can be settled with this method. An effective proof is provided for the later analysis of damage stress of fractured rock mass.
Authors: Wei Chen Shi
Abstract: Damage distribution and evolution of the HRR field are characterized by means of a two-scalar damage variable approach under the consideration of isotropic damage. This theory is based on the definition of thermodynamic conjugate forces and the postulation that the plastic damage surface corresponds to the initiation of plastic damage. An asymptotic solution is applied for the non-linear plastic damage evolution equations. It is shown that both the damage variables may be expressed as a function of the accumulated amount of overall damage respectively in exponential and tangential types, which determine the damage characteristics in different areas. It is also revealed that the damage evolution coefficient plays an important role to determine the distributions of the damage variables, effective Young’s modulus and Poisson’s ratio. The obtained largest damage variable, which characterizes the deterioration of the material, and the lowest effective Young’s modulus around the crack tip locate at and respectively for Mode I and II problems.
Authors: Le Wen Zhang, Shu Cai Li, Ying Wang
Abstract: Based on the hypothesis of equivalent strain energy and the theories of fracture mechanics and damage mechanics,the constitutive model and fracture damage mechanism of bolted discontinuous jointed rockmass are systematically studied under the state of complex stresses. Initially , considering the equivalent strain energy , the constitutive relation of anchored discontinuous jointed rockmass is derived under the state of compression-shear stresses. The constitutive relation under the state of tension-shear stresses is also developed according to the theory of self-consistence. Next,the damage evolution equations of discontinuous multi-crack rockmass under compression-shear and tension-shear are put forward according to the wing crack-initiating criterion. Finally,based on the above constitutive models and the damage evolution equations three-dimensional finite element procedures have been developed to evaluate the stability and deformability of the surrounding rock mass during excavation and supporting. The calculated results indicate that above-mentioned constitutive relation and the damage evolution equations are available.
Authors: Run Nian Yang, De Min Wei
Abstract: The static failure can be seen as a special fatigue failure, which means the static failure is the fatigue failure only bearing one cycle under the ultimate-strength loading. By learning from the analysis of fatigue damage, the stress- strain curve and damage of steel fiber reinforced concrete under uniaxial loading have been studied in this paper. The damage evolution equation can be derived from the damage theory, and it can be used to describe the relationship between the damage variable and strain. According to the strain equivalence principle, the corresponding constitutive equation considering damage can be obtained. Finally, comparisons among test results, the model and ansys simulation results show that the model is suitable to describe the uniaxial stress-strain curves of steel fiber reinforced concrete.
Authors: Quan Sheng Liu, Bin Liu, Wei Gao
Abstract: 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.
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