SIMULATION OF THE STOCHASTIC DAMAGE EVOLUTION PROCESS UNDER LOW CYCLE FATIGUE BY THE FINITE ELEMENT METHOD

A numerical simulation of stochastic damage evolution process in the condition of low cycle fatigue loading is discussed. The relations between damage variables and micro-cracks are obtained by means of the micro-mechanics model of the representative volume element proposed by Lemaitre and Dufailly([10]). The stochastic Initial damage values are introduced in consideration of the inherent micro-defects In materials. The model combined with a finite element method is applied to simulate the damage evolution process under low cycle fatigue loading. The micro-cracks on the sur face of a specimen of 19Mn6 alloy steel are measured with a replica technique. The numerical results show that the nonhomogeneity of damage and the localization of the fatigue failure are well shown by the proposed simulations, and the fatigue lives are reasonably predicted.

Fuzzy stochastic damage mechanics(FSDM) based on fuzzy auto-adaptive control theory

In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

A unified stochastic damage model for concrete based on multi-scale energy dissipation analysis

This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model(MMSF), the nonlinear energy dissipation process of the microspring from nanoscale to microscale is investigated. In nanoscale, the rate process theory is adopted to describe the crack growth rate;therefore, the corresponding energy dissipation caused by a representative crack propagation can be obtained. The scale gap from nanoscale to microscale is bridged by a crack hierarchy model. Thus, the total energy dissipated by all cracks from the nanoscale to the microscale is gained. It is found that the fracture strain of the microspring can be derived from the above multi-scale energy dissipation analysis. When energy dissipation is regarded as some microdamage to the microspring, the constitutive law of the microspring is no longer linearly elastic, as previously assumed. By changing the expression of the damage evolution law from fracture strain to energy dissipation threshold, the new damage evolution model is derived. The proposed model can not only replicate the original static model but also extend to cases of rate dependence. By deriving the fracture strain under different strain rates, the rate sensitivity of concrete materials can be reflected. The model parameters can be conveniently obtained by identifying them with experimental data. Finally, several numerical examples are presented to verify the proposed model.

Crack propagation with different radius local random damage based on peridynamic theory

Drawing from the advantages of Classical Mechanics,the peridynamic theory can clarify the crack propagation mechanism by an integral solution without initially setting the factitious crack and crack path.This study implements the peridynamic theory by subjecting bilateral notch cracked specimens to the conditions of no local damage,small radius local damage,and large radius local damage.Moreover,to study the effects of local stochastic damage with different radii on the crack propagation path and Y-direction displacement,a comparison and contact methodology was adopted,in which the crack propagation paths under uniaxial tension and displacement in the Y-direction were compared and analyzed.This method can be applied to steel structures under similar local random damage conditions.