Relation of Damage Variable and Gas Permeability Coefficient of Concrete under Stress

Compressive stress and tensile stress were applied to concrete specimens using test rigs designed by RILEM TC 246-TDC. Ultrasonic wave velocity and autoclam permeability system were used to characterize the damage variable and gas permeability coefficient of concrete, respectively. The experimental results show that the strain value of concrete increases with the increasing of stress level and loading time. The damage variable and gas permeability coefficient of concrete under compressive stress decrease at first and increase after a threshold value between 0 and 0.6. When the concrete is under tensile load, the damage variable and gas permeability coefficient increase with tensile stress, with a significant increase from 0.3 to 0.6 tensile stress. There is a strong linear relationship between the damage variable and the gas permeability coefficient, suggesting both as good indicators to characterize the damage of concrete under stress.

Bi-variable damage model for fatigue life prediction of metal components

Based on the theory of continuum damage mechanics,a bi-variable damage mechanics model is developed,which,according to thermodynamics,is accessible to derivation of damage driving force,damage evolution equation and damage evolution criteria. Furthermore,damage evolution equations of time rate are established by the generalized Drucker＇s postulate. The damage evolution equation of cycle rate is obtained by integrating the time damage evolution equations,and the fatigue life prediction method for smooth specimens under repeated loading with constant strain amplitude is constructed. Likewise,for notched specimens under the repeated loading with constant strain amplitude,the fatigue life prediction method is obtained on the ground of the theory of conservative integral in damage mechanics. Thus,the material parameters in the damage evolution equation can be obtained by reference to the fatigue test results of standard specimens with stress concentration factor equal to 1,2 and 3.

Prediction of damage potential in mainshock–aftershock sequences using machine learning algorithms

Assessing the potential damage caused by earthquakes is crucial for a community’s emergency response.In this study,four machine learning(ML)methods—random forest,extremely randomized trees,AdaBoost(AB),and gradient boosting(GB)—were employed to develop prediction models for the damage potential of the mainshock(DIMS)and mainshock–aftershock sequences(DIMA).Building structures were modeled using eight single-degree-of-freedom(SDOF)systems with different hysteretic rules.A set of 662 recorded mainshock–aftershock(MS-AS)ground motions was selected from the PEER database.Seven intensity measures(IMs)were chosen to represent the characteristics of the mainshock and aftershock.The results revealed that the selected ML methods can well predict the structural damage potential of the SDOF systems,except for the AB method.The GB model exhibited the best performance,making it the recommended choice for predicting DIMS and DIMA among the four ML models.Additionally,the impact of input variables in the prediction was investigated using the shapley additive explanations(SHAP)method.The high-correlation variables were sensitive to the structural period(T).At T=1.0 s,the mainshock peak ground velocity(PGVM)and aftershock peak ground displacement(PGDA)significantly influenced the prediction of DIMA.When T increased to 5.0 s,the primary high-correlation factor of the mainshock IMs changed from PGVM to the mainshock peak ground displacement(PGDM);however,the highcorrelation variable of the aftershock IMs remained PGDA.The high-correlation factors for DIMS showed trends similar to those of DIMA.Finally,a table summarizing the first and second high-correlation variables for predicting DIMS and DIMA were provided,offering a valuable reference for parameter selection in seismic damage prediction for mainshock–aftershock sequences.

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

To describe the deformation and strength characteristics of the corroded rock-like specimens containing a single crack under uniaxial compression,a damage constitutive model combining hydro-chemical damage with coupling damage of micro-flaws and macro-cracks is proposed.Firstly,based on phenomenological theory,the damage variable of the rock-like specimens subjected to water environment erosion and chemical corrosion is obtained.Secondly,a coupled damage variable for cracked rock-like specimens is derived based on the Lemaitre strain equivalence hypothesis,which combines the Weibull statistical damage model for micro-flaws and the fracture mechanics model for a macro single crack.Then,considering the residual strength characteristics of the rock-like materials,the damage variable is modified by introducing the correction coefficient,and the damage constitutive model of the corroded rock-like specimens with a single crack under uniaxial compression is established.The model is verified by comparing the experimental stress−strain curves,and the results are in good agreement with those provided in the literature.Finally,the correction coefficient of the damage variable proposed in this paper is discussed.The damage constitutive model developed in this paper provides an effective method to describe the stress−strain relationship and residual strength characteristics of the corroded rock-like specimens with a single crack under uniaxial compression.

Constitutive modeling of viscoelastic-viscoplastic behavior of short fiber reinforced polymers coupled with anisotropic damage and moisture effects

In this paper, a combined viscoelasticity-viscoplasticity model, coupled with anisotropic damage and moisture effects, is developed for short fiber reinforced polymers (SFRPs) with different fiber contents and subjected to a variety of strain rates. In our model, a rate-dependent yield surface for the matrix phase is employed to identify initial yielding of the material. When an SFRP is loaded at small deformation before yielding, its viscoelastic behavior can be described using the generalized Maxwell model, while when plasticity occurs, a scalar internal state variable (ISV) is used to capture the hardening behavior caused by the polymeric constituent of the composite. The material degradation due to the moisture absorption of the composite is modeled by employing another type of ISV with different evolution equations. The complicated damage state of the SFRPs is captured by a second rank tensor, which is further decomposed to model the subscale damage mechanisms of micro-voids/cracks nucleation, growth and coalescence. It is concluded that the proposed constitutive model can be used to accurately describe complicated behaviors of SFRPs because the results predicted from the model are in good agreement with the experimental data.

Mesomechanics coal experiment and an elastic-brittle damage model based on texture features

To accurately describe damage within coal, digital image processing technology was used to determine texture parameters and obtain quantitative information related to coal meso-cracks. The relationship between damage and mesoscopic information for coal under compression was then analysed. The shape and distribution of damage were comprehensively considered in a defined damage variable, which was based on the texture characteristic. An elastic-brittle damage model based on the mesostructure information of coal was established. As a result, the damage model can appropriately and reliably replicate the processes of initiation, expansion, cut-through and eventual destruction of microscopic damage to coal under compression. After comparison, it was proved that the predicted overall stress-strain response of the model was comparable to the experimental result.

A Study of the Structural Evolution and Strength Damage Mechanisms of PishaSandstone Cement Soil Modified with Fly Ash

In the present study,in order to investigate the effects of fly ash on the structural evolution and strength damage mechanism of Pisha-sandstone cement soil,unconfined compressive strength tests of Pisha-sandstone cement soil with different fly ash content levels and various ages were carried out.The apparent morphology,microstructures,and chemical compositions of the samples were observed and analyzed using ultra-depth three-dimensional microscopy,scanning electron microscopy,and XRD methods.The results revealed that the unconfined compressive strength levels of Pisha-sandstone cement soil samples displayed increasing trends with the increases in fly ash content and age.For example,when the fly ash content levels were increased from 12%to 15%,the strength of Pisha-sandstone cement soil had only slightly increased under the curing ages of 7,28,and 60 days.In addition,the unconfined compressive strength levels of the samples with 15%fly ash content only increased 0.02%,0.51%,and 0.54%,respectively,when compared with the samples containing 12%fly ash.It was observed that with the increases in the fly ash content,the number of pores on the outer surfaces of the samples were significantly reduced.Also,the height differences of cross-sectional gullies were reduced,and the apparent morphology was observed to be flatter.Since cement hydration creates a strong alkaline environment for reaction systems,the active degrees of the pozzolanic reactions of the fly ash were stimulated in this study.Moreover,a significant amount of the C-S-H gel phase and the stable five-membered ring structure of the mordenite and ettringite were generated,which connected the loose Pisha-sandstone particles to form a skeleton.The internal microstructures were then observed to be denser and more uniform.At the same time,the micro-pores were filled and refined by the unreacted micro-bead fly ash.Consequently,the defects in the internal microstructures were improved.Also,based on the Weibull distribution,a damage evolution model of the Pisha-sandstone cement soil was established.The analysis results of the damage variable D values during the initial damage stage,damage evolution stage,and residual damage stage of the damage process showed that the damage variables during all three stages displayed decreasing trends with the increases in the fly ash content levels and age.Therefore,based on this study’s findings,it was considered that the incorporation of fly ash could effectively improve the damage degrees of Pisha-sandstone cement soil under external force conditions.

Mechanical properties and damage constitutive model of sandstone after acid corrosion and high temperature treatments

Aiming at the problem of temperature-mechanics-chemical(T-M-C)action encountered by rocks in underground engineering,sandstone was selected as the sample for acid corrosion treatment at pH 1,3,5 and 7,the acid corrosion treated samples were then subjected to high-temperature experiments at 25,300,600,and 900℃,and triaxial compression experiments were conducted in the laboratory.The experimental results show that the superposition of chemical damage and thermal damage has a significant impact on the quality,wave velocity,porosity and compression failure characteristics of the rock.Based on the Lemaitre strain equivalent hypothesis theory,the damage degree of rock material was described by introducing damage variables,and the spatial mobilized plane(SMP)criterion was adopted.The damage constitutive model can well reflect the stress-strain characteristics of the rock triaxial compression process,which verified the rationality and reliability of the model parameters.The experiment and constitutive model analyzed the change law of mechanical properties of rock after chemical corrosion and high temperature thermal damage,which had certain practical significance for rock engineering construction.

Triaxial elastoplastic damage constitutive model of unreinforced clay brick masonry wall

Due to differences in the properties of composition materials and construction techniques,unreinforced masonry is characterized by low strength,anisotropy,nonuniformity,and low ductility.In order to accurately simulate the mechanical behavior of unreinforced brick masonry walls under static and dynamic loads,a new elastoplastic damage constitutive model was proposed and the corresponding subroutine was developed based on the concrete material constitutive model.In the proposed constitutive model,the Rankine strength theory and the Drucker-Prager strength theory were used to define the tensile and compressive yield surface function of materials,respectively.Moreover,the stress updating algorithm was modified to consider the tensile plastic permanent deformation of masonry materials.To verify the accuracy of the proposed constitutive model,numerical simulations of the brick masonry under monotonic and cyclic uniaxial tension and compression loads were carried out.Comparisons among the numerical and theoretical and experimental results show that the proposed model can properly reflect the masonry material mechanical properties.Furthermore,the numerical models of four pieces of masonry walls with different mortar strengths were established.Low cyclic loadings were applied and the results show that the proposed constitutive model can properly simulate the wall shear failure characteristics,and the force-displacement hysteretic curves obtained by numerical simulation are in good agreement with the tests.Overall,the proposed elastic-plastic damage constitutive model can simulate the nonlinear behavior of unreinforced brick masonry walls very well,and can be used to predict the structural response of masonry walls.

Damage detection on framed structures: modal curvature evaluation using Stockwell Transform under seismic excitation

The key parameters for damage detection and localization are eigenfrequencies, related equivalent viscous damping factors and mode shapes. The classical approach is based on the evaluation of these structural parameters before and after a seismic event, but by using a modern approach based on time-frequency transformations it is possible to quantify these parameters throughout the ground shaking phase. In particular with the use of the S-Transform, it is possible to follow the temporal evolution of the structural dynamics parameters before, during and after an earthquake. In this paper, a methodology for damage localization on framed structures subjected to strong motion earthquakes is proposed based on monitoring the modal curvature variation in the natural frequency of a structure. Two examples of application are described to illustrate the technique: Computer simulation of the nonlinear response of a model, and several laboratory(shaking table) tests performed at the University of Basilicata(Italy). Damage detected using the proposed approach and damage revealed via visual inspections in the tests are compared.

Damage evolution of metallic materials during high temperature plastic deformation

The damage evolution of high temperature plastic deformation of metallic materials was studied by use of continuum damage mechanics (CDM) theory. Based on thermodynamics, on a damage variable D and Zener Hollomon parameter Z , and on the effective stress concept, a damage evolution model of high temperature plastic deformation was derived and was used to analyze the damage evolution of 1420 Al Li alloy during high temperature plastic deformation. The model that is verified by tests can also be applied to the materials that are loaded prorata or out of proportion during high temperature plastic deformation. It extends the applied scope of damage mechanics.

Damage Mechanics of Ferrite Ductile Iron under Uniaxial Stress

According to the principle of damage mechanics,the damage characteristics of ferrite nodular cast iron under uniaxial stress were studied by measuring electric resistance. The results show that the damage in nodular cast iron occurs when the applied stress is more than a certain extent,and the damage variable increases with stress. The evolutional law of damage variable as a function of stress was obtained.The damage threshold of nodular cast iron increases with nodularity,but it is below the yield strength,which provides reference significance to the design of machinery structure and the choice of materials.The critical damage variable is not related to the nodularity,which is about 0. 060-0. 068.

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.

A method for calculating damage evolution in adiabatic shear band of titanium alloy

A method for calculating the evolution of the local damage variable at the adiabatic shear band(ASB)center was proposed.In the present method,the JOHNSON-COOK model and the nonlocal theory were adopted,and the damage variable formula applicable for the bilinear(linearly elastic and strain-softening)constitutive relation was further generalized to consider the plastic deformation occurring in the strain-hardening stage.Aiming at Ti-6Al-4V,the effect of strain rate on the evolution of the local damage variable at the ASB center was investigated.In addition,a parametric study was carried out,including the effects of strain-hardening exponent,strain rate sensitive coefficient,thermal-softening exponent,static shear strength,strain-hardening modulus,shear elastic modulus,work to heat conversion factor,melting temperature and initial temperature.The damage extent at the ASB center in the radial collapse experiment was assessed.It is found that at higher strain rates the damage in the ASB becomes more serious at the same average plastic shear strain of the ASB.

DAMAGE THEORY OF MATERIALS WITH MICROSTRUCTURE

A new form of damage theory of materials is proposed,that is valid for the case of nonconservative stresses.The partial entropy,strain and microstructure parameters are taken as the state variables.Without assuming the free energy to be a state function,the basic governing equations are derived.According to the balance of released and dissipated energy,the general form of damage evolution equation is obtained.Further,assuming the existence of independent damage mechanisms, the normality of damage evolution equation is proven.The generalized damage variables are dis- cussed.Finally,some examples are given to show the applications of the theory.

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.

Fracture and Damage Behaviors of Concrete in the Fractal Space

The fracture toughness, the driving force and the fracture energy for an infinite plate with a fractal crack are investigated in the fractal space in this work. The perimeter-area relation is adopted to derive the transforma-tion rule between damage variables in the fractal space and Euclidean space. A plasticity yield criterion is introduced and a damage variable tensor is decomposed into tensile and compressive components to describe the distinct behaviors in tension and compression. A plastic damage constitutive model for concrete in the Euclidean space is developed and generalized to fractal case according to the transformation rule of damage variables. Numerical calculations of the present model with and without fractal are conducted and compared with experimental data to verify the efficiency of this model and show the necessity of considering the fractal effect in the constitutive model of concrete. The structural response and mesh sensitivity of a notched unre-inforced concrete beam under 3-point bending test are theoretical studied and show good agreement with the experimental data.

Damage of Historical Stone Masonry Buildings： Combined Effects of Spatial Variability of Stone Properties and Environmental Conditions

The everyday fluctuations of temperature and humidity lead to fluctuation of stress on the stones constituting many constructions and produce in long term some kinds of fatigue damage. This paper investigates the combined role of stone properties variability and environmental conditions on the generation and the amplification of stress variation and fatigue. Thus, the randomness and spatial variability 0fthe mechanical, thermal and hydraulic properties are taken into account in a finite elements model of typical stone wall masonry of Chambord Castle. The quantification of the impact of this spatial variability on the variability of generated stress is performed.

Damage Analysis of Circulating Soaked Rock Sample Based on Sonic-test Trials

Circulating soaked sandstone and mudstone samples sonic parameters were tested and analyzed, using RSM-SY5 sonic instrument, the variation between soaked times and the velocity of longitudinal wave and shear wave was studied, calculation and analysis of the damage variable of circulating soaked rock samples were taken, with sonic measurement results and the empirical formula, the damage variable formulas associated with cycle times was established. The results showed that： the attenuation of sonic velocity basically in line with the exponential relationship, with cycle times increasing; The results of the critical calculation of damage variables and the strength test are well matched, which further confirms that the occurrence and expansion of new crack inside the rock mass resulted from circulating soaked lead to the decrease of the rock strength; The trend of sonic parameters attenuation and damage variable growth are good correspondence.

APPLICABILITY OF DAMAGE DEFINITION BASED ON HYPOTHESIS OF STRAIN EQUIVALENCE

The hypothesis of strain equivalence is used to measure damage in materials. The physical meaning of the elastic modulus of damaged materials defined in the hypothesis is discussed in this paper. The inapplicability of the hypothesis to be used to determine the damage and its evolution in elasto plastic materials are analyzed. It is emphasized that the method in which the relaxed modulus is taken as the deformed modulus, i.e. the elastic modulus defined in the hypothesis, is only applicable for measuring the damage in elastic materials. A new damage variable is proposed, which is applicable for both elastic and elastoplastic materials.