An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Constitutive equations for high temperature flow stress prediction of 6063 Al alloy considering compensation of strain

In order to develop the appropriate constitutive equation which can precisely model high temperature flow stress of 6063 Al alloy, a series of isothermal hot compression tests were performed at temperatures from 573 to 773 K and strain rates from 0.5 to 50 s?1 on a Gleeble?1500 thermo-simulation machine. Zener–Hollomon parameter in an exponent-type equation was used to describe the combined effects of temperature and strain rate on hot deformation behaviour of 6063 Al alloy, whereas the influence of strain was incorporated in the developed constitutive equation by considering material constants (α,n,Q andA) to be 4th order polynomial functions of strain. The results show that the developed constitutive equation can accurately predict high temperature flow stress of 6063 Al alloy, which demonstrates that it can be suitable for simulating hot deformation processes such as extrusion and forging, and for properly designing the deformation parameters in engineering practice.

An elasto-plastic constitutive model for soft rock considering mobilization of strength

A new elasto-plastic constitutive model is presented in the framework of plasticity theory. The strength characteristics of a diatomaceous soft rock is investigated. The friction angle and cohesion of soft rock are mobilized as a function of plastic strain. A hyperbolic hardening function for the mobilized friction and a mixed parabolic and exponential equation for the mobilized cohesion are proposed. In view of the unified strength theory and the mobilizations of strength components, a yield function is given. A plastic potential function is determined by using the non-associated plastic flow rule. An elasto-plastic constitutive model is developed and verified. The results indicate that the proposed model can predict the behavior of soft rock accurately. The advantages of the proposed constitutive model are analyzed. The evidences support that the proposed constitutive model is a mixed hardening/softening model. A hump hardening/softening function for mobilized friction is extended to a more generalized condition.

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.

Establishment of a novel constitutive model considering dynamic recrystallization behavior of Ti-22Al-25Nb alloy during hot deformation

The hot deformation behavior of Ti-22Al-25Nb alloy fabricated by hot compressed sintering was investigated under various conditions of compression tests in the deformation temperature range of 975-1075 °C with 20 °C intervals and the strain rate range of 0.001-1.0 s^-1. Based on the experimental data, a novel constitutive relation combining a series of models was developed, including Zener-Hollomon parameter (Z), DRX critical model and kinetics model. The results show that the hot-deformed activation energy Q is calculated to be 410.172 kJ/mol, the ratio of critical strain (εc) to peak strain (εp) is a constant value of about 0.67. The predicted stress obtained by the established constitutive equations matches well with the true stress from experimental data. Despite large errors occur at the stage where strain rate is 0.1 s^-1 and the values of true strain are less than 0.1, the stage of large strain should be more concerned during plastic forming. Furthermore, the predicting accuracy with the DRX kinetics model was testified by an electron back-scattered diffraction (EBSD) technique.

Fecal-associated microbiome differences between traditional Chinese medicine qi-deficiency and balanced constitutions

Objective:To explore the structural and functional characteristics of the fecal-associated microbiome(FAM)in a traditional Chinese medicine(TCM)qi-deficiency constitution(QDC)by comparing with balanced constitution(BC)and screen the related biomarkers.Methods:In this cross-sectional study,the TCM constitutions of subjects were determined based on published the Classification and Determination of constitution in TCM and further confirmed by a TCM clinician.Clinical characteristics were recorded,and fecal samples were collected for 16S rDNA sequencing using the Illumina Miseq platform.The FAM structure was described using alpha-diversity indexes,beta-diversity indexes,and the relative abundances of the dominant taxa.Differences in the FAM distribution and function were analyzed with a Wilcoxon rank-sum test,MetagenomeSeq,and LEfSe analysis,after which a receiver operating characteristic curve based on the specific operational taxonomic units(OTUs)was constructed to calculate the area under the curve.Results:Our study population was composed of 22 BCs and 9 QDCs.There were no significant differences between the two groups in the distribution of clinical characteristics or alpha-diversity indexes,except for the sweets preference and blood glucose level.In principal coordinate analysis and partial least squares discriminant analysis,the bacterial communities in the BC group samples and QDC group samples clustered separately.Notably,there were 214 OTUs significantly distributed between groups in the MetagenomeSeq analysis,200 OTUs identified by the Wilcoxon rank-sum test,and 6 OTUs found by the LEfSe analysis.Predicted function analysis revealed that six metabolic pathways were distinctly distributed between the two groups.The area under the curve for the receiver operating characteristic curve based on the four specific OTUs was 0.88.Conclusion:Unique FAM structural and related functional characteristics are displayed in individuals with a QDC,and four specific OTUs could be used as QDC biomarkers to assist in clinical diagnosis.

An improved hypoplastic constitutive model of rockfill considering effect of stress path

An incrementally nonlinear hypoplastic constitutive model was introduced, which was developed without recourse to the concepts in elastoplasticity theory such as yield surface, plastic potential and the decomposition of the deformation into elastic and plastic parts. Triaxial drained tests on rockfill were conducted on a large scale triaxial apparatus under two types of stress paths, which were the stress paths of constant stress ratio and the complex stress paths with transitional features. Motivated by the effect of stress path, the Gudehus-Bauer hypoplastic model was improved by considering the parameter variations with different ratios of stress increment. Fitting parameter a presents a piecewise linear relationship with cosine of the slope angle θ determined by instantaneous stress path. The improved hypoplastic model can present peak stress increasing and volumetric strain changing from dilatancy to contractancy with the increase of transitional confining pressure σ3t and the decrease of slope angle θ of stress path. Compared with the test data, it is shown that the model is capable of fully considering the effect of stress path on rockfill.

Constitutive Model of Friction Stir Weld with Consideration of its Inhomogeneous Mechanical Properties

In practical engineering, finite element（FE） modeling for weld seam is commonly simplified by neglecting its inhomogeneous mechanical properties. This will cause a significant loss in accuracy of FE forming analysis, in particular, for friction stir welded（FSW） blanks due to the large width and good formability of its weld seam. The inhomogeneous mechanical properties across weld seam need to be well characterized for an accurate FE analysis. Based on a similar AA5182 FSW blank, the metallographic observation and micro-Vickers hardness analysis upon the weld cross-section are performed to identify the interfaces of different sub-zones, i.e., heat affected zone（HAZ）, thermal-mechanically affected zone（TMAZ） and weld nugget（WN）. Based on the rule of mixture and hardness distribution, a constitutive model is established for each sub-zone to characterize the inhomogeneous mechanical properties across the weld seam. Uniaxial tensile tests of the AA5182 FSW blank are performed with the aid of digital image correlation（DIC） techniques. Experimental local stress-strain curves are obtained for different weld sub-zones. The experimental results show good agreement with those derived from the constitutive models, which demonstrates the feasibility and accuracy of these models. The proposed research gives an accurate characterization of inhomogeneous mechanical properties across the weld seam produced by FSW, which provides solutions for improving the FE simulation accuracy of FSW sheet forming.

Controlling floor heave of extraction opening by reinforcing sides and roof

The effect of reinforcing roof, sides and floor corners to control floor heave of extraction opening was analyzed, It was proved by engineering practice and numerical simulation that reinforcing any part of surrounding rock have certainly control effect for floor heave, in the basis of this, the new way that roof, sides and floor corners were rein-forced to control floor heave was put forward. Contrasting control result of reinforcing floor with this, it is determined that reinforcing is more suitable to control floor heave of extrac-tion opening than reinforcing floor when advancing abutment pressure is in some range.

Evaluation on prediction abilities of constitutive models considering FEA application

Constitutive model plays an important role in the numerical simulations of metal forming. However, th~ influence of the models on the calculation is vague. Based on the stress-strain data of A1 7050 and Ti-6A1-4V alloy generated by isothermal compressive tests, the Johnson-Cook （JC） and Arrhenius-type （A-type） hyperbolic sine model were fitted to obtain the constants. Flow stresses directly calculated by the equations were compared with th~ experiment results, and rigid-plastic finite element analyses （FEA） utilizing these models were employed to simulate th~ same compression processes. The results show that A-type model has higher accuracy in the direct prediction of roy stress, even outside of the fit domain. The simulation results using A-type model also have higher agreement with th~ experiment; however, the suitability is affected by the referential parameters employed in the regression process, h terms of the overall deformation and strain distributions, there are slight differences among the simulation results usint these two models.

Novel uniaxial concrete constitutive model considering bond-slip effect

A uniaxial concrete constitutive model considering the bond-slip effect is proposed and its finite element analysis(FEA)implementation on a fiber section of a beam-column element is presented.The tension-stiffening,crackclosing,crack-opening,cyclic degradation of the tensile capacity of reinforced concrete are modeled,which reveals the significance of energy dissipation resulting from bond slip during crack opening and closing under cyclic loading.The model is based on a simplified mechanical concept in a smeared manner and verified through quasi-static test results of X-type slender RC columns.The FEA results using a common concrete model with no consideration of bond slip present significant pinching when predicting the hysteretic loop of slender columns,which is not consistent with the test results and underestimates the capacity of energy dissipation of cracking during cyclic load.The results obtained with the proposed model show good agreement with the test results,which can reflect the degradation of stiffness and strength as well as the energy dissipation of the crack opening and closing due to the bond slip effect.Considering its simplicity and computational efficiency,it is more applicable for analyzing large-scale structures than other methods that consider the bond-slip effect,especially for slender columns,such as those used in cooling towers and subjected to seismic excitation.

Predicting the electromechanical properties of small caliber projectile impact igniter using PZT dynamic damage constitutive model considering crack propagation

Block piezoelectric ceramics(PZTs)are often used in impact igniters to provide activation energy for electric initiators.Under the action of strong impact stress,PZTs release electric energy accompanied by crack initiation,propagation and crushing.At present,the electrical output performance of PZTs in projectile is usually calculated by quasi-static piezoelectric equation without considering the dynamic effect caused by strong impact and the influence of crack propagation on material properties.So the ignition parameters are always not accurately predicted.To tackle this,a PZT dynamic damage constitutive model considering crack propagation is established based on the dynamic impact test and the crack propagation theory of brittle materials.The model is then embedded into the ABAQUS subroutine and used to simulate the electromechanical response of the impact igniter during the impact of a small caliber projectile on the target.Meanwhile,the experiments of projectile with impact igniter impact on the target are carried out.The comparison between experimental and numerical simulation results show that the established dynamic damage model can effectively predict the dynamic electromechanical response of PZTs in the missile service environment.

A rate-dependent constitutive model for saturated frozen soil considering local breakage mechanism

A rate-dependent constitutive model for saturated frozen soil is vital in frozen soil mechanics,especially when simultaneously describing the nonlinearity,dilatancy and strain-softening characteristics.The distribution of the non-uniform strain rate of saturated frozen soil at the meso-scale due to the local icecementation breakage is described by a newly binary-medium-based homogenization equation.Based on the field-equation-based approach of the meso-mechanics theory,the interaction expression of the strain rate at macro-and meso-scale is derived,which can give the strain rate concentration tensor at different crushed degrees.With the thermodynamics and empirical assumption,a breakage ratio in the rate-dependent form is determined.This overcomes the limitations of the existing binary-medium-based models that are difficult to simulate rate-dependent mechanical response.Based on these assumptions,a newly binary-medium-based rate-dependent model is proposed considering both the ice bond breakage and material composition characteristics of saturated frozen soil.The proposed constitutive model has been validated by the test results on frozen soils with different temperatures and strain rates.

Research on the Correlation Between Physical Examination Indexes and TCM Constitutions Using the RBF Neural Network

Objective To establish correlation models between various physical examination indexes and traditional Chinese medicine(TCM)constitutions,and explore their relationships based on the radial basis function(RBF)neural network.Methods The raw data of physical examination indexes and TMC constitutions of 650 subjects who underwent a physical examination were cleaned,classified and sorted,on the basis of which valid data were retrieved and categorized into a training dataset and a test dataset.Subsequently,the RBF neural network was applied to the valid samples in the training set to establish correlation models between various physical examination indexes and TCM constitutions.The accuracy and the error margin of the correlation model were then verified using the valid samples in the test set.Results Of all selected samples,the highest accuracy rates were 80% for the blood lipid index-TCM constitution model;100% for the renal function index-TCM constitution model;100% for the blood routine(male)index-TCM constitution model;88.8% for the blood routine(female)index-TCM constitution model;84.1%for the urine routine index-TCM constitution model;and 100% for the blood transfusion index-TCM constitution model.Conclusions The samples selected in this study suggested that there is a strong correlation between physical examination indexes and TCM constitutions,making it feasible to apply the established correlation models to TCM constitution identification.

Correlation between Tibetan and traditional Chinese medicine body constitutions: A cross-sectional study of Tibetan college students in the Tibet Autonomous Region

Objective:To evaluate the correlation between the body constitution types of Tibetan medicine and traditional Chinese medicine (TCM).Methods:The cluster sampling method was employed to recruit participants from a university in the Tibet Autonomous Region.Tibetan medicine and TCM questionnaires were respectively used to assess the participants' constitution information.Descriptive statistics were applied to analyze the baseline and constitution characteristics of the participants.Two-factor correlation analysis and the paired chi-square test were applied to analyze the correlation between Tibetan and TCM constitution types.Results:Data from 466 Tibetan students were analyzed.The mean scores of the rlung,mkhris pa,and bad kan constitution types in Tibetan medicine were 43.2 (11.1),42.1 (10.1),and 45.0 (8.0),respectively;participants with the three-factor convergence body constitution type accounted for 13.7% of the whole population.Among the TCM constitution types,qi stagnation was the most common (21.5%),followed by the balance type (16.5%);the other constitutions detected were qi deficiency,yin deficiency,and yang deficiency.The rate of consistency for the identification of the three-factor convergence constitution in Tibetan medicine and the balance constitution in TCM was 89.1%,with a Kappa coefficient of 0.57 (P >.05).The rlung constitution in Tibetan medicine was associated with the yin deficiency,yang deficiency,and blood stasis constitutions in TCM.The mkhhris pa constitution in Tibetan medicine was associated with the damp heat and yin deficiency constitutions in TCM.The bad kan constitution in Tibetan medicine was associated with the phlegm dampness,qi deficiency,and yin deficiency constitutions in TCM.Conclusion:There is a correlation between the body constitution types of Tibetan medicine and TCM.The reliability and validity of the Questionnaire for TibetanMedicine Constitution requires improvement,and more studies with larger sample sizes and more varied populations are warranted to verify the correlation between Tibetan medicine and TCM constitutions.

Class of numerical methods for differential-algebraic systems with discontinuous right-hand sides

Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS).

Analysis of the sensory threshold between paretic and nonparetic sides for healthy rehabilitation in hemiplegic patients after stroke

The purpose of this study was to investigate the differences in the sensory threshold between the paretic and nonparetic sides of hemiplegic patients. 28 patients who were hemiplegic post-stroke (14 men and 14 women) participated in the electrical sensory and pain thresholds study;22 patients who were hemiplegic post-stroke (13 men, 9 women) participated in a study measureing the sensory threshold with light touch. Electrical sensory and pain thresholds were measured in the forearm via transcutaneous electrical nerve stimulation. The light-touch threshold was measured in the forearm using monofilaments. The light-touch, electrical sensory, and pain thresholds for the paretic side were significantly higher than for the nonparetic side in our population, respectively. In both the nonparetic and paretic sides, the male group generally showed higher thresholds for pain and sensation than did the female group. These results suggest that the different evaluations of sensory thresholds performed in this study for healthy rehabilitation will be a valuable clinical tool in hemiplegic patients after stroke.

Dynamic constitutive model for soils considering asymmetry of skeleton curve

Based on the asymmetric characteristic of skeleton curve obtained from dynamic tests on soils,a function with double asymptotes is proposed for describing the dynamic constitutive relations of soils.The hysteresis loops observed during unloading and reloading show the same form as the skeleton curve and are constructed by taking the ultimate stress as the corresponding asymptote.The coeffcient of initial unloading modulus is used to ensure that the constructed hysteresis loop fts well with the experimental data.Then,a new dynamic constitutive model considering the asymmetry of skeleton curve is elaborated.The verifcation tests on saturated Nanjing fne sand are performed using a hollow cylinder apparatus to verify the applicability of the UD model.It is found that the predicted curves by the UD model agree well with the test data.

Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve

Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.

Discrimination of TCM constitutions by biochemical and routine urine indexes

Objective:To investigate whether the specific traditional Chinese medicine(TCM)constitution of individuals can be defined by certain biological indexes instead of answering the questionnaire,and to explore the possibility of discriminating nine TCM constitutions from each other simultaneously using biological indexes.Methods:Blood and urine samples from 152 individuals with nine TCM constitutions were collected,and the related biological indexes were analyzed combining ANOVA,multiple comparison,discriminant analysis,and support vector machine.Results:We found that 4 out of 24 blood routine indexes,7 out of 10 urine routine indexes,and 12 out of 32 biochemical indexes showed differences among the constitutions.High-sensitivity C-reactive protein,apolipoprotein A1,and alkaline phosphatase were potential candidates for screening out individuals with unbalanced constitutions.Combining uric acid,high-density lipoprotein,apolipoprotein A1,creatine kinase,total protein,aspartate aminotransferase,total bile acid,dehydrogenase,sodium,and calcium levels had the potential to directly distinguish the nine TCM constitutions from each other.Among these indexes,the highest ratio of discriminant analysis between two constitutions was 95.5%,while the lowest was 66.1%.Conclusion:Our results suggest that some biochemical and urine indexes are related to various TCM constitutions,and thus they have the potential to be used for TCM constitution classification.