Three-dimensional constitutive model for magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy single crystals

Existing experimental results have shown that four types of physical mechanisms, namely, martensite transformation, martensite reorientation, magnetic domain wall motion and magnetization vector rotation, can be activated during the magneto-mechanical deformation of NiMnGa ferromagnetic shape memory alloy (FSMA) single crystals. In this work, based on irreversible thermodynamics, a three-dimensional (3D) single crystal constitutive model is constructed by considering the aforementioned four mechanisms simultaneously. Three types of internal variables, i.e., the volume fraction of each martensite variant, the volume fraction of magnetic domain in each variant and the deviation angle between the magnetization vector, and easy axis are introduced to characterize the magneto-mechanical state of the single crystals. The thermodynamic driving force of each mechanism and the thermodynamic constraints on the constitutive model are obtained from Clausius's dissipative inequality and constructed Gibbs free energy. Then, thermodynamically consistent kinetic equations for the four mechanisms are proposed, respectively. Finally, the ability of the proposed model to describe the magneto-mechanical deformation of NiMnGa FSMA single crystals is verified by comparing the predictions with corresponding experimental results. It is shown that the proposed model can quantitatively capture the main experimental phenomena. Further, the proposed model is used to predict the deformations of the single crystals under the non-proportional mechanical loading conditions.

A Nonlinear Magneto-Mechanical Coupled Constitutive Model for the Magnetostrictive Material Galfenol

In order to predict the performance of magnetostrictive smart material and pushits applications in engineering, it is necessary to build the constitutive relations for themagnetostrictive material Galfenol. For Galfenol rods under the action of the pre-stress andmagnetic field along the axial direction, the one-dimensional nonlinear magneto-mechanicalcoupling constitutive model is proposed based on the elastic Gibbs free energy, where theTaylor expansion of the elastic Gibbs free energy is made to obtain the polynomial forms. Andthen the constitutive relations are derived by replacing the polynomial forms with the propertranscendental functions based on the microscopic magneto-mechanical coupling mechanism.From the perspective of microscopic mechanism, the nonlinear strain related to magneticdomain rotation results in magnetostrictive strain changing with the pre-stress among theelastic strains induced by the pre-stress. By comparison, the predicted stress-strain,magnetostrictive strain, magnetic induction and magnetization curves agreed well withexperimental results under the different pre-stresses. The proposed model can describe notonly the influences of pre-stress on magnetostrictive strain and magnetization curves, butalso nonlinear magneto-mechanical coupling effect of magnetostrictive materialsystematically, such as the Young’s modulus varying with stress and magnetic field. In theproposed constitutive model, the key material constants are not chosen to obtain a good fitwith the experimental data, but aremeasured directly by experiments, such as the saturationmagnetization, saturation magnetostrictive coefficient, saturation Young’s modulus, linearmagnetic susceptibility and so on. In addition, the forms of the new constitutive relationsare simpler than the existing constitutive models. Therefore, this model could be appliedconveniently in the engineering applications.

Intelligent method to develop constitutive relationship of Ti-6Al-2Zr-1Mo-1V alloy

The isothermal compression tests were carried out in the Thermecmastor-Z thermo-simulator at temperatures of 800, 850, 900, 950, 1000 and 1050 ℃ and the strain rates of 0.01, 0.1, 1 and 10 s-1. The influence of deformation temperature and strain rate on the flow stress of Ti-6Al-2Zr-IMo-IV alloy was studied. Based on the experimental data sets, the high temperature deformation behavior of Ti-6A1-2Zr-IMo-IV alloy was presented using the intelligent method of artificial neural network （ANN）. The results indicate that the predicted flow stress values by ANN model is quite consistent with the experimental results, which implies that the artificial neural network is an effective tool for studying the hot deformation behavior of the present alloy. In addition, the development of graphical user interface is implemented using Visual Basic programming language.

Effects of hot deformation parameters on flow stress and establishment of constitutive relationship system of BT20 titanium alloy

The hot compression experiments were performed to investigate the effects of hot deformation parameters on the flow stress of BT20(Ti-6Al-2Zr-1Mo-1V) titanium alloy. The results show that the flow stress decreases with the increment of deformation temperature and increases with the growth of strain rate. The peak stress moves toward the direction of strain reducing and the strain rate sensitivity increases with the rising deformation temperature. There is obvious deformation heating created during hot deformation under relatively higher strain rate and lower deformation temperature. The improved back propagation(BP) neural network with 3-20-16-1 architecture has been employed to establish the prediction model of flow stress using deformation degree, deformation temperature and strain rate as input variables. The predicted values obtained by BP network agree well with the measured values, the relative error is within 6.5% for the sample data and not bigger than 9% for the non-sample data, which indicates that the ANNs adopted can predict the flow stress of BT20 alloy effectively and can be used as constitutive relationship system applied to FEM simulation of plastic deformation.

Numerical Method for Modeling the Constitutive Relationship of Sand under Different Stress Paths

A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic constitutive relationship of sand was established for three paths： the constant proportion of principle stress path, the conventional triaxial compression （CTC） path, and the p=constant （TC） path. The yield lines of plastic volumetric strain and plastic generalized shear strain were given. Through visualization, the three dimensional surface of the stress-strain relationship in the whole stress field （p, q） obtained under the three paths was plotted. Also, by comparing the stress-strain surfaces and yield locus of the three stress paths, the differences were found to be obvious, which demonstrates that the influence of the stress paths on constitutive law was not neglected. The numerical modeling method overcame the difficulty of finding an analytical expression for plastic potential. The results simulated the experimental data with an accuracy of 90% on average, so the constitutive model established in this paper provides an effective constitutive equation for this kind of engineering, reflecting the effect of practical stress paths that occur in sands.

CONSTITUTIVE RELATIONSHIP OF IN718 ALLOY FOR THERMOVISCOPLASTIC AND MICROSTRUCTURE EVOLUTION COUPLED ANALYSIS

The interaction between thermomechanical parameters and microstructure evolution is so intense that it must be considered during the finite element method （FEM） simulation of the hot plastic working process, for materials that are difficult to deform. Taking the microstructure evolution into account, a novel type of constitutive relationship has been put forward for the IN718 alloy. The microstructure evolution model was first established for the dominant microstructure evolution processes. Then the microstructure evolution models and the method to determine the local flow stress of the corresponding microstructure for current thermomechanical parameters and deformation history were presented. Once the local flow stresses of different structures and their volume contributions were defined, the apparent flow stress of the material could be determined as the weighted sum of the local flow stresses and volume contributions. To validate the proposed method, a thermoviscoplastics and microstructure evolution coupled analysis for a forging process of a critical IN718 disk forging was performed. The predicting results were in close agreement with the experimental data.

Mechanical Properties and Constitutive Relationship of the High-Durable Parallel Strand Bamboo

Engineered bamboo has recently received lots of attention of civil engineers and professional researchers due to its better mechanical performance than that of softwood timber.Parallel strand bamboo is one important part of engineered bamboo for its excellent durable performance compared to the laminated veneer bamboo.The required curing temperature in hot-pressing process is usually higher than 120°C to reduce the content of nutri-tional ingredients and hemy cellulose,and to avoid the decay from the environment and insects.Nonetheless,the appearance of engineered bamboo gets darker with the increase of temperature during the hot-pressing process.In order to minimize the color deepening while maintaining the durability,a high-durable parallel strand bamboo(HPSB)with relative high hot-pressing temperature(140°C)was produced and tested.The present study inves-tigates the mechanical performance through tension,compression,shear and bending tests.The experimental behavior of the specimens was identified,including the failure mode and load-displacement relationship.It was demonstrated that the HPSB material had better mechanical performance parallel to grain,making it as a considerable structural material.The average elastic modulus parallel to grain was 14.1 GPa,and the tensile and compressive strengths were 120.7 MPa and 121.0 MPa,respectively.The tension perpendicular to grain should be avoided in the practical application due to the lower strength and elastic modulus.Two stress-strain relationships of tension and compression parallel to grain,including three-linear and quadratic function models,were proposed and compared with the experimental results.The three-linear model was then applied to the finite element model.The finite element analysis using ANSYS software was conducted to validate the feasibility of the constitutive relationship.The quadratic function model showed better agreement with the experimental results,but the three-linear relationship was also precise enough to analyze the bending tests of HPSB material,whereas being less accurate to describe the elastic-plastic compression behavior.

Constitutive relationship of ionic polymer-metal composite and static response character of its cantilever setup to voltage

As a new ionic polymer-metal composite(IPMC) for artificial muscle,the mechanical performance parameters and the relationship between the deformation and the electrical parameters of the IPMC were studied. With the digital speckle correlation method,the constitutive relationship of the IPMC was confirmed. With non-contact photography measurement,a cantilever setup was designed to confirm the relationship between the deformation of the IPMC film and the applied voltage. The relationship curve of tip displacement of the IPMC cantilever setup vs the voltage was achieved. The results indicate that the IPMC is isotropic,its elastic modulus is 232 MPa and Poisson ratio is 0.163. The curve achieved from the test of the tip displacement of the IPMC cantilever setup shows that the tip displacement reaches the maximum when the stimulated voltage is 5 V. And the tip displacement descends largely when the frequency of the applied voltage is between 30 mHz and 100 mHz.

ARTIFICIAL NEURAL NETWORK MODEL OF CONSTITUTIVE RELATIONSHIP FOR 2A70 ALUMINUM ALLOY

The hat deformation behavior of 2A70 aluminum alloy was investigated by means of isothermal compression tests performed on a Gleeble-1500 thermal simulator over a wide range of temperatures 360-480℃ with strain rates of 0.01-1s^-1 and the largest deformation of 60%, and the true stress of the material was obtained under the above-mentioned conditions. The experimental results shows that 2A70 aluminum alloy is a kind of aluminum alloy with the property of dynamic recovery; its flow stress declines with the increase of temperature, while its flow stress increases with the increase of strain rates. On the basis of experiments, the constitutive relationship of the 2A70 aluminum alloy was constructed using a BP artificial neural network. Comparison of the predicted values with the experimental data shows that the relative error of the trained model is less than ±3% for the sampled data while it is less than ±6% for the nonsampled data. It is evident that the model constructed by BP ANN can accurately predict the flow stress of the 2A70 alloy.

CONSTITUTIVE RELATIONSHIP OF SUPERALLOY IN718

Isothermal constant speed compression tests of superalloy IN718 were conducted using a computer-controlled MTS machine at temperatures from 960 to 1040℃, with initial strain rates from 0.001 s￣(1) to 1.0 s￣(1) and engineering strain from 0.1 to 0. 7.The variations of flow stress with deformation temperature, initial strain rate and engineering strain were analyzed in the paper. It was found that there was an obvious power-law relationship between flow stress and initial strain rate, which showed the behavior of strain rate hardening of superalloy IN718 at elevated temperatures.The relationship between flow stress and temperature could be described by an inverse trigonometric function.And the turning point on the curve may be related to the behavior of δ phase at 1000℃. Meanwhile, it was found that there was a complicated relationship between flow stress and strain,which was indicative of the comprehensive effect of work hardening and dynamic softening on flow stress during hot deformation. From the results of these tests, a constitutive equation of superalloy IN718 was developed.

bStudy on constitutive relationship of coal based on conventional triaxial compression test

Constitutive relationship of coal under triaxial compression must be determined during solving the theoretical calculation and numerical simulation about coal body failure. This paper carried out conventional triaxial compression test on No.3 coal of Baodian Colliery using MTS815.03 servo-controlled rock mechanical test system. The results indicate that the failure process of coal can be divided into 5 stages： densification stage, apparent linear elastic deformation stage, accelerated inelastic deformation stage, fracture and developing stage and plasticity flow stage. Combined with the test results, the constitutive relationship model of coal can be simplified as the four segments of straight line model of elastic-plastic hardening-plastic softening-residual perfectly plastic. Through fitting calculation of test data, the segmented constitutive equation of coal can be obtained.

Johnson-Cook dynamic constitutive relationship for TC16 titanium alloy

The true stress-strain curves of TC16 alloy with a wide range of strain rates were investigated under uniaxial quasi-static tension and uniaxial dynamic compression with the Instron 8032 test machine and the split Hopkinson bar respectively. The results indicate that the true stress increases with increasing strain rate,while decreases with increasing temperature. Under the 105 s-1 high strain rate and temperature higher than 673 K,the true stress would even be less than that under quasi-static condition. A new method incorporating TC16's stress-strain curve developing item was proposed to determine the coefficients in J-C model easily and to avoid the estimation of the adiabatic temperature rising. The Johnson-Cook dynamic constitutive relationship for TC16 was obtained for the first time. Good agreement was obtained between the model prediction and the experimental stress-strain curves for TC16 under both quasi-static and dynamic loadings.

Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations

A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green＇s function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α , the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.

Constitutive analysis of AZ31 magnesium alloy plate

The plastic deformation simulation of AZ31 magnesium alloy at different elevated temperatures （from 473 to 723 K） was performed on Gleeble-1500 thermal mechanical simulator at the strain rates of 0.01, 0.1, 1, 5 and 10 s-t and the maximum deformation degree of 80%. The relationship between the flow stress and deformation temperature as well as strain rate was analyzed. The materials parameters and the apparent activation energy were calculated. The constitutive relationship was established with a Zener-Hollomon （Z） parameter. The results show that the flow stress increases with the increase of strain rate at a constant temperature, but it decreases with the increase of deformation temperature at a constant strain rate. The apparent activation energy is estimated to be 129-153 kJ/mol, which is close to that for self-diffusion of magnesium. The established constitutive relationship can reflect the change of flow stress during hot deformation.

Relationship Research between the Chinese Medicine Constitution and Sub-Health

With further development of the bio-psycho-social medical model, people began to re-examine the knowledge of disease and health. The concept of sub-health has also been proposed in western medicine. Because of the lack of a specific standard, it is difficult to make clinical diagnosis and treatments for sub-health. Chinese medicine constitution theory has been widely accepted in China, and has a set of executable standards. This paper puts forward a new research method that connects the sub-health in western medicine and Chinese medicine constitution theory together. The potential relationships and influences between Chinese medicine constitution theory and sub-health were analyzed and key content and research progress were discussed. The research method in this paper will provide new ideas for sub-health research.

TEST AND STUDY ON THE CONSTITUTIV ERELATIONSHIP OF DESERT SAND UNDER MOVING VEHICLE

The mechanical properties of the sand of Takelamagan desert in Xinjiang under moving vehicle are studied by soil dynamic triaxial test apparatus. The nonlinear elastic constitutive model of the sand under moving vehicle is established first. These results lay the foundations for studying the interaction between vehicle running gear and the sand of Takelamagan desert in Xinjiang. and developing sand vehicle.

早龄期机制砂混凝土抗压强度与弹性模量时效关系及本构模型试验研究

为了研究早龄期机制砂混凝土在单轴受压状态下抗压强度与弹性模量的时效关系和本构模型,通过对8组不同龄期的C60机制砂混凝土试件进行立方体抗压强度试验、静力受压弹性模量试验和单轴受压应力-应变曲线试验,并参考多种已有研究模型,建立了早龄期机制砂混凝土在单轴受压状态下的抗压强度与弹性模量时效关系模型和分段式应力-应变本构模型。结果表明,采用的抗压强度与弹性模量时效关系模型和分段式应力-应变本构模型与试验数据吻合效果理想,能够较好地描述早龄期C60机制砂混凝土在单轴受压状态下的力学性能。

基于深度学习的塑性变形理论建模研究进展

传统塑性理论模型由于引入了适当的假设和简化,面对复杂变形机制和复杂变形条件时具有局限性。基于深度学习的理论建模作为数据驱动的建模新范式,具有精度高、通用性强的特点,是塑性理论建模的重要方向。介绍了深度学习的建模方法,如传统神经网络模型、物理启发式神经网络模型和神经算子网络,分析了各个模型的特点。总结了近年来基于深度学习的塑性理论建模方法在本构关系、损伤断裂模型、微观组织模型和多尺度模型等方面应用的研究进展,并分析了提高模型精度、泛化能力和可解释性的方法。最后提出了基于深度学习的塑性理论建模方法面临的挑战和未来发展方向。

两种新型炸药的准静态力学性能

为推动炸药在侵爆战斗部中的应用,采用万能材料试验机对HMX基压装高聚物粘结炸药(polymer bonded explosive,PBX)和DNAN基熔铸炸药的准静态力学性能进行研究。获得2种炸药在2.0×10-5 s-1~1.0×10-3 s-1应变率范围内的应力应变试验数据。结果表明:2种炸药的力学性能均具有明显的应变率效应,但前者失效应变约为后者的6倍,呈现出较大区别。基于唯象方法,建立描述2种炸药1维准静态压缩力学行为的幂指数硬化本构模型,并拟合得到本构模型参数。通过与试验结果对比表明,模型计算结果与试验结果误差小于3%,吻合较好。该研究结果可为描述2种炸药的力学行为提供参考。

基于截面配筋率的钢筋混凝土统一本构关系研究

为避免数值化分析中直接处理钢筋与混凝土之间的复杂关系,推导出钢筋混凝土构件轴心受压统一理论公式,做了不同配筋率与不同混凝土强度等级下的钢混棱柱体轴心受压试验,利用试验量测的荷载位移数据,结合Matlab曲线拟合工具的线性回归与拟合功能,建立了一种基于截面配筋率的能够描述钢筋混凝土材料力学性能的统一本构关系。对试验梁进行数值化分析表明,所建立的数值化模型应力应变特征与试验结果吻合较好,证明了该模型在钢筋混凝土实际运用过程中的可行性与适用性。