延性金属层裂模型比较

在平面一维弹塑性流动有限差分计算程序中加入4种延性金属层裂模型,对平板撞击层裂实验进行数值模拟。结果表明：简单最大拉伸应力模型和简单损伤累积模型能定性反映层裂的物理现象,由于忽略损伤对本构的影响,计算结果和实验有偏差,但模型要求参数较少,对于一些精度要求不是很高的工程问题,可以采用;从材料损伤断裂物理本质出发,采用微损伤统计方法得到的NAG模型和封加波损伤度函数模型,能很好地再现实测的自由面速度剖面,数值计算结果与实验吻合很好。     

Evaluation of constitutive models for voided solids

In this work four constitutive models for voided solids are reviewed and evaluated; namely, Gurson's, Green's, Liao's et al. and Shima-Oyane's models. Two modified forms of Gurson's model and a non-quadratic form of Green's model are developed for normal anisotropy prevailing in the analysis of sheet metal forming. A simplified version — more amenable to analytical derivations — of Gurson's yield function and its modified forms are proposed for plane stress conditions. The associated flow rules are presented and the laws governing void growth with accumulated strain are derived using the above models. Their predictions are compared with experiments. As an application, the flow curves of voided materials of known initial porosities are predicted and compared with experiments.     

Comparison of different kinetic models for the heat transfer problem

The steady-state heat transfer problem between two parallel plates is investigated using kinetic models of the Boltzmann equation: BGK, S-model and ES-model. The discrete velocity method is used to determine the values of physical parameters: density, bulk velocity, temperature and heat flux. The obtained results are compared with the analytical expressions and some experimental data.     

Non linear constitutive models for lattice materials

We use a computational homogenisation approach to derive a non linear constitutive model for lattice materials. A representative volume element (RVE) of the lattice is modelled by means of discrete structural elements, and macroscopic stress–strain relationships are numerically evaluated after applying appropriate periodic boundary conditions to the RVE. The influence of the choice of the RVE on the predictions of the model is discussed. The model has been used for the analysis of the hexagonal and the triangulated lattices subjected to large strains. The fidelity of the model has been demonstrated by analysing a plate with a central hole under prescribed in plane compressive and tensile loads, and then comparing the results from the discrete and the homogenised models.     

Anisotropy of direction-based constitutive models for rubber-like materials

A study of direction-based models for the representation of isotropic and anisotropic hyperelastic behaviour of rubber-like materials is proposed. The interest in such models is sustained by their ability to account for the Mullins effect induced anisotropy. For such a purpose, the directional models should be initially isotropic and representative of the hyperelastic behaviour of rubber-like materials. Various models were defined according to different sets of directions. Models were tested in terms of their initial anisotropy and their ability to reproduce the classic full-network hyperelastic behaviour. Various models were proved to perform very well.     

Anatomy of coupled constitutive models for ratcheting simulation

This paper critically evaluates the performance of five constitutive models in predicting ratcheting responses of carbon steel for a broad set of uniaxial and biaxial loading histories. The models proposed by Prager, Armstrong and Frederick, Chaboche, Ohno-Wang and Guionnet are examined. Reasons for success and failure in simulating ratcheting by these models are elaborated. The bilinear Prager and the nonlinear Armstrong-Frederick models are found to be inadequate in simulating ratcheting responses. The Chaboche and Ohno-Wang models perform quite well in predicting uniaxial ratcheting responses; however, they consistently overpredict the biaxial ratcheting responses. The Guionnet model simulates one set of biaxial ratcheting responses very well, but fails to simulate uniaxial and other biaxial ratcheting responses. Similar to many earlier studies, this study also indicates a strong influence of the kinematic hardening rule or backstress direction on multiaxial ratcheting simulation. Incorporation of parameters dependent on multiaxial ratcheting responses, while dormant for uniaxial responses, into Chaboche-type kinematic hardening rules may be conducive to improve their multiaxial ratcheting simulations. The uncoupling of the kinematic hardening rule from the plastic modulus calculation is another potentially viable alternative. The best option to achieve a robust model for ratcheting simulations seems to be the incorporation of yield surface shape change (formative hardening) in the cyclic plasticity model.     

Identification of quasi-static displacement for constitutive models of viscoelasticity

I.IntroductionQuasi-staticdisplacementbasedtechniqueofinverseanalysisfortheconstitutlveparametersisbeingwidlyusedintheundergroundengineeringandsomeotherfields.Anumberofprogresshasbeenachievedinthefieldofidentificationfortheviscoelasticconstitutiveparallleters.XueandYang(1986)l'].Liu(1986)l=lemployedintegraltransformationtechniquetoidentifyviscoelasticconstitutiveparameters;a3-DinverseanalysisfortheviscoelasticconstitutiveparameterswasconductedbyYang(199I)l'];YallgandWu(1996)l'Jproposedagen…     

Homogenization-based constitutive models for magnetorheological elastomers at finite strain

This paper proposes a new homogenization framework for magnetoelastic composites accounting for the effect of magnetic dipole interactions, as well as finite strains. In addition, it provides an application for magnetorheological elastomers via a “partial decoupling” approximation splitting the magnetoelastic energy into a purely mechanical component, together with a magnetostatic component evaluated in the deformed configuration of the composite, as estimated by means of the purely mechanical solution of the problem. It is argued that the resulting constitutive model for the material, which can account for the initial volume fraction, average shape, orientation and distribution of the magnetically anisotropic, non-spherical particles, should be quite accurate at least for perfectly aligned magnetic and mechanical loadings. The theory predicts the existence of certain “extra” stresses—arising in the composite beyond the purely mechanical and magnetic (Maxwell) stresses—which can be directly linked to deformation-induced changes in the microstructure. For the special case of isotropic distributions of magnetically isotropic, spherical particles, the extra stresses are due to changes in the particle two-point distribution function with the deformation, and are of order volume fraction squared, while the corresponding extra stresses for the case of aligned, ellipsoidal particles can be of order volume fraction, when changes are induced by the deformation in the orientation of the particles. The theory is capable of handling the strongly nonlinear effects associated with finite strains and magnetic saturation of the particles at sufficiently high deformations and magnetic fields, respectively.     

Solution existence conditions for elastoplastic constitutive models of granular materials

In this paper, the conditions of solution existence for stress rates under given strain rates are investigated. The focus of the solution existence investigation is on the non-associated flow rule and elastic stress–strain relationship. Granular materials characterized with strong non-associated plastic flows are used as a particular example for analysis. Various flow rules for granular materials are analyzed, including Rowe’s, Roscoe’s flow rules and their modified versions. In the elastic stress–strain relationships of materials, the effects of Poisson’s ratio on solution existence are investigated. Both isotropic and anisotropic elasticity are considered. Given a granular material and its states, it is found that there exists a critical Poisson’s ratio for a particular non-associated flow rule. When the Poisson’s ratio of a material is above this critical Poisson’s ratio, its constitutive model is susceptible to solution non-existence. It is suggested that special attentions should be paid to the selection of material Poisson’s ratio and non-associated flow rule to ensure the existence of elastoplastic solutions.     

New flow rules in elasto-viscoplastic constitutive models for spheroidal graphite cast-iron

A specific flow rules and the corresponding constitutive elasto-viscoplastic model combined with new experimental strategy are introduced in order to represent a spheroidal graphite cast-iron behaviour on a wide range of strain, strain rate and temperature. A “full model” is first proposed to correctly reproduce the alloy behaviour even for very small strain levels. A “light model” with a bit poorer experimental agreement but a simpler formulation is also proposed. These macroscopic models, whose equations are based on physical phenomena observed at the dislocation scale, are able to cope with the various load conditions tested – progressive straining and cyclic hardening tests – and to correctly describe anisothermal evolution. The accuracy of these two models and the experimental databases to which they are linked is estimated on different types of experimental tests and compared with the accuracy of more standard Chaboche-type constitutive models. Each test leads to the superiority of the “full model”, particularly for slow strain rates regimes. After developing a material user subroutine, FEM simulations are performed on Abaqus for a car engine exhaust manifold and confirm the good results obtained from the experimental basis. We obtain more accurate results than those given by more traditional laws. A very good correlation is observed between the simulations and the engine bench tests.     

进化算法与确定性算法在优化控制问题中的收敛性对比

对比了进化算法(基因算法)与确定性算法(共轭梯度法)在优化控制问题中的优化效率．两种方法都与分散武优化策略-Nash对策进行了结合,并成功地应用于优化控制问题。计算模型采用绕NACA0012翼型的位流流场．区域分裂技术的引用使得全局流场被分裂为多个带有重叠区的子流场,使用4种不同的方法进行当地流场解的耦合,这些算法可以通过当地的流场解求得全局流场解。数值计算结果的对比表明．进化算法可以得到与共轭梯度法相同的计算结果．并且进化算法的不依赖梯度信息的特性使其在复杂问题及非线性问题中具有广泛的应用前景。     

On a class of constitutive models for highly deforming compressible materials

Summary The physical admissibility of a constitutive model for highly deforming hyperelastic compressible materials, introduced in [1], is examined in the light of the classical Backer-Ericksen, ordered forces and strengthened tension-extension inequalities. A generalization of this material model is also given, and the conditions for its physical adminissibility are discussed.

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Über eine Klasse von konstitutiven Modellen für hoch formveränderliche, kompressible Materialien

Übersicht Die physikalische Zulässigkeit eines konstitutiven Modells für hoch formveränderliche, hyperelastische, kompressible Materialien, die in [1] dargestellt sind, wird anhand der Backer-Ericksen-Ungleichungen, der Ungleichungen der Folge der Spannungsgrößenordnungen und anhand der Ungleichungen des positiven Tangentenmoduls geprüft. Es wird auch eine Verallgemeinerung dieses Materialmodells dargestellt. Die Bedingungen für seine physikalische Zulässigkeit werden erörtert.

     

方向余弦矩阵中四元数提取算法比较

在捷联惯性导航系统姿态算法中,用四元数取代方向余弦阵来描述姿态变化具有计算量小、精度高、不存在奇异问题的优点。在实际工程应用中常常需要从方向余弦矩阵中提取对应的旋转四元数,但是经典的提取算法可能会出现平方根计算时根号内出现负值的情况,从而使四元数的提取失败。针对这一问题,总结了现有文献中提出的两种新算法,并从计算量和计算精度的角度对这几种算法进行了分析对比,通过比较发现基于特征值和特征向量的提取算法实现了计算量和精度的最佳组合,为工程应用提供了有价值的参考。     

Comparison of linear viscoelastic constitutive equations for non-uniform polymer melts

Linear-viscoelastic properties of polydisperse and randomly-branched polymer melts were fit with several proposed relaxation functions by non-linear regression. Three polymer systems were investigated, including 1) crosslinked polyethylenes, 2) polydisperse linear poly(dimethylsiloxane)s, and 3) Marlex polyethylenes, which are polydisperse and probably contain long-chain branching. Four relaxation functions were evaluated, including the Rouse, reptation, stretched-exponential, and stretched-exponential-power-law (SEPL) relaxation functions. The SEPL best described each series of polymers, and therefore may be a general relaxation function for non-uniform polymer melts. The flow activation energy for crosslinked polyethylene may be coupled to a breadth-of-relaxation index, indicating that a coupling between a characteristic short relaxation time and longest relaxation time, as suggested by Ngai and Plazek (J. Polym. Sci. Polym. Phys. Ed. 1985, 23:2159–2180), may hold for some non-uniform polymers.     

Investigation on gradient-dependent nonlocal constitutive models for elasto-plasticity coupled with damage

IntroductionIntheframeworkofconventionalplasticity ,materialinstabilityisoneoftheprincipalfactorsthatresultinginthestrainlocalizationphenomenon .Byusingtheterminology‘homogenized’ ,itisreferredtothefactthatinitialflawsandboundaryconditionsnecessarilyinduceanon_homogeneousstressstateinaspecimenduringtesting .Inparticularintheprocessofprogressivefailure ,theflawsandlocalstressconcentrationwillcausestronglyinhomogeneousdeformationofthespecimen[1,2 ].Asthedeformation_inducedfracture/damagephenom…     

Fracture energy based constitutive models for tensile fracture of metal powder compacts

Diametral compression test or the Brazilian disc test is commonly used to characterise the tensile strength of brittle materials. A general fracture model based on energy assumptions is proposed for simulation of the discrete and localised tensile fracturing process in metal powder. The characteristics of the tensile fracture development of the central crack in diametral tested specimen is numerically studied. The softening rate of the model is obtained from the corresponding rate of the dissipated energy. Finite element simulations of the diametral compression test are performed with the proposed tensile fracture model used in conjunction with a Cap model for the deformation of the powder material. The results agree reasonably with experiments.     

Comparison of SIMPLE- and PISO-type algorithms for transient flows

Various pressure-based schemes are proposed for transient flows based on well-established SIMPLE and PISO algorithms. The schemes are applied to the solution of unsteady laminar flow around a square cylinder and steady laminar flow over a backward-facing step. The implicit treatment and the performance of the various schemes are evaluated by using benchmark solutions with a small time step. Three different second-order-accurate time derivatives based on different time levels are presented. The different time derivatives are applied to the various schemes under consideration. Overall the PISO scheme was found to predict accurate results and was robust. However, for small time step values, alternative schemes can predict accurate results for approximately half the computational cost. The choice of time derivative proved to be very significant in terms of the accuracy and robustness of a scheme. Significantly, the one-sided forward differencing scheme was the most successful used in conjunction with a strongly implicit-based algorithm. However, a greater degree of accuracy was achieved using the standard PISO algorithm with the Crank–Nicolson time derivative. Recommendations for future work are discussed. © 1998 John Wiley & Sons, Ltd.     

循环硬化材料本构模型的隐式应力积分和有限元实现

针对新发展的、能够描述循环硬化行为应变幅值依赖性的粘塑性本构模型,讨论了它的数值实现方法。首先,为了能够对材料的循环棘轮行为（Ratcheting）和循环应力松弛现象进行描述,对已有的本构模型进行了改进;然后,在改进模型的基础上,建立了一个新的、全隐式应力积分算法,进而推导了相应的一致切线刚度（Consistent Tangent Modulus）矩阵的表达式;最后,通过ABAQUS用户材料子程序UMAT将上述本构模型进行了有限元实现,并通过一些算例对一些构件的循环变形行为进行了有限元数值模拟,讨论了该类本构模型有限元实现的必要性和合理性。     

Comparison of different models for non-equilibrium CO2 flows in a shock layer near a blunt body

The paper presents results of a numerical simulation of a supersonic two-dimensional (2D) viscous flow containing CO₂ molecules near a spacecraft entering the Mars atmosphere. The gas–dynamic equations in the shock layer are coupled to the equations of non-equilibrium vibrational and chemical kinetics in the five-component mixture CO₂/CO/O₂/C/O. Transport and relaxation processes in the flow are studied on the basis of the rigorous kinetic theory methods; the developed transport algorithms are incorporated in the numerical scheme. The influence of the vibrational excitation of CO₂ and chemical reactions on the gas flow parameters and heat transfer is analyzed. The obtained results are compared with those found using two simplified models based on the two-temperature and one-temperature vibrational distributions in CO₂. The accuracy of the simplified models and the limits of their validity within the shock layer are evaluated. The effect of bulk viscosity in a flow near a re-entry body is discussed. The role of different diffusion processes, chemical reactions, and surface catalytic properties in a flow of the considered mixture in the shock layer is estimated.