Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature

In gas–solid flat-base spout bed with a jet, the flow of particles must go through an intermediate regime where both kinetic/collisional and frictional contributions play a role. In this paper, the statistical framework is proposed to define the generalized granular temperature which sums up the configurational temperature and translational granular temperature. The configurational temperature, translational and rotational granular temperatures of particles are simulated by means of CFD-DEM (discrete element method) in a 3D flat-base spout bed with a jet. The configurational temperatures of particles are calculated from instantaneous overlaps of particles. The translational and rotational granular temperatures of particles are calculated from instantaneous translational and angular velocities of particles. Roughly, the simulated translational and rotational granular temperatures increase, reach maximum, and then decrease with the increase of solids volume fractions. However, the configurational temperature increases with the increase of solids volume fractions. At high solid volume fraction, the predicted configurational temperatures are larger than the translational and rotational granular temperatures, indicating that the rate of energy dissipation do contributes by contact deformation of elastic particles. The generalized granular temperature is proposed to show the relation between the variance of the fluctuation velocity of deformation and the variance of the translational fluctuation velocity of particles. The constitutive relations of particle pressure, viscosity, granular conductivity of fluctuating energy and energy dissipation in rapid-intermediate-dense granular flows are correlated to the generalized granular temperature. The variations of particle pressure, shear viscosity, energy dissipation and granular conductivity are analyzed on the basis of generalized granular temperature in a flat-base spout bed with a jet. The axial velocities of particles predicted by a gas–solid two-fluid model of rapid-intermediate-dense granular flows agree with experimental results in a spout bed.     

基于对偶法捷联惯导圆锥与划桨算法一般结果

首先,利用多项式拟合角速度和比力,得出任意子样数的陀螺角增量和加速度计速度增量的一般形式,进而经过一系列的数学形式的变换推导出了任意子样数圆锥效应补偿算法的通用形式;然后,介绍了对偶性原理.利用圆锥效应项与划桨效应项之间的对偶性,通过一个简单的数学方程便可得到任意子样数划桨效应补偿算法的一般形式.这两种补偿算法中的系数均可用计算机简单的计算获得,无需人工的繁琐推导.而且上述方法分析推导过程简洁明了.最后,根据对偶原理给出了划桨效应补偿算法三子样和四子样的精度仿真结果.     

On the assumption of Saint-Venant's problem

In this paper we obtain uniquely the solution of Saint- Venant’s problem under theassumption of ∂^m/∂z^mσ_z=0(m≥2) for noncircular prismatic bars.     

Predictions of plastic stress-strain relations of polycrystals based on the Lin model

A uniaxial stress-strain curve is calculated for a polycrystal consisting of numerous nonhardening FCC crystals based on the Lin model. The coefficient matrix relating the deviation of plastic strain to the one of stress in the Lin model turned out to be singular. The simplex method is used to determine slips of all slip systems in constituent crystals. The calculated curves lie between the KBW model and the Hill model.     

液压减振器随机热力学模型与油温变化研究

为了获得具有更多信息和更加接近工程实际的液压减振器油温热力学模型,将随机不确定性理论引入到液压减振器油温传统热力学模型中进行研究。将液压油密度、导热系数、比热容和运动粘度作为随机变量,运用求解函数数字特征的代数综合法建立减振器随机热力学模型,进而获得油液传热过程规律。将油温随机热力学模型研究结果和传统模型的计算结果与实验结果进行比较,证明随机不确定性理论的引入可行且随机热力学模型比传统模型更加优越。     

基于梁平截面假设的复杂细长结构动力模型简化方法

针对纵向尺度显著大于横向的复杂细长结构,提出了一个基于梁平截面假设的模型简化方法,建立了具有物理意义的基向量。同时考虑这类结构截面变形的翘曲模式,增加了翘曲基向量,得到精度较高的简化动力模型。这样的简化模型可以用于原结构在不同边界条件的动力分析。结构频率计算的两个具体算例表明了简化方法的有效性。     

An experimental approach to low-cycle fatigue damage based on thermodynamic entropy

This paper presents an experimental approach to fatigue damage in metals based on thermodynamic theory of irreversible process. Fatigue damage is an irreversible progression of cyclic plastic strain energy that reaches its critical value at the onset of fracture. In this work, irreversible cyclic plastic energy in terms of entropy generation is utilized to experimentally determine the degradation of different specimens subjected to low cyclic bending, tension-compression, and torsional fatigue. Experimental results show that the cyclic energy dissipation in the form of thermodynamic entropy can be effectively utilized to determine the fatigue damage evolution. An experimental relation between entropy generation and damage variable is developed.     

A thermodynamic formulation of finite-deformation elastoplasticity with hardening based on the concept of material isomorphism

This paper presents a thermodynamic formulation of a model for finite deformation of materials exhibiting elastoplastic material behaviour with non-linear isotropic and kinematic hardening. Central to this formulation is the notion that the form of the elastic constitutive relation be unaffected by the plastic deformation or transformation in the material, as commonly assumed in particular in the context of crystal plasticity. When generalized to the phenomenological context, this implies that the internal variable representing plastic deformation is an elastic material isomorphism. Among other things, this requirement on the plastic deformation leads directly to the standard elastoplastic multiplicative decomposition of the deformation gradient. In addition, a dependence of the plastic part of the free energy on the plastic deformation itself yields a thermodynamic form for the centre of the elastic range of the material, i.e. the back stress. Finally, we show how this approach can be applied to formulate thermodynamic forms for linear, and non-linear Armstrong-Frederick, kinematic hardening models.     

Compatibility equations in systems based on generalized Cauchy kinematic relations

We obtain integrability conditions for systems of linear partial differential equations based on generalized Cauchy kinematic relations. The generalization pertains to both the dimension of the Euclidean space and the rank of the object corresponding to displacement vector in the classical case. The integrability conditions, or the compatibility equations, are written out as the conditions of vanishing of all components of either the generalized incompatibility tensor introduced here or the generalized Riemann-Christoffel tensor obtained from the incompatibility tensor by convolutions with the Levi-Civita symbols. The ranks and number of independent components of these tensors are found.     

Constitutive relations for single crystal based on two surface description

A two surface model is used to describe single crystal slip. The evolution of the yield surface and outer yield surface are proposed to be directly related to the development of dislocation structures. The anisotropy of inner yield surface is attributed to both the long range and short range dislocation interactions, whereas anisotropy of the outer yield surface is assumed to depend solely on the short range interactions. The outer yield surface is not isotropic as assumed in most two surface models of other researchers. This surface is able to evolve even when the stress state is within the outer yield surface.     

Basis free relations for the conjugate stresses of the strains based on the right stretch tensor

In this paper, general relations between two different stress tensors T^f and T^g, respectively conjugate to strain measure tensors f(U) and g(U) are found. The strain class f(U) is based on the right stretch tensor U which includes the Seth–Hill strain tensors. The method is based on the definition of energy conjugacy and Hill’s principal axis method. The relations are derived for the cases of distinct as well as coalescent principal stretches. As a special case, conjugate stresses of the Seth–Hill strain measures are then more investigated in their general form. The relations are first obtained in the principal axes of the tensor U. Then they are used to obtain basis free tensorial equations between different conjugate stresses. These basis free equations between two conjugate stresses are obtained through the comparison of the relations between their components in the principal axes, with a possible tensor expansion relation between the stresses with unknown coefficients, the unknown coefficients to be obtained. In this regard, some relations are also obtained for T⁽⁰⁾ which is the stress conjugate to the logarithmic strain tensor lnU.     

ANALYTICAL RELATIONS BETWEEN EIGENVALUES OF CIRCULAR PLATE BASED ON VARIOUS PLATE THEORIES

Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT), the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory (RPT), analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates.     

Elasticity reconstruction: Beyond the assumption of local homogeneity

Elasticity imaging is a novel domain which is currently gaining significant interest in the medical field. Most inversion techniques are based on the homogeneity assumption, i.e. the local spatial derivatives of the complex-shear modulus are ignored. This analysis presents an analytic approach in order to overcome this limitation, i.e. first order spatial derivatives of the real-part of the complex-shear modulus are taken into account. Resulting distributions in a gauged breast lesion phantom agree very well with the theoretical expectations. An in-vivo example of a cholangiocarcinoma demonstrates that the new approach provides maps of the viscoelastic properties which agree much better with expectations from anatomy.     

Measurement of stress based upon universal relations in acoustoelasticity

A new approach to ultrasonic measurement of stress was proposed recently by Man and Lu. That approach is based on universal relations that result from material symmetry in an acoustoelastic theory applicable to plastically deformed bodies for which superimposed ultrasonic waves can be taken as elastic. When applicable, the Man-Lu approach circumvents the two main difficulties of the acoustic-birefringence method, namely those of unknown initial texture and plastic deformation. An experiment was performed to verify a new universal relation derived by Man and Lu in their earlier work. Plastic strain was developed during the test. The results were in basic accord with the prediction of the theory.     

Limitations of the Coulomb friction assumption in fretting fatigue analysis

A significant factor in the fretting process, both experimentally and analytically, is the Coulomb friction. Most analyses of fretting fatigue consider a constant coefficient of friction (CCOF) in modeling a contact geometry. This work reevaluates the constant assumption of the Coulomb friction coefficient, and develops a Coulomb friction model based on a non-classical model allowing the coefficient of friction (COF) to be a function of local contact pressure and local slip magnitude. Here, the Coulomb COF varies locally along the contact surface. Results of computations using this model are applied to fretting fatigue experiments utilizing several specific contact geometries, which have nominally identical fatigue lives experimentally. The analysis shows that certain combinations of parameters in the variable coefficient of friction model can produce nominally identical stress states. Such results cannot be obtained using a CCOF.     

A note on the Cauchy relations

The Cauchy relations originated in the context of the molecular theory of elasticity. Assuming them implies a reduction of the independent elastic constants which characterize the constitutive tensor in the linear anisotropic case. This paper brings to light a property of the elastic tensor through its decomposition into a symmetric part and into a skew part in the 2nd and 3rd indices. The skew part, which vanishes if and only if the Cauchy relations hold, is connected with a self-equilibrated stress field. The isotropic case is examined as a particular example.

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Sommario Le relazioni di Cauchy ebbero origine nell'ambito della teoria molecolare dell'elasticità; la loro assunzione implica una riduzione delle costanti elastiche indipendenti che caratterizzano il tensore costitutivo nel caso anisotropo lineare. In questa breve nota si mette in luce una proprietà del tensore elastico attraverso la sua decomposizione in una parte simmetrica ed in una antisimmetrica nel 2° e 3° indice: la parte antisimmetrica, che risulta nulla se e solo se valgono le relazioni di Cauchy, è associata ad un campo di tensioni autoequilibrate. Si analizza, come caso particolare, il caso isotropo.

     

Three-dimensional constitutive relations for granular materials based on the dilatant double shearing mechanism and the concept of fabric

An extension of a three-dimensional model proposed by Anand and Gu (2000) for amorphous granular materials to include the effects of initial and induced anisotropy is presented in this paper. The proposed model can also be considered as a three-dimensional generalization of a model recently developed by Zhu et al. (2005) for the planar deformation of granular materials. The main ingredients of the model include the dilatant double shearing mechanism (Spencer, 1964, Mehrabadi and Cowin, 1978), the concept of fabric (Oda, 1972), and an extension of the Mohr–Coulomb yield criterion (Shield, 1955, Spencer, 1982) to three dimensions.The constitutive equations are implemented in the finite element program ABAQUS/Explicit (ABAQUS, 2001) by developing a user-material subroutine to conduct numerical triaxial compression tests for samples of granular materials with different initial anisotropy. The numerical results agree with the observed behavior and show that the extended constitutive model is capable of capturing the strength anisotropy of granular materials. Employing the anisotropic model developed here, we have also repeated the numerical simulation of the stress state in a static conical sand pile conducted earlier by Anand and Gu (2000). We find that fabric has little or no influence on the vertical stress distribution except at the base of the sand pile where the peak value of this stress is slightly higher than that predicted by the model of Anand and Gu (2000) which does not include the effects of fabric. We also find that the direction of the principal compressive stress changes from vertical at points away from the center of the pile to almost horizontal at points close to the center of the pile. This result provides a possible explanation for the observed dip in the vertical stress distribution in sand piles.