On mechanics of saturated granular materials

A continuum theory of saturated granular materials is formulated. The basic balance laws for the solid phase as well as for the fluid phase are presented. The constitutive equations are derived and the basic equations of motion of the solid and fluid continua are obtained. Several cases of interest, such as incompressible granules saturated with liquids are discussed. It is shown that the theory contains, as its special cases, the Mohr-Coulomb criterion for a granular material as well as Darcy's law of flow through porous media.     

Elasto-viscoplastic-viscous theories of granular and porous media

The mechanics of granular and porous media is considered in the light of the modern theories of structured continuum. The basic laws of motion are presented and several constitutive relations are derived. The special case of elastic porous media is considered in detail and the basic field equations are derived and the possible application of the results to soil dynamics is pointed out. The theory of the flow of granular media is also considered and basic equations of motion are derived where the results of Goodman and Cowin are recovered. The viscoplastic flow of porous media is studied and the possible application to soil mechanics is also discussed.     

Volume-weighted mixture theory for granular materials

In the present work we treat granular materials as mixtures composed of a solid and a surrounding void continuum, proposing then a continuum thermodynamic theory for it. In contrast to the common mass-weighted balance equations of mass, momentum, energy and entropy for mixtures, the volume-weighted balance equations and the associated jump conditions of the corresponding physical quantities are derived in terms of volume-weighted field quantities here. The evolution equations of volume fractions, volume-weighted velocity, energy, and entropy are presented and explained in detail. By virtue of the second law of thermodynamics, three dissipative mechanisms are considered which are specialized for a simple set of linear constitutive equations. The derived theory is applied to the analysis of reversible and irreversible compaction of cohesionless granular particles when a vertical oscillation is exerted on the system. In this analysis, a hypothesis for the existence of a characteristic depth within the granular material in its closely compacted state is proposed to model the reversible compaction.     

Flow through isotropic granular porous media

A generalization of the Navier-Stokes equation is developed to include laminar flow through a rigid isotropic granular porous medium of spatially varying permeability. The model is based on a theory of interspersed continua and the mean geometrical properties of an idealized granular porous microstructure. The derived momentum transport equations are applicable to granular porous media over the entire porosity range from zero through unity. No restriction with respect to flow velocity is imposed, except for the assumption of laminar flow within the pores. The results provide useful and versatile equations and substantiate many of the empirical equations currently in use. One of the major advantages of the generalized momentum equation is its adaptability to numerical simulation.     

Short-Term Microdamage of a Granular Material under Physically Nonlinear Deformation

The structural theory of short-term damage is generalized to the case where the undamaged components of a granular composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for a granular composite with porous components whose skeletons deform nonlinearly. Microvolumes of the composite components meet the Huber–Mises failure criterion. Damaged microvolume balance equations are derived for the physically nonlinear materials of the components. Together with the equations relating macrostresses and macrostrains of a granular composite with porous nonlinear components, they constitute a closed-form system. The system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the microdamage–macrostrain relationship and plotting deformation diagrams are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardened matrix and do not in the inclusions, which are linearly elastic     

Prediction on dispersion in elastoplastic unsaturated granular media

This study focuses on the propagation of the plane wave in the elastoplastic unsaturated granular media, and the wave equations and dispersion equations are derived for the media under the framework of Cosserat theory. Due to symmetry, five different wave modes are considered and predicted for the elastoplastic unsaturated granular media based on the Cosserat theory, including two longitudinal waves, one rotational longitudinal wave and two coupled transverse–rotational transverse waves. The correspondence is discussed between these Cosserat wave modes and the classical wave modes. Based on the dispersion equations, the dispersion behaviors are obtained for the five Cosserat wave modes. The results indicated that the different stress-strain stages,including the elastic, hardening and softening stages, have obvious effect on the dispersion behaviors of the Cosserat wave modes.     

On the flow of a fluid–particle mixture between two rotating cylinders, using the theory of interacting continua

Mixture theory is used to develop a model for a flowing mixture of solid particulates and a fluid. Equations describing the flow of a two-component mixture consisting of a Newtonian fluid and a granular solid are derived. These relatively general equations are then reduced to a system of coupled ordinary differential equations describing Couette flow between concentric rotating cylinders. The resulting boundary value problem is solved numerically and representative results are presented.     

A kinetic model for rapid flows of granular materials

A kinetic model for rapid flows of granular material is considered. An evolution equation for the first order distribution function is developed which includes the effects of intergranular friction force in an average sense. The collision operator is approximated by the BGK relaxation model. The fundamental equations of motion including an equation for dynamics of the fluctuation energy are derived and discussed. The gravity and the plane Couette flows of granular materials are treated as examples of the applications of the present theory.     

On the Formation of Discontinuities of Wave Fronts in a Saturated Granular Body

The paper deals with propagation of plane wave fronts in a solid with a non-linear relation between stress and deformation. The objective is to calculate the distance that a wave front covers before it loses continuity. The formulae derived for a general quasi-linear system of two equations are applied to the propagation of plane compression waves in dry and partially saturated granular bodies. In the case of a saturated body with gas bubbles, the influence of gas and capillary pressure on the stiffness of the body is taken into account. Numerical calculations relevant to soil mechanics are presented. For the numerical calculations a constitutive equation of the hypoplasticity theory for granular materials has been used. Received November 1, 1997     

A Variational Principle for the Revised Goodman–Cowin Theory with Internal Length

In the present study a variational principle is proposed for the revised Goodman–Cowin theory with internal length for cohesionless granular materials (Fang et al. in Continuum Mech Thermodyn in press). The balance equations of the internal variables employed in the theory in equilibrium states, the equilibrium expressions of the constitutive variables and the corresponding natural boundary conditions are derived by use of the proposed variational principle for both cases of compressible and incompressible grains. It is demonstrated that the derived results coincide with those obtained by use of the thermodynamic analysis. The current work serves as a supplementary variational verification of the constitutive theory proposed in Fang et al. (in Continuum Mech Thermodyn in press).     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

IntroductionThispaperisadirectcontinuationofRef.[1 ] .InitthecoupledconservationlawofenergypresentedinRef.[2 ]wasextendedandtherathercompletesystemsofbasicbalancelawsandequationsformicropolarcontinuumtheoryhavebeenconstitutedbycombiningtherenewedresultsandthetraditionalconservationlawsofmassandmicroinertiaandtheentropyinequality .Thepurposeofthispaperistorestablishthesystemsofbasicbalancelawsandequationsformicromorphiccontinuumtheoryandcouplestresstheoryviadirecttransitionsandreductionsfromth…     

Statics of hybrid structures composed of interacting membranes and strings

The equations governing large deformations of hybrid structures are derived from basic principles of mechanics. The considered structures comprise membrane elements with strings arranged inside and possibly along boundaries of the entire structure. No special assumptions are imposed on the mechanical properties of membrane and string elements. The principle of virtual work is formulated under weak continuity hypotheses so that the derived theory takes into account general types of membrane-string attachments. The theory of mechanical constitutive equations for the considered structures is developed and the form of elastic constitutive equations is discussed. A number of specific aspects of string-membrane interactions are analyzed and possible applications of the developed theory are indicated.     

Theory of Short-Term Microdamageability of Granular Composite Materials

The theory of microdamageability of granular composites is outlined through the simulation of microdamages in the components by pores filled with compression-resisting particles of a destroyed material. The damage criterion for a microvolume of a component is taken in the Schleicher–Nadai form, which allows for the difference between the ultimate tensile and compressive loads. The ultimate strength is a random function of Weibull-distributed coordinates. The stress–strain state and the efficient properties of the material are determined from the stochastic equations of elastic theory for a granular composite with porous components. The equations of deformation and microdamage are closed by the equations of porosity balance in the components. Nonlinear diagrams of the concurrent processes of deformation in the granular material and microdamage in the matrix are plotted. The effect of the physical and geometrical parameters on them is studied     

On the influence of prebuckling deformations on the buckling of thin elastic shells

A buckling theory valid for finite prebuckling deformations is presented for thin homogeneous, isotropic and elastic shells. It is subject to the restriction of the Kirchhoff hypothesis. A set of stability equations is derived by decomposing strain and stress components into four classes according to their characteristics.The influence of the prebuckling deformations on the buckling of thin circular cylindrical shells under lateral pressure is investigated with the aid of the basic equations derived above and the results are compared with the solutions of the Flügge equations and those obtained by Yamaki.     

RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

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高温气体反应流中的物理力学问题

从气体动理论(kinetic theory of gases)的原理出发导出了非平衡条件下高温气体反应流基本守恒方程组.讨论了出现在方程组中的各种通量在非平衡条件下的意义,给出了从微观出发的输运系数表达式.介绍各种物理动理论与化学动理论过程的微观理论,讨论了在非平衡条件下现有理论的困难.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CON-TINUUM THEORIES (Ⅱ)—MICROMORPHIC CONTINUUM THEORY AND COUPLE STRESS THEORY

The purpose is to reestablish the balance laws of momentum, angular momentum and energy and to derive the corresponding local and nonlocal balance equations for micromorphic continuum mechanics and couple stress theory. The desired results for micromorphic continuum mechanics and couple stress theory are naturally obtained via direct transitions and reductions from the coupled conservation law of energy for micropolar continuum theory, respectively. The basic balance laws and equations for micromorphic continuum mechanics and couple stress theory are constituted by combining these results derived here and the traditional conservation laws and equations of mass and microinertia and the entropy inequality. The incomplete degrees of the former related continuum theories are clarified. Finally, some special cases are conveniently derived. Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931≈)     

The influence of the drag force due to the interstitial gas on granular flows down a chute

Fully-developed steady flow of granular material down an inclined chute has been a subject of much research interest, but the effect of the interstitial gas has usually been ignored. In this paper, new expressions for the drag force and energy dissipation caused by the interstitial gas (ignoring the turbulent fluctuations of the gas phase) are derived and used to modify the governing equations derived from the kinetic theory approach for granular–gas mixture flows, where particles are relatively massive so that velocity fluctuations are caused by collisions rather than the gas flow. This new model is applied to fully-developed, steady mixture flows down an inclined chute and the results are compared with other simulations. Our results show that the effect of the interstitial gas plays a significant role in modifying the characteristics of fully developed flow. Although the effect of the interstitial gas is less pronounced for large particles than small ones, the flowfields with large particles are still very different from granular flows which do not incorporate any interactions with the interstitial gas.     

弹性体表面分层压缩失稳问题的数学弹性力学解

采用数学弹性力学的稳定平衡方程并结合富氏积分变换的方法研究了含表面平行裂纹的弹性体在压缩载荷下的表面分层失稳问题。导出了一级显式的精确齐次奇异积分方程组,然后.通过Gauss-Chebyshev积分公式,得到一组齐次代数方程组,从而求出临界压缩载荷。并将结果与经典的材料力学梁板稳定的研究方法所得结果进行了比较,指出经典方法误差太大而不适于求解此问题。最后,利用数学弹性力学解求出的等效弹性支承常数给出一个简单精确的临界压缩载荷计算公式。     

Three dimensional elasticity solution for vibration problem of thick plate

I.Introduction'TheclassicalplatetheoryofvibrationisbasedontheKirchhoffhypotllcsis.andtheeffectoftransversesheardeformationandrotatoryinertiaareneglected.111[lltllcfreevibratiollfrequenciesofthinplates,allkindsofboundaryconditionshavebeensolved.Fortheanalysisofthevibrationalproblemsofthickplate,thetheoryofReissuer,MindlinandHenkyisused.Accordingtothedegreesoftheeffectsoftransverseshearstress,transversenormalstressandrotatoryinertia,somedynamicproblemsinEngineeringhavebeensolvedl:l.Regardless…