Structural Modeling in the Mechanics of Porous Materials

A new method for analyzing the deformation behavior of rigid and elastic foams with a small volume content of solid phase ( < 0.2) is developed. Various structural models for describing the elastic behavior of rigid and elastic plastic foams are used and compared. The results of structural simulation of anisotropic auxetic (i.e., having a negative Poisson ratio) foams with concave cells are presented. For cyclic uniaxial compression of rigid foams and volumetric deformation of elastic foams, the stress-strain curves are obtained. The general shape of the curves agrees well with the nonlinearly elastic behavior of plastic foams observed in experiments.     

On Finite Displacement of an Elastoviscoplastic Material in a Gap between Two Rigid Coaxial Cylindrical Surfaces

In the framework of the theory of large deformations, we obtain the solution of a boundary value problem on the flow of an elastoviscoplastic material in a gap between two rigid coaxial cylindrical surfaces under pressure drop changing with time. It is assumed that slip of the material is possible on both surfaces. We consider reversible deformation, the development of viscoplastic flow under the increasing and constant pressure drop, deceleration of the flow under the decreasing pressure drop, and the unloading of the medium.     

The pressing of an elastoviscoplastic material between rigid coaxial cylindrical surfaces

An analytical solution of the problem of the pressing of an incompressible elastoviscoplastic material between two rigid coaxial cylindrical surfaces is obtained using the theory of large strains. The velocity of motion of the elastic core, the change in the dimensions of the zones of irreversible deformation and the stresses and strains both in the elastic core and in the flow region are calculated as a function of the variable pressing force.     

Three-dimensional contact problem for a prestressed elastic body : PMM vol. 42, no. 6, 1978, pp 1080–1084

A half-space of an incompressible neo — Hookean [1,2] material subjected to a homogeneous bi-axial tension or compression along its boundary, is considered. A small deformation caused by the action of a smooth rigid stamp on the boundary of the half-space is superimposed on the initial finite deformation. An integral equation is obtained for the contact pressure. A solution of this equation is obtained for an inclined elliptic stamp with a flat base, and for an elliptic stamp with a curved base, for the cases when the extension coefficients in two directions are either identical, or differ little from each other. The influence of the inital loading on the distribution of the contact pressure, the displacement of the stamp and the form of the contact zone, is analysed.     

Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension

A rectangular bar made of a hyperelastic, but brittle, incompressible homogeneous and isotropic material is subject to uniaxial extension. We prove that the energy minimizers are, depending on the toughness coefficient of the material, either the homogeneous deformation, or the family of deformations for which a horizontal fracture breaks the material in two rectangular pieces, each of which is a rigid motion of the undeformed piece.     

Viscosimetric flow of an incompressible elastoviscoplastic material under the presence of a lubricant on the boundary surfaces

Generalizing the model of large deformations by accounting for the viscous properties of materials, we obtain the analytical solutions of some quasistatic boundary value problems concerning the viscosimetric flows of an elastoviscoplastic material in the gap between the rigid coaxial cylindrical surfaces when, in the neighborhood of one of the rigid cylinders (either internal or external), there is a layer of an elastic non-Newtonian lubricant, and the rigid adhesion conditions are satisfied on boundary surfaces. The conditions are studied of origination of a flow in the lubricant layer and in the basic material. The values of the maximum velocity are specified under which the flow does not tresspass the lubricant layer.     

大位移Timoshenko转轴三维耦合动力学分析

对于高速柔性转轴,综合考虑滑移、弯曲、剪切变形、旋转惯性、陀螺效应和动不平衡等因素,运用Timoshenko旋转梁理论,给出弹性体空间运动的一般性描述,通过Hamilton原理建立弯曲-扭转-轴向三维耦合非线性动力学方程,应用参数摄动方法和假设振型方法进行化简,并用数值模拟分析了轴向刚性滑移、剪切变形、截面尺寸和转速等因素对转轴动力学响应的影响。     

Fluid-structure interaction in porous media for loaded filter pleats

Currently, the known simulation efforts with respect to fluid-structure interaction (FSI) are mainly restricted to the study of flow interacting with deformable solid bodies. On the other hand, there is extensive literature on simulation of flow through porous media. In particular, algorithms and software for CFD simulations of filtration processes in the case of rigid filtration medium were presented earlier by Fraunhofer ITWM, see, e.g., [1, 2]. In these papers the deformation of the solid skeleton is neglected. In many cases of water filtration, filtration for hydraulic applications, and even in certain air filtration regimes, the fluid pressure can be quite high, and the deformation of the pleats can be an issue. The deflection of pleats and its effect on the filtration process merits examination because under operating conditions (and especially after a partial loading of the media) the pleats often cannot be anymore considered as rigid porous media. Therefore, in this paper, the deflection is considered for clean media, as well as for partially loaded media. A new model describing the coupled flow and deformation, and corresponding numerical results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rigid–flexible coupling dynamic analysis on a mass attached to a rotating flexible rod

A rigid–flexible coupling dynamic analysis is presented where a mass is attached to a massless flexible rod which rotates about an axis. The rod is limited to small deformation so that the mass is constrained to move in the plane of rotation. A strongly nonlinear model of the system is established based on the couplings between the elastic deflections of the mass and rigid rotation, in which the mass deflection and rigid rotation are both treated as unknown variables. The additional inertia forces on the mass and coupling mechanism are elucidated in the system model. In the case of varied but prescribed rigid rotation, a set of time-varying differential equations governing mass motion is obtained. The trajectories of mass motion are examined for the spin-up and spin-down rotation. Under constant rigid rotation, a set of ordinary differential equations is further attained, and the issues with dynamic frequencies and critical angular velocity of the system are analyzed. The effects of the centrifugal, Coriolis and tangential inertia forces on the dynamic responses are discussed.     

An approach to solving the one-dimensional problem on compression of a viscoelastic layer dispersedly reinforced with elastic inclusions

A simplified approach to investigating the combined effect of a dispersed filler with different elastic characteristics, physical nonlinearity, and hereditary properties, and of temperature and moisture on the compression of a rectilinear layer is proposed. Various combinations of filler concentration, temperature, and moisture are considered. The investigation is performed in two variants. In the first one, it is assumed that the prevailing characteristics are the instantaneous ones; in the second variant, the deformation is mainly determined by the long-term material characteristics. The instantaneous deformation diagram is assumed nonlinear. For both the variants, analytical relations for the degree of compression as a function of initial parameters (in particular, of initial concentration of the rigid inclusions and their relative rigidity) are obtained. The time-dependent inclusion concentration diagrams are constructed for different levels of load, temperature, and moisture. Graphically, effects of the rigid inclusions and temperature on deformation of the layer are revealed. The combinations of filler concentration and temperature are determined at which their effects on compression of the layer annihilate each other. Analytical relations for the effect of moisture on compression of the dispersedly re in forced layer are obtained, and the corresponding calculated diagrams are presented. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 441-456, May-June, 2009. An erratum to this article can be found at     

Modeling of large deformation frictional contact in powder compaction processes

In this paper, the computational aspects of large deformation frictional contact are presented in powder forming processes. The influence of powder–tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A general formulation of continuum model is developed for frictional contact and the computational algorithm is presented for analyzing the phenomena. It is particularly concerned with the numerical modeling of frictional contact between a rigid tool and a deformable material. The finite element approach adopted is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder–tool interface. The constitutive relations for friction are derived from a Coulomb friction law. The frictional contact formulation is performed within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder material. Finally, the numerical schemes are examined for efficiency and accuracy in modeling of several powder compaction processes.     

固壁近旁Stokes流中粘性液滴的运动和变形

发展了一种模拟固壁近旁轴对称Stokes流中粘性液滴的运动和变形及直接计算固壁上应力的边界积分方法．用此方法对不同的液滴-固壁初始相对间距、粘度比、表面张力和浮力联合参数以及环境流动参数情况进行了数值实验．数值结果显示,由于环境流动和浮力的作用,随着时间的推进,液滴在轴向压缩,在径向拉伸．当环境流动的作用弱于浮力作用时,随着时间的推移,液滴上升并向上弯,固壁上由液滴运动所引起的应力不断减小．当环境流动的作用强于浮力作用时,随着时间的推移,液滴变得越来越扁．在这种情形,当大初始间距时,壁面上的应力随液滴的演变而增大;当小初始间距时,由环境流动、浮力及壁面对流动的较强作用的联合影响,此应力随液滴的演变而减小．由于液滴运动所引起的壁面应力的有效作用仅限于对称轴附近的一个小范围内,且此范围随液滴与固壁的初始间距增大而增大．应力的大小随初始间距增大而大为减小．表面张力对液滴变形有阻止作用．液滴粘性会减小液滴的变形和位置迁移．     

Rotationless formulation for large deformations in flexible multibody dynamics

Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method. In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

3D FEA of Size Effects in Deformation of Thin Metallic Films

The purpose of this work is to analyze size effects in the deformation occurring during nanoindentation-tests of thin metallic films on ceramic substrates. It is well known that classical phenomenological theories of plasticity are hardly applicable in cases of very small dimensions of a body [1]. Thus, the dependency of the mechanical behavior of thin films on the thickness can not be studied in the framework of classical theories. In order to simulate numerically the deformation, a specific material model has been chosen which is able to account for size effects. It bases on the theory of ”Mechanism Strain Gradient” (MSG) plasticity [2] in conjunction with the deformation theory of plasticity. The material model has been implemented via the user defined element subroutine (UEL) in the commercial FE code ABAQUS/Standard as a ten-node tetrahedron-element. With the developed subroutine the deformation of thin copper films on Si substrates during nanoindentation-tests has been simulated. Different material models of the indentor (rigid and elastic) as well as different friction conditions between the film and the pyramidal indentor were tested. Furthermore, the influence of an additional oxide layer on the films surface has been analysed. In order to verify the numerical investigations, results from nanoindentation experiments have been used for comparison [4]. The FE simulations for different thicknesses in the range of 100-600nm showed a very good agreement with the experiments. In particular, the size dependency of the force-displacement curves, calculated by using the developed subroutine, is in rather good agreement with experiments. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transient flow in a rotating porous annulus due to suction at the walls

A highly porous material occupies the annular region between two coaxial infinitely long cylinders. A viscous incompressible fluid fills this porous medium and is initially in a state of rigid rotation together with the medium. The flow has been disturbed by imposing suction/injection at the outer/inner cylindrical boundaries respectively. The Brinkman's law has been used to represent the fluid motion. The exact solution for the resulting unsteady flow is obtained by Laplace transformation technique. The transient evolution of the boundary layers and the response of steady boundary layers to the resistance of the medium are discussed.     

Effect of steady-state flow of a polyisobutylene solution on its dynamic characteristics measured in the direction of flow

The effect of steady-state flow on the linear dynamic characteristics of a 10% solution of polyisobutylene in cetane, measured in the direction of flow, is investigated. The material characteristics in steady-state flow quantitatively describe the dynamic viscosity and elasticity at deformation frequencies small as compared with the steady-state shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 913–919, September–October, 1970.     

Strength of welded joints in polymer films and means of increasing it

The behavior of welded joints in films of elastic and rigid polymers under delaminating and shearing loads is analyzed. A dependence of the strength of welded joints on the character of stress distribution in them and the deformation properties of the material being welded is indicated. In this connection, means of raising the strength of lap and T-shaped joints are examined, which consist in lowering the stress concentration in them by increasing the volume of material in the seam zone which absorbs the load, or in strengthening it in the direction of action of the distorting force.     

Spatial contact problems for rough elastic bodies under elastoplastic deformations of the unevenness

On the basis of /1, 2/, a model is constructed for the contact between a rigid stamp and a rough body taking elastoplastic deformations of the unevenness into account. The contact model for rough bodies with elastic deformations of the unevenness is a special case. A classical approach utilizing boundary integral equations is applied in the mathematical formulation of the contact problem. Under quite general assumptions (for instance, the multiconnectedness of the contact domain desired), the uniqueness and existence of the solution are investigated. A method is developed to determine the contact pressure, the closure of the bodies, and also the contact area which consists of two parts in the general case, a zone of elastoplastic deformation of the unevenness and a zone of their elastic deformation. The efficiency of the method is shown in examples of new contact problems. The solution is represented in a convenient form for analysing the influence of the roughness. This is of considerable value for material testing by a contact method. A fairly complete survey of research on contact problems for rough bodies can be found in /1–4/.     

High-frequency periodic deformation of polymers in the viscous-flow state

The propagation of high-frequency periodic vibrations in melts and solutions is considered in the case where the acoustic characteristics of the material are determined by the deformation amplitude. It is shown that in sufficiently large specimens the consequences of periodic deformation are concentrated near the vibration source, as a result of which a layer of material with strongly modified mechanical characteristics develops. It is suggested that when periodic high-frequency deformation is superimposed on steady-state flow, owing to the presence of a boundary layer there is effective slippages of the material at the vibration-emitting surfaces.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 722–728, July–August, 1973.     

Elastoplastic torsion of a cylindrical rod for finite deformations

A solution of the problem of the torsion of a cylindrical rod was obtained in /1/ for a general, isotropic, incompressible elastic material. The present paper gives an analytical solution of the elastoplastic torsion problem for finite deformations, written in terms of quadratures of elliptic functions. The non-linear kinematics of elastoplastic deformation is introduced into the defining equations with the help of a multiplicative decomposition of the deformation gradient into elastic and plastic components /2, 3/. The elastic deformation and rate of plastic deformation are related to the state of stress of the body, in accordance with the defining Mooney-Rivlin equations /4/ and the law of flow for finite deformations associated with the Tresca yield condition /5/. A non-linear first-order partial differential equation and the initial data at the elastoplastic boundary are obtained in order to determine the angle of rotation within the plastic zone of the basis formed from the eigenvectors of the stress tensor, relative to the radial direction. The integration of the resulting equation is reduced to determining the general integral of the Ricatti equation with right-hand side determined from the angular velocity of flow of the material within the plastic zone. It is shown that neglecting the finiteness of the deformation leads to too high an estimate of the rigidity of the rod.