Critical thought experiment to choose the driving force for interface propagation in inelastic materials

The problem of defining the driving force for interface propagation in inelastic materials is discussed. In most publications, the driving force coincides with the Eshelby driving force, i.e. it represents a total dissipation increment on the moving interface due to all the dissipative processes (phase transition (PT) and plasticity). Recently (Levitas, V.I., 1992a. Post-bifurcation Behaviour in Finite Elastoplasticity. Applications to Strain Localization and Phase Transitions. Universität Hannover. Insititut für Baumecharik and Numerische Mechanik, [BNM-Bencht 1JP 585-LC, 92/5, Hannover; Int. J. Eng. Sci. 33 (1995) 921; Mech. Res. Commun. 22 (1995) 87; J. de Physique III 5 (1995) 173; J. De Physique III 5 (1995) 41; Int. J. Solids Struct. 35 (1998) 889], an alternative approach was developed in which the driving force represents the dissipation increment due to PT only, i.e. total dissipation minus plastic dissipation. The aim of this paper is to prove the contradictory character of application of the Eshelby driving force to inelastic materials. For this purposes, a problem on the interface propagation in a rigid–plastic half-space under homogeneous normal and shear stresses is solved using both definitions, along with the principle of the maximum the driving force. Finite strain theory is used. It appears that the first approach exhibits some qualitative contradictions, which are not observed in our approach. In particular, even for shape memory alloys, when transformation strain can be accommodated elastically (or even without internal stresses), maximization of the Eshelby driving force requires as much plasticity as possible. When applied shear stress tends to the yield stress in shear of a new phase, the driving force tends to infinity, i.e. PT has to always occur at the beginning of plastic flow. Note that in this paper plasticity means dislocation plasticity rather than plasticity due to twinning. Twinning during martensitic PT is the appearance of several martensitic variants which are in twin relation to each other. Consequently, for twinned martensite one has microheterogeneous transformation strain without plastic dissipation term, i.e. both approaches coincide.     

Inelastic material behavior and fracture mechanics: a variational approach

Summary A variational principle is presented, which relates the macroscopic fracture response of a mechanical component to its microscopic, inelastic material behavior. The principle allows a comparison between the crack driving force, expressed by the J-integral, and an integral expression of the fracture resistance. On this basis, the critical values of J are calculated for a Griffith crack under mixed-mode loading. The preliminary check with data available in literature shows a fairly good agreement. Received 18 July 1998; accepted for publication 9 February 1999     

Dynamics analysis of a parallel hip joint simulator with four degree of freedoms (3R1T)

For a hip joint simulator with a 3SPS+1PS spatial parallel manipulator as the core module, a formulation based on the Kane equation was derived for the dynamic characteristics of the simulator from the kinematics analysis of the model. The relationships of the velocities and accelerations between the moving platform and active branched-chains were deduced. The velocity and angular velocity components of the moving platform were served as the generalized velocities. And the dynamic model was established by obtaining the generalized active forces and inertial forces. Then the driving forces and powers of the active branched-chains and the constraint reaction forces of the intermediate branched-chain were simulated in the numerical method. The results showed that the active driving forces of the branched-chains reached their respective maximum when the moving platform rotated into 0.13^° around X-axis, 2^° around Y-axis, and 18^° around Z-axis. And the intermediate branched-chain needed to balance the driving and inertia forces, as well as support the moving platform and load the force of hydraulic cylinder. Therefore, the maximum constraint reaction force of the intermediate branched-chain is along the Z-axis. The research works provided a theoretical basis for the design of the active branched-chains driving system and the structural parameters of the intermediate branched-chain, as well as for the control system.     

非理想,非完整约束轮对动力学

推导了铁道车辆轮轨接触的非完整约束方程,考虑动坐标系产生的惯性力和轮对转子的陀螺力矩效应,用绝对坐标法建立了任意曲线轨道动坐标系下轮对的动力学方程,通过迭代Ｌａｇｒａｎｇｅ乘子同时得到接触点法向力（理想约束反力）和蠕滑力（非理想约束反力）针对两点接触引起的数值积分不稳定,提出了等铲一点接触模型,最后通过验算了Ｐａｓｃａｌ考题和仿真自由轮对的蛇行运动,验证了本文轮轨模型的正确性,为开发通用车辆动力学     

大射电天文望远镜悬索馈源系统驱动力的研究

针对大射电天文望远镜馈源系统中悬索呈现出的柔性特征，在已知馈源舱的位置，姿态，速度和加速度的情况下，将悬索离散为柔性索杆单元，建立了系统的逆运动学及逆动力学模型。分析计算了悬索上各离散点的位置、速度、加速度和惯性力，推导了在重力和惯性力共同作用下悬索的空间挠曲线方程，研究了悬索的刚体位移和弹性变形。在此基础上，通过刚体-柔性的迭代计算，求出悬索馈源系统的驱动力，为高精度的大射电天文望远镜提供了必要的设计参数。     

热液体动力扭带清洗动力学及其工程应用

为了解决传统扭带存在自转动力矩弱和传热强化幅度低的问题,研究入口反旋斜齿扭带的动力学理论,方法是将总动力矩分解为虚拟的光滑扭带动力矩和虚拟光滑扭带下的螺旋液流对斜齿的冲推力矩之和,运用动量矩定理分析建立了动力矩计算式．以此式指导结构优化和工程应用,使自转动力矩和传热系数均比传统扭带有了成倍提高,设备总阻力仍然在工程许可范围内,成为可以广泛应用于较低流速下自动清洗防垢与高效强化传热的新元件．     

On the universality of the thermomechanics of forces driving singular sets

Summary It is shown that the formal expression of the driving force acting on a one- dimensional or two-dimensional singular set of material points (crack tip in fracture, phase-transition front or shock wave) and of the accompanying dissipation in an irreversible progress of the set is independent of the precise material behaviour at regular points. A four-dimensional space-time canonical formalism is introduced establishing the necessary consistency between the power expended by the driving force (spatial component) and the resulting heat source (timelike component) localized at the singular set. Possible extensions of this result are discussed. Received 8 April 1999; accepted for publication 4 May 1999     

The Moving Plane Inhomogeneity Boundary with?Transformation Strain

Within the context of linear elastodynamics, the radiated fields (including inertia) for a plane inhomogeneous inclusion boundary with transformation strain (or eigenstrain), moving in general motion under applied loading, have been obtained on the basis of Eshelby??s equivalent inclusion method, by using the strain field of a moving homogeneous inclusion boundary previously obtained. This dynamic strain field, obtained from the dynamic Green??s function (for an isotropic material), is unique, and has as initial condition the limit of the spherical Eshelby inclusion, as the radius tends to infinity, which is the minimum energy solution for the half-space inclusion. With the equivalent dynamic eigenstrain (which is dependent on the velocity of the boundary), the radiated fields for the inhomogeneous plane inclusion boundary can be obtained, and from them the driving force on the moving boundary can be computed, consisting of a self-force (which is the rate of mechanical work (including inertia) required to create an incremental region of inhomogeneity with eigenstrain), and of a Peach-Koehler force associated with the external loading. While for an expanding plane homogeneous inclusion boundary the Peach-Koehler force is independent of the boundary velocity, in the case of an inhomogeneous one it is not.     

Analysis of repeated impacts on a steel rod with visco-plastic material behavior

In machine dynamics impacts are usually common phenomena, resulting from collisions of moving bodies. Even low velocity impacts might produce high stresses in the contact region, which result in inelastic deformation. Thereby, visco-plastic materials, such as steel, show a significant increase of the yield stress with the strain rate. In machine dynamics repeated collisions occur, resulting in repeated impacts on a previously deformed contact area. Then, inelastic deformation and the resulting residual stresses produced by previous impacts have an influence on the behavior of the following impacts. Thus, the impact behavior varies with the number of impacts. This paper presents a numerical and experimental evaluation of repeated impacts with identical impact velocity up to 3 m/s, whereby the deformation history of the contact area, due to previous impacts, is included. The approach is applied to longitudinal impacts of an elastic steel sphere on a steel rod with distinct visco-plastic material behavior which is identified by Split Hopkinson Pressure Bar tests. A Finite Element analysis and experimental verification using two Laser-Doppler-Vibrometers are performed. It is shown that for an accurate impact simulation the FE model must include the visco-plastic material behavior of the steel. Further it is found that the maximal contact force, the rebound velocity and the coefficient of restitution increase with the number of impacts, while the contact duration decreases with the number of impacts. After several impacts these quantities show saturation to a constant value, indicating no significant additional inelastic deformation in the later impacts. Further, the residual stress distribution, the maximal von Mises stress distribution and the local deformation at the contact point are evaluated and a characteristic force-deformation diagram is obtained. Finally, an analysis is performed to describe the relation between maximal force and remaining crater at the contact point.     

A material force method for inelastic fracture mechanics

A material force method is proposed for evaluating the energy release rate and work rate of dissipation for fracture in inelastic materials. The inelastic material response is characterized by an internal variable model with an explicitly defined free energy density and dissipation potential. Expressions for the global material and dissipation forces are obtained from a global balance of energy-momentum that incorporates dissipation from inelastic material behavior. It is shown that in the special case of steady-state growth, the global dissipation force equals the work rate of dissipation, and the global material force and J-integral methods are equivalent. For implementation in finite element computations, an equivalent domain expression of the global material force is developed from the weak form of the energy-momentum balance. The method is applied to model problems of cohesive fracture in a remote K-field for viscoelasticity and elastoplasticity. The viscoelastic problem is used to compare various element discretizations in combination with different schemes for computing strain gradients. For the elastoplastic problem, the effects of cohesive and bulk properties on the plastic dissipation are examined using calculations of the global dissipation force.     

A micromechanical model of phase boundary movement during solid–solid phase transformations

Summary  Understanding the kinetics of phase boundary movement is of major concern in e.g. martensitic transformation in related engineering applications. The main goal of this paper is to develop such kinetics on the basis of thermodynamic principles at the material microlevel. After a short literature survey in the introduction, the jump condition and thermodynamic force on the interface are discussed based on laws of conservation and thermodynamics. This leads to a relation for the driving force of the transformation front. In particular, the propagating front of a phase-transforming sphere within an elastic-plastic medium is considered. Due to density change, which is implicitly expressed in the transformation volume strain, strains and accompanying stresses are induced which hamper the propagation and influence the transformation kinetics. Together with the latent heat, the heat due to plastic dissipation occurs as a source term in the heat conduction equation. Since kinetics are influenced by temperature, the heat conduction equation and the kinetics equation are coupled. Using Green's function techniques, an integral equation is derived and solved numerically. The results of a parameter study are discussed. Received 10 February 2000; accepted for publication 18 October 2000     

Determination of the driving force acting on a kinked crack

Summary A variational principle is formulated for a body containing a crack in equilibrium. An expression for the driving force acting on the crack admitting nontangential virtual crack extensions is derived. As a consequence of a variational principle, crack equilibrium criterion under mixed-mode loading conditions is obtained. For general 3-D problems, the magnitude as well as the direction of the driving force are precisely determined. Fracture locus for three combined modes is calculated. Received 18 June 1998; accepted for publication 7 January 1999     

An efficient algorithm for elasto-viscoplastic vibrations of multi-layered composite beams using second-order theory

An efficient time-domain algorithm for plane non-linear flexural vibrations of multi-layered composite beams, which are driven into the inelastic range by severe transverse loadings, is presented. The influence of an axial static preload is considered in the sense of the quasi-linear second-order theory of structures. The inelastic parts of strain are treated as additional sources of selfstress in the linear elastic background-structure, driving the elastic response into the inelastic one. The efficiency of this exact formulation lies in the fact that linear solution techniques can be used in their most powerful form: Rubin's useful formulation for the quasi-static second-order transfer-matrix of linear elastic structures is applied in combination with modal analysis. Having in mind multi-metal beams, the classical lamination theory is assumed to be valid. Beams with overhang composed of ideal elastic-plastic and viscoplastic layers are studied as example structures. The fictitious sources of selfstress are calculated from the different material laws of the layers in a numerical time-stepping procedure, where a generalized midpoint-rule in combination with Crisfield's secant-Newton procedure is used.     

Fracture and Singularities of the Mass-Density Gradient Field

A continuum mechanical theory of fracture without singular fields is proposed. The primary contribution is the rationalization of the structure of a ‘law of motion’ for crack-tips, essentially as a kinematical consequence and involving topological characteristics. Questions of compatibility arising from the kinematics of the model are explored. The thermodynamic driving force for crack-tip motion in solids of arbitrary constitution is a natural consequence of the model. The governing equations represent a new class of pattern-forming equations.     

The instability mechanism of single and multilayer Newtonian and viscoelastic flows down an inclined plane

The instability mechanism of single and multilayer flow of Newtonian and viscoelastic fluids down an inclined plane has been examined based on a rigorous energy analysis as well as careful examination of the eigenfunctions. These analyses demonstrate that the free surface instability in single and multilayer flows in the limit of longwave disturbances (i.e., the most dangerous disturbances) arise due to the perturbation shear stresses at the free surface. Specifically, for viscoelastic flows, the elastic forces are destabilizing and the main driving force for the instability is the coupling between the base flow and the perturbation velocity and stresses and their gradient at the free surface. For Newtonian flows at finite Re, the driving force for the interfacial instability in the limit of longwaves depends on the placement of the less viscous fluid. If the less viscous fluid is adjacent to the solid surface then the main driving force for the instability is interfacial friction, otherwise the bulk contribution of Reynolds stresses drives the instability. For viscoelastic fluids in the limit of vanishingly small Re, the driving force for the instability is the coupling of the base flow and perturbation velocity and stresses and their gradients across the interface. In the limit of shortwaves the interfacial stability mechanism of flow down inclined plane is the same as plane Poiseuille flows (Ganpule and Khomami 1998, 1999a, b). Received: 20 October 2000/Accepted: 11 January 2001     

Inverse dynamics of the HALF parallel manipulator with revolute actuators

Recursive matrix relations for kinematics and dynamics of the HALF parallel manipulator are presented in this paper. The prototype of this robot is a spatial mechanism with revolute actuators, which has two translation degrees of freedom and one rotation degree of freedom. The parallel manipulator consists of a base plate, a movable platform and a system of three connecting legs, having wide application in the fields of industrial robots, simulators, parallel machine tools and any other manipulating devices where high mobility is required. Supposing that the position and the motion of the moving platform are known, an inverse dynamics problem is solved using the principle of virtual powers. Finally, some iterative matrix relations and graphs of the torques and powers for all actuators are analysed and determined. It is shown that this approach is an effective means for kinematics and dynamics modelling of parallel mechanisms.     

Mechanics and thermodynamics of surface growth viewed as moving discontinuities

Surface growth is presently described as the motion of a moving interface of vanishing thickness, physically representing the generating cells, separating a zone not yet affected by growth from a domain in which growth has occurred. The jump conditions of density, velocity, momentum, energy, and entropy over the moving front are expressed from the general balance laws of open systems in both physical and material format. The writing of the jump of the internal entropy production in material format allows the identification of a driving force for surface growth, thermodynamically conjugated to the material velocity of the moving front.