L.A.S. and Negative Schwarzian Derivative Do Not Imply G.A.S. in Clark’s Equation

It has been conjectured that a locally attracting equilibrium of Clark’s equation \(x_{n+1}=\alpha x_n + (1-\alpha )h(x_{n-k})\) is also globally attracting whenever h is a unimodal or decreasing map with negative Schwarzian derivative. The main aim of this paper is to show that the conjecture is false when \(k\ge 3\). This is done by studying the (Neimark–Sacker) bifurcation at the parameter \(\alpha \) where the locally attracting equilibrium of the equation becomes unstable. Our results, on the other hand, reinforce the validity of the conjecture in the cases \(k=1,2\).     

Craft––a plastic-damage-contact model for concrete. I. Model theory and thermodynamic considerations

A framework is described for the development of a thermodynamically consistent plastic directional-damage-contact model for concrete. This framework is used as a basis for a new model, named Craft, which uses planes of degradation that can undergo damage and separation but which can regain contact according to a contact state function. The thermodynamic validity of the resulting model is considered in detail, and is proved for certain cases and demonstrated numerically for others. The model has a fully integrated plasticity component that uses a smooth triaxial yield surface and frictional hardening–softening functions. A new type of consistency condition is introduced for simultaneously maintaining both local and global constitutive relationships as well as stress transformation relationships. The introduction of contact theory provides the model with the ability to simulate the type of delayed aggregate interlock behavior exhibited by fully open crack surfaces that subsequently undergo significant shear movement. The model has been implemented in a constitutive driver program as well as a finite element program. The model is assessed against a range of experimental data, which includes data from uniaxial tension tests with and without unloading–reloading cycles, tests in which cracks are formed and then loaded in shear, and uniaxial, biaxial and triaxial compression tests.     

Discussion of “The asymmetry of stress in granular media”: [J.P. Bardet and I. Vardoulakis,Int. J. Solids Struct. 2001, Vol. 38, No. 2, pp. 353–367]

The discussion concerns a recently proposed definition of average stress for granular materials, one which can manifest asymmetry in the absence of surface couples, body couples, and contact couples. The average stress was derived from a new postulate that employs virtual work terminology. The discussion shows that the postulate leads to a non-unique average stress and to a non-unique stress asymmetry.     

Effects of a.c. Electric Field and Rotation on Bénard–Marangoni Convection

The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory instability and discussed the competition between both stationary and oscillatory convections. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analysis of Motion Resisted by Friction. I. Constant Coulomb and Linear/Coulomb Friction∗

ABSTRACT

An exact method for analysis of the transient and steady-state response of harmonically excited frictional oscillators is presented. This method does not postulate antiperiodic type of motion. The method is used to analyze the motion of the constant Coulomb oscillator, under the following conditions: (a) transient conditions; (b) steady-state conditions in the region of multiple stops per cycle and in the presence of viscous damping, where it is shown that viscous damping tends to reduce the number of stops; and (c) at degenerate values of the ratio of driving frequency to natural frequency, where it is shown that unsymmetric motion with only one stop per cycle exists. Furtherfore, the method is applied in analysis of the motion of a linear/Coulomb oscillator, in the region of multiple stops per cycle.     

ACTA MECHANICA SOLIDA SINICA The Chinese Society of Theoretical and Applied Mechanics Vol.20,No.1-No.4,2007 CONTENTS

A simple eonstitutive rnodel for ferroeleetrie eeramies under eleetrieal/mechanieal loading……，...........……，......……LIYu，Shouwenyu，Xiqiao Feng工一1 The rate一indePendent eonstitutive modelling for Porous and multi一Phase nano- erystalline materials.，…，…Jianqiu Zhou，Yuanling Li，Zhenzhong Zhangl一13 Some Problems with the method of fundamental solution using radial basis functions，....................................……Hul叭乞ng，Qinghua Qinl一21 The meshless virtual bo…     

Comments on “Dynamics of the general Lorenz family” by Y. Liu and W. Pang

A paper, “Dynamics of the general Lorenz family,” was published in the journal Nonlinear Dynamics. The authors investigate the general Lorenz family $\dot{x} = a(y-x)$ , $\dot{y} = dx + cy - xz$ , $\dot{z} = -bz + xy $ , considering that it contains four independent parameters. However, we show that, generically (for c≠0), this family is equivalent to the Lorenz system and, thus, the results they provide for the general Lorenz family are easily obtained from the corresponding results on the Lorenz system. Moreover, in the case c=0, it is sufficient to consider a two-parameter system.     

A. A. Il’yushin’s scientific heritage and development of his ideas in mechanics

We present a survey of the main results and scientific ideas due to the 20th century prominent scientist Aleksey Antonovich Il’yushin, which can be regarded today, at his hundredth birthday anniversary, as his scientific heritage. The survey material is arranged (mainly, chronologically) in the key directions of Il’yushin’s activities such as the theory of viscoplastic flow, hydrodynamic stability, dynamics of deformable media, supersonic aerodynamics and related flatter problems, theory of elastoplastic processes, theory of plastic flow, thermoviscoelasticity and thermodynamics, strength of polymer bodies and structures, general theory of constitutive relations in classical continuum mechanics, and nonclassical models of continuum.