Thermomechanical instability associated with heat release during plastic flow

The effect of heat generation accompanying plastic deformation on instability of uniform plastic flow is considered. Linear stability analysis is performed taking into account both classical necking (geometrical effect) and thermomechanical coupling. Two types of conditions imposed in tensile testing are considered: those of constant (time and coordinate independent) imposed load and constant imposed cross-head velocity. A central issue in the paper is instability of plastic flow at extremely low temperatures (4.2 K to 10 K). Instability conditions are formulated, taking into account the temperature dependence of the thermal parameters. An example of tensile deformation of a thin Al-Mg rod is considered in some detail. Available experimental data are explained on the basis of stability analysis.     

Borsuk's problem and the chromatic numbers of metric spaces

In this paper, we will give a short survey of various old and new results concerning two closely connected problems of combinatorial geometry - that of K. Borsuk and that of E. Nelson - P. Erdös - H. Hadwiger. We will also present here our very recent achievements on Ramsey numbers.     

Theoretical and experimental studies on the aerodynamic instability of a two-dimensional circular cylinder with a moving attachment

Rain–wind induced vibration of cables in cable-stayed bridges is a worldwide problem of great concern. The effect of the motion of water rivulets on the instability of stay cables has been recognized as one of the mechanisms of this complex phenomenon. In order to investigate how the motion of rivulets affects the unstable vibration of cables without considering the effects of axial flow and axial vortex, a real three-dimensional cable was modeled as a two-dimensional circular cylinder, around which an attachment representing the rivulet can move. This could also be regarded as a new kind of two-dimensional 2-dof dynamic system. This paper studies the aerodynamic instability of the system theoretically and experimentally. Equations governing the motions of the cylinder and the attachment are first established. The Lyapunov stability criterion is applied to the equations of motion to derive the criterion for the unstable balance angle of the attachment. Moreover, a new two-dimensional 2-dof cable model system with a movable attachment is designed and tested in a wind tunnel. Parametric studies are carried out to investigate the effects of major factors such as wind speed, frequency and damping of the dynamic system on the unstable balance angle of the rivulet attachment. Theoretical and experimental results match well. These results may be valuable in elucidating the mechanism of rain–wind induced vibration of stay cables.     

Edge cracks in plastically deforming surface grains

A selection of surface crack problems is presented to provide insights into Stage I and early Stage II fatigue crack growth. Edge cracks at 45^o and 90^o to the surface are considered for cracks growing in single crystals. Both single crystal slip and conventional plasticity are employed as constitutive models. Edge cracks at 45^o to the surface are considered that either (i) kink in the direction perpendicular to the surface, or (ii) approach a grain boundary across which only elastic deformations occur.     

On plastic anisotropy of constitutive model for rate-dependent single crystal

An algorithm for single crystals was developed and implemented to simulate plastic anisotropy using a rate-dependent slip model. The proposed procedure was a slightly modified form of single crystal constitutive model of Sarma and Zacharia. Modified Euler method, together with Newton-Raphson method was used to integrate this equation which was stable and efficient. The model together with the developed algorithm was used to study three problems. First, plastic anisotropy was examined by simulating the crystal deformation in tension and plane strain compression, respectively. Secondly, the orientation effect of some material parameters in the model and applied strain rate on plastic anisotropy for single crystal also is investigated. Thirdly, the influence of loading direction on the active slip system was discussed.     

Bi-directional evolutionary topology optimization of geometrically nonlinear continuum structures with stress constraints

This paper proposes a design method to maximize the stiffness of geometrically nonlinear continuum structures subject to volume fraction and maximum von Mises stress constraints. An extended bi-directional evolutionary structural optimization (BESO) method is adopted in this paper. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low density elements. The maximum von Mises stress is approximated by the p-norm global stress. By introducing one Lagrange multiplier, the objective of the traditional stiffness design is augmented with p-norm stress. The stiffness and p-norm stress are considered simultaneously by the Lagrange multiplier method. A heuristic method for determining the Lagrange multiplier is proposed in order to effectively constrain the structural maximum von Mises stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topology variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several benchmark design problems.     

Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105

This paper introduces a biparametric family of Lyapunov functions for a non-linear mathematical model based on the FitzHugh-Nagumo equations able to reproduce some main features of the X-ray bursting behaviour exhibited by the microquasar GRS 1915+105. These functions are useful to investigate the properties of equilibrium points and allow us to demonstrate a theorem on the global stability. The transition between bursting and stable behaviour is also analyzed.     

The ferroelectric field effect on the two-dimensional electron gas at LaAlO3/SrTiO3 (001) interface: Insights from first principle simulations

We perform first-principles calculations to explore the possibility of tuning the two-dimensional electron gas at the LaAlO₃/SrTiO₃ (001) interface through BaTiO₃ substrate. A metal-to-insulator transition is found at the interface as the polarization of BaTiO₃ reverses. Through the potential analysis of the LaAlO₃/SrTiO₃/BaTiO₃ superstructure, we find that the intrinsic electric field of LaAlO₃ is significantly suppressed as the polarization points away from the LaAlO₃/SrTiO₃ interface, while it is enhanced with the polarization pointing to the interface. The ferroelectric field control of the intrinsic electric field, and therefore the electronic reconstructions at the interface, originating from the screening of polarization charges, opens the way to the development of novel nanoscale electronic devices.