USING EIGENMODULI AND EIGENSTATES TO EVALUATE THE POSSIBILITY OF MARTENSITIC PHASE TRANSFORMATIONS

Journal of Applied Mechanics and Technical Physics - The possibility of phase transitions (martensitic transformations) in shape-memory alloys is evaluated using the concept of eigenmoduli...     

层状弹塑性板动力变形的数值研究(英文)

本文研究了搁置在任意形状轴承上的层状平板,加上脉冲载荷(如炸药爆炸),结果产生塑性流动,改变了板和轴承的接触和破坏了层状板之间的接合,使之发生滑移,最后板形成残余形变,强动载冲击板产生形变的实际过程可分为两个阶段:第一阶段为应力波的传播和在板内应力波的相互作用,主要是从自由面反射的应力波和从轴承面反射的应力波,波经重复几次反射后,造成板的屈曲状态,其间,板的中间层始终保持中线弹性状态。第二阶段为板内某些截面发生塑性形变,随厚度不同而不同地收缩,同时所有的板均拉伸而增加了板的弯曲,最后,塑性形变消耗掉能量后,板各单元变为弹性状态而产生某种模型的振动。     

Design of laminar and fibrous composites with given characteristics

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 136–150, March–April, 1990.     

Computer simulation of a twisted nanotube buckling

We develop procedures for solving the problems of dynamic nanostructure deformation and buckling numerically. The procedures are based on discretization with respect to time of the nonlinear equations of molecular mechanics whose matrices and vectors are determined using the Morse potential for the central forces of interaction between atoms and fictitious truss elements accounting for the variations of the angle between atomic bonds. To determine the critical values of deformation parameters and the shapes of buckling nanostructures we use a stability loss criterion for solutions to nonlinear ordinary differential equations on a finite time interval. We implemented our procedures in the PIONER code, using which we solve the problem of a twisted nanotube buckling in the conditions of a quasistatic deformation. To determine the postcritical equilibrium modes we solve the same problem in a dynamic formulation. We show that the modes of equilibrium configurations of the nanotube in the initial postcritical deformation correspond to a buckling mode obtained both at the bifurcation point of quasistatic solutions and at the quasibifurcation point of dynamic solutions.     

Determination of the ultimate states of elastoplastic bodies

The equations of quasistatic deformation of elastoplastic bodies are considered in a geometrical linear formulation. After discretization of the equations with respect to spatial variables by the finite-element method, the problem of determining equilibrium onfigurations reduces to integration of a system of nonlinear ordinary differential equations. In the ultimate state of a body of an ideal elastoplastic material, the matrix of the system degenerates and the problem becomes singular. A regularization algorithm for determining solutions of the problems for the ultimate states of bodies is proposed. Numerical solutions of test problems of determining the ultimate loads and equilibrium configurations for ideal elastoplastic bodies confirm the reliability of the regularization algorithm proposed. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 196–204, September–October, 2000.     

Optimization of thermoelastic laminar bodies

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 156–163, March–April, 1989.     

Plane elastic problem for an inhomogeneous layered body

A plane elastic problem for an inhomogeneous elastic layered body bounded by equidistant convex curves is considered. A numerical algorithm for solving the problem is proposed and implemented.     

Modeling the deformation of rock with rough surfaces of block contact under quasistatic and dynamic loading conditions

The effect of layers consisting of small particles or asperities on contact surfaces on the deformation of a block medium as a whole and the failure of the blocks constituting the medium was studied experimentally. The samples were subjected to quasistatic uniaxial compression perpendicular to the contact surfaces. Numerical modeling was performed of wave propagation during pulse loading of a pair of blocks having rough surfaces of contact and made of a material with elastic characteristics close to the characteristics of marble and limestone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 173–178, May–June, 2007.     

Molecular mechanics method applied to problems of stability and natural vibrations of single-layer carbon nanotubes

The molecular mechanics (MM) method is used to determine the frequencies and natural vibration shapes and to determine the buckling critical parameters and the postcritical deformation shapes of single-walled carbon nanotubes with twisted ends. The following two variants of the MM method are used: the standard MM method and the mixed method of molecular mechanics/molecular structure mechanics method (MM/MSM). Computer simulation shows that the MM/MSM method allows one to obtain acceptable values of frequencies and natural vibration shapes as well as of critical angles of twist, appropriate buckling modes, and postcritical deformation configurations of nanotubes compared with the same characteristics of nanotube free vibrations and buckling obtained by the standard MM method.     

A transversely isotropic elastic model of geomaterials

Under consideration is the choice of parameters of a transversely isotropic elastic model for describing the linear deformation of geomaterials. We also discuss some analytical and numerical methods of solving the corresponding dynamic equations.