On the loading criterion

A mechanical background of [1958] loading criterion, which is applicable not only to hardening but also to perfectly plastic and softening behaviors, is revealed, and an inequality that has to be fulfilled by a direction of plastic stretching is derived under the loading criterion.     

On the correctness of the energy criterion in fracture mechanics

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 10, pp. 28–34, October, 1995.     

On the criterion for the absolute stability of the control system

In this paper, firstly we give the criterion for the absolute stability of the second canonical form for the control system, including the equation of the longitudinal motions of a plane as a particular example. The corresponding result in [8], [9] is a particular example given in this paper. Secondly, we give the criteria for the absolute stability of the first canonical form in the usual case and in the critical case. Finally, we give some criteria for the absolute stability of the general form for the direct control system.All the results in this paper merely depend upon the relations between the parameters of the system itself to give an explicit algebraic discriminant.     

On the circumferential strain factor criterion of mixed mode brittle fracture

In this paper, the criteria of mixed mode brittle fracture are carefully examined. It has been shown that, the circumferential strain factor criterion is rational and safe.With the exception of opening mode, mixed mode plane strain fracture of comparatively ductile materials(metals), in general, does not follow the theory of linear elastic fracture mechanics.Like the stress intensity factor that which is concerned is playing an important role in pure opening mode crack problems. We believe that, in mixed mode crack problems, the circumferential strain factor will become a parameter to determine the rate of fatigue crack propagation per cycle, and of stress corrosion cracking per unit time.First published in Nanking Aeronautical Institute Report of Science and Technology, No. 680, Jan., 1980 (in Chinese).     

On the zero-curvature criterion for structures with material strengthening and geometrical non-linearity

A zero-curvature criterion is proposed to determine the practical collapse load. Six tests have been carried out on spherical pressure vessels with cylindrical nozzle. Results of these tests and other experimental data quoted from different references are discussed in order to compare the new criterion with various previously proposed criteria. It is concluded that: (1) the zero-curvature point is a characteristic point of the experimental curve and that the new criterion is an objective criterion without any artificial coefficient. (2) the deviation of the collapse load estimated by the new criterion is smaller than that estimated by other criteria.Supported by the Chinese National Foundation of Natural Science.     

On the non-oscillation criterion for multiplicative anisotropic plasticity at large simple shear deformation

The criterion for non-oscillatory stresses under monotonic large simple shear deformation in the context of multiplicative anisotropic plasticity is discussed. In particular, evolving anisotropy combined with a Hill type of yield criterion is considered. It is shown that a sufficient, but not necessary, criterion for a non-oscillatory stress is ellipticity of the first Piola–Kirchhoff stress. Loss of ellipticity corresponds to a critical value h_cr of the generalized plastic modulus. Similarly, the absence of limit points on the stress–strain relation motivates an alternative criterion in terms of a critical value h_sh  h_cr. Finally, this criterion is demonstrated analytically as well as numerically for an important class of models with evolving anisotropy of the saturation type.     

准定常强激波反射马赫杆突出变形准则的探讨

分析了滑移线延长线与楔面交点附近的流动特点,研究了准定常强激波反射中马赫杆的变形,建立了马赫杆突出变形消失的过渡准则,并用激波极曲线方法进行了求解。对马赫杆的变形过程进行了描述,研究了比热比、马赫数的变化对马赫杆突出变形消失条件的影响,并对突出变形消失区域与终点双马赫反射区域进行了比较。结果表明:马赫杆突出变形的消失是低比热比介质中出现的一种激波反射现象。马赫杆突出变形的消失,导致出现一种新的无射流、直马赫杆的双马赫反射结构。     

On the aerostatic divergence of suspension bridges: A cable-length-based criterion for the stiffness degradation

Motions of a suspension bridge immersed in turbulent wind flows, including both mean and stochastic, can under certain conditions lead to the degradation of the structure׳s torsional stiffness and ensuing aerodynamic torsional divergence (ATD). It is the incompressibility of the main cables that determines their effectiveness as supporting members be limited in a tension state, and dropping out of either one cable from a tension state could result in the vanish of the torsional stiffness contributed by the whole cable system. Although the physical conception is quite explicit, evaluation of the critical threshold of ATD of a suspension bridge, when experiencing stochastic aerodynamic responses, can be complicated by the deformations of the towers, the lateral oscillations of the deck and cables, and other high-order modes participating in the vibration. In view of this, a criterion based on the tracking of the length of the main cables is presented in this study. It is shown that, with the numerical example, the advent of ATD, the degradation of the system׳s stiffness, as well as some striking post-ATD behaviors, can be well explained with the proposed model by tracking the cable lengths.     

A new three-dimensional Hoek-Brown strength criterion

The Hoek-Brown(HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass,while evolving ever since.However,negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version.At the same time,several three-dimensional(3D) HB strength,which can takes into account the influence of the intermediate principal stress,have already been proposed,among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one.However,the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface.In this paper,a new 3D HB strength criterion is presented based on a generalized form of the HB criterion,which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion.In addition,this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion.Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion.The results show that this new criterion may over-predict or underpredict the polyaxial strength of rocks but the errors are relatively small,and similar results are also found for the Zhang 3D HB criterion,which one is better depends on the type of the rock under estimation.     

SIF-based fracture criterion for interface cracks

The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e.,■ and s~(-iε), so that K = ■ s~(-iε), s is a characteristic length and ε is the oscillatory index. ■ has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with■, as Irwin(ASME J. Appl. Mech. 24:361–364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack,it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor(SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.     

Instability criterion for conservative system equilibrium

International Applied Mechanics -     

Strain-energy failure criterion for rigid-plastic bodies

In the framework of the theory of strain-hardening rigid-plastic bodies, we suggest a strain-energy failure criterion. The strain states of a rigid-plastic body are depicted as points in the principal strain space and form a third-order hyperbolic surface for incompressible bodies. The strain processes are depicted by lines on this surface. The loading surface related to the strain surface lines is introduced, which permits calculating the energy dissipation as a parameter determining the failure.     

Correction of the Gurson yield criterion

The correction in the derivation of the Gurson yield criterion is reported. A prerequisite kinematical condition ignored in Gurson's paper is imposed, and a parameter (C₁), which was unreasonably set to zero, is restored.     

A stress criterion for crack growth

A stress criterion for crack growth was developed from test results with 7075-T6 aluminum-sheet specimens containing transverse machined cracks. Stress distributions near the crack tip were obtained using strain gages and by reducing the strain data to stresses with the aid of Reuss plasticity theory. These distributions indicated the biaxial nature of stress at the crack tip, the high stress gradients a short distance from the tip, and the variation in stress-concentration factor with crack length. Crack growth was found to occur when the effective stress at the crack root reached the engineering ultimate strength.     

传递对准中滤波器的收敛判据

惯性导航系统传递对准结束的判断通常是根据经验以时间作为滤波器的收敛条件,往往过于保守.针对滤波器在传递对准中的应用,基于数据的统计特性,提出了一种利用滤波结果进行收敛性判断的方法.通过滑动计算方法,在线计算滤波结果的统计特征,并通过分析影响收敛判断的因子,得到收敛判断的参数选取方法和收敛判据的阈值条件.对设计的收敛判据分别进行了数学仿真和采用真实数据的半物理仿真,验证了收敛判据的合理性和有效性,证实了采用收敛判据判断可以一定程度上缩短对准时间,提高系统的快速反应能力.     

A yield criterion for perforated sheets

Summary A criterion of yielding for homogenized materials with an internal structure generated by perforation is developed using the stress and the mixed stress-perforation tensor invariants. For a square pattern of perforation an experimental homogenization procedure is used to determine components of the perforation tensor introduced. A yield condition for the studied materials is proposed and compared with experiments conceived and performed for the purpose.

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Übersicht Es wird ein Fließkriterium entwickelt für Materialien mit durch Perforation erzeugter innerer Struktur. Die Herleitung gründet sich auf gemischte Invarianten von Spannungs- und Perforationstensor. Für ein rechteckiges Perforationsmuster wird eine experimentelle Homogenisierung zur Ermittlung der Komponenten des Perforationstensors durchgeführt. Der vorgeschlagene Fließort wird mit experimentellen Ergebnissen verglichen.

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Dedicated to Prof. Th. Lehmann on the occasion of his 60th birthday