Fixed point theorems in probabilistic inner product spaces

The purpose of this paper is to introduce a new maditying detinition for probabilistie inner product space, and to establish seveeral new fixed point theorems for mappings on such kind of spaces, As an example of applications. we utilize the results of this paper to study the existence and uniqueness of solution of Uryson’s integral equation in IV.     

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.     

Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.     

Relationship between refined Griffith criterion and power laws for cracking

Rice [J. Mech. Phys. Solids 26 (1978) 61] proposes a refined Griffith criterion, at any local crack front, where G is the Irwin's energy release rate, γ is the surface free energy and is the rate of crack advance. The refined version implies that the entropy production inequality should holds locally rather than globally from the thermodynamic point of view. Within the irreversible thermodynamic framework developed by Rice [J. Mech. Phys. Solids 19 (1971) 433; Constitutive Equations in Plasticity, 1975, p. 23], it is revealed in this paper that the entropy production inequality holds for each internal variable if its rate is a homogeneous function in its conjugate force. It is further shown that widely-used power laws for crack growth are just certain homogeneous kinetic rate laws, so it is concluded that the power laws directly lead to the refined Griffith criterion.     

PREDICTION OF MODE Ⅰ CRACK PROPAGATION DIRECTION IN CARBON-FIBER REINFORCED COMPOSITE PLATE

A newly developed Z fracture criterion for the composite materials was introduced,the new concepts of in-plane average strain,in-plane dilatational strain energy density factor and reciprocal characteristic function were presented.Many experimental results show that the Z fracture criterion can be well used to predict the crack propagating direction for mode Ⅰ crack in carbon-fiber reinforced composite laminates.     

基于SMP破坏准则的饱和砂土弹塑性本构模型

利用土体的塑性流动理论，提出了用于描述饱和砂土在单调荷载作用下的应力一应变反应性质的弹塑性本构模型。土体总的变形由三部分组成：即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变，其中与剪切屈服机制相关的塑性应变的得出是基于SMP破坏准则。通过将模型预测的结果与试验结果进行对比，表明该模型能够较为准确地描述饱和砂土在单调加载条件下的反应性质。     

直杆塑性动力屈曲的双特征参数解

在关于轴向弹塑性压缩波下直杆塑性动力屈曲的研究中,将临界应力和屈曲惯性项指数参数作为一对特征参数求解.由动力屈曲发生瞬间的能量转换和守恒准则,导出波阵面上的屈曲变形补充约束条件.失稳控制方程、边界条件、塑性波阵面上的连续条件和补充约束条件构成定量求解两个特征参数和动力屈曲模态的完备条件.     

一种考虑静水压力和偏应力共同作用的相变临界准则

同时考虑静水压力和偏应力的影响,分别建立了"应力诱发"和"形变诱发"相变的临界准则.准则在主应力空间中给出的相变临界曲面呈现明显的拉压不对称性.在弹性阶段,偏应力对相变总是起促进作用.塑性屈服后,偏应力通过塑性功产生的温升影响相变临界面,从而对高温相到低温相转变起阻碍作用,反之起促进作用.静水压力对相变可能起促进作用,也可能起阻碍作用,取决于相变时材料的体积是膨胀还是收缩.建立的相变临界准则对准静态加载条件下的Fe-20%Ni-0.5%C合金和Fe-30%Ni合金和一维应变冲击条件下的Fe-32%Ni-0.035%C合金中的γ-α相变进行了拟合和预测,预测与实验结果有较好的吻合.在主应力空间中柱形屈服面可能与锥形相变临界面相交,从而在一定条件下将发生"形变诱发"相变和"应力诱发"相变间的转变,这一推论有待实验的验证.     

压缩载荷作用下岩石类材料的断裂模式研究

为了解岩石类材料在压缩条件下的裂纹扩展规律,本文对含有内部倾斜裂纹的石膏板试件进行了双轴压缩实验. 研究表明:在通常情况下岩石裂纹按I 型张拉模式扩展,但随着裂纹表面摩擦系数μ和围压与纵向荷载比值λ的提高,翼裂纹扩展的偏转角随之减少.当裂纹表面摩擦系数和围压与纵向荷载比值足够大时,例如,μ=0.83和λ=0.315,岩石裂纹按Ⅱ型剪切模式扩展.然而,当裂纹表面摩擦系数和围压与纵向荷载比值进一步增加时,石膏板试件将发生强度破坏.本文提出了一个理论模型用以解释和描述这一实验现象.     

广义双剪应力准则角隅模型

本文将广义双剪应力准则变换为π平面和静水应力轴的柱坐标方程,然后将其角隅光滑化,得到了新的光滑、外凸的广义双剪应力准则角隅模型,研究结果表明,近年来作为光滑化Mohr-Coulomb理论提出的各种角隅模型,实际上并不是光滑化的Mohr-Coulomb理论,而是光滑化的广义双剪应力理论。