非线性断裂动力学中的路径无关积分和断裂准则

本文考虑非线性断裂动力学中的路径无关积分和断裂准则.在讨论中计入了动力效应和裂纹的传播现象,考虑了裂纹在非线性弹性介质中的传播以及在弹塑性介质中的传播二种情况,作出了一些相应的路径无关积分.作为例子.讨论了裂纹的定常传播情况.最后,给出了这种路径无关积分的力学意义.说明它可用来作为非线性断裂动力学的一种断裂准则.     

论非线性连续介质热-力耦合系统中的动力裂纹传播

在许多工程问题中,热-力耦合是重要的,而不能加以忽略.核反应堆工程就是这样的一个例子.本文讨论非线性连续介质的热-力耦合系统中的裂纹传播问题.各种的非线性介质,包括非线性弹性、弹塑性介质,被加以考虑,并且给出了相应情况下的各种路径无关积分.为了解释这些积分的物理含义,通过考虑一个缺口试件的裂纹传播,证明热-力耦合系统中的动力裂纹扩展力就等于这一路径无关积分.因此,就可利用这些积分来构作热-力耦合系统断裂动力学的非线性断裂准则.     

复合材料平面断裂中的J积分

本文采用复变函数方法,首先将裂纹尖端应力和位移代入J积分的一般公式得到了线弹性正交异性复合材料单向板复合型裂纹尖端的J积分的复形式,其次证明了该J积分的路径无关性,最后推出了该J积分的计算公式.作为特例,给出了线弹性正交异性复合材料单向板Ⅰ,Ⅱ型裂纹尖端的J积分的复形式,路径无关性和计算公式.     

线弹性正交异性复合材料板Ⅰ,Ⅱ型裂纹尖端的J积分

本文借助于复变函数方法,通过将J积分化为复形式,首先证明了线弹性正交异性复合材料板Ⅰ、Ⅱ型裂纹尖端附近的J积分的路径无关性,继而推出了该J积分在Δ<0和Δ>0两种情况下的计算公式.这对于将J积分应用于复合材料平面断裂的理论研究和实验校核中去,具有一定的参考价值.     

关于复合材料单层板裂纹尖端的J积分

该文采用复变函数方法,通过将裂纹尖端的应力和位移代入J积分的一般公式,推出了线弹性正交异性复合材料单层板受对称载荷作用的非弹性主方向的裂纹尖端犑积分的复形式－ 复变函数积分的实部,证明了该J积分的路径无关性,得到了它的具体计算公式     

幂律非线性粘弹性材料中的裂纹扩展*

对蠕变不可压幂律非线性粘弹性材料中裂纹的蠕变扩展进行了分析,为描述银纹带中的力学行为,假设在裂纹尖端邻域中断裂过程区中分布着阻抗裂纹张开的粘聚应力б_f,.通过对均匀应力参考状态平凡解的摄动,将非线性粘弹性问题化成线性问题处理.对于幂指数.n≌1的弱非线性情况得到了应力与位移表达式.提出断裂过程区局域能量判据,导出了裂纹孕育时间t*与蠕变扩展率a的预测公式.     

层状陶瓷的材料力和裂纹力评估方法

用J积分理论分析了层状陶瓷受弯曲载荷作用时J_(far(0)),J far(a),J_(far(a))-J_(far(0))和J_(tip)的特点,这里J_(far(0)),J_(far(a))分别表示无裂纹时和裂纹长度为a时的远场J积分,J_(tip)表示裂尖J积分.裂纹是垂直于界面的表面裂纹,基本假设是裂纹只影响局部应力应变场.由于积分路径所包围的材料界面长度随积分路径变化,导致J_(far(0))和J_(far(a))都随积分路径变化,但当积分路径远离裂纹影响区域时J_(far(a))-J_(far(0))不再随路径变化.J_(far(a))-J_(far(0))可作为非均匀材料断裂的远场驱动力参量,J_(tip)-(J_(far(a))-J_(far(0)))可用来评价材料非均匀性对裂纹扩展驱动力的促进或抑制作用.     

一类奇异二阶边值问题的正周期解

考察了一类奇异二阶周期边值问题,其中非线性项f(t,u)是局部Caratheódory函数.主要工具是高度函数,它描述了非线性项f(t,u)在有界集合上的增长特性.通过考察高度函数的积分获得了单个或多重正解存在的几个充分条件.我们的工作表明这种存在性与非线性项f(t,u)在u=0附近的性质无关.     

层状弹性材料界面J积分的产生和特征

层状弹性材料的裂纹方向垂直于界面时,沿围绕裂尖的任意一条封闭路径Γ的J积分（J_Г）由两部分组成,J_Г=J_tip+J_int,这里J_tip表示裂尖产生的J积分,J_int表示Γ所包围的界面产生的J积分.裂尖产生的J积分不随Γ变化,物理含义是裂纹扩展能量释放率;界面产生的J积分随Γ变化,物理含义与裂纹扩展能量释放率无关.界面J积分的产生使J_Г失去了路径无关特性,也失去了实际物理意义.为了有助于理解非均匀材料J积分的含义和局限性,分析了层状弹性材料界面J积分的产生原因和特点.由不同均匀弹性材料组成的层状材料中,应变能密度的跳跃是界面J积分产生的原因,而弹性模量和残余应力在界面处的跳跃可使应变能密度在界面处产生跳跃.层状弹性材料的界面J积分之间具有相互抵消的作用.     

关于含裂纹的复合材料的一个细观断裂模型

本文研究复合材料的小范围屈服断裂过程.首先,提出了含裂纹复合材料的一个细观断裂模型,其中对裂纹顶端的外部地区采用连续介质各向异性描述,对裂纹顶端的小范围地区则采用多相的描述.多相区中考虑三种材料成分,即纤维、界面和基体,它们都可被看作是非线性的,并计入有限变形的影响.我们应用边界层——非线性有限元方法作出本问题的解.     

Global approaches for accurate loading analyses and crack path predictions at single and two-cracks systems

Based on the work by Eshelby, the path-independent J_k-, M-, L- and interaction- or I_k-integrals were introduced and applied to cracks for the accurate calculation of crack tip loading quantities. Applying the FE-method to solve boundary value problems with cracks, numerically inaccurate values are observed within the crack tip region affecting the accuracy of local approaches. Simulating crack paths, local approaches face further problems as cracks are running towards interfaces, internal boundaries or other crack faces. Within global approaches, path-independent integrals are calculated along remote contours far from the crack tip, essentially exploiting numerically reliable data requiring special treatment only for the near-tip crack faces. To provide path-independence, additional integrals along interfaces, internal boundaries and crack faces are necessary. In this paper, new global approaches of path-independent integrals are presented and applied to the calculation of crack paths at two-cracks systems. A second focus is directed to the accurate loading analysis and crack path prediction considering anisotropic properties and material interfaces. The numerical model provides crack paths which are in good agreement with those obtained from crack growth experiments. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Induced Surfaces and Their Integrable Dynamics

A method is considered to induce surfaces in three-dimensional (pseudo) Euclidean space via the solutions to two-dimensional linear problems (20 LPs) and their integrable dynamics (deformations) via the 2 + 1-dimensional nonlinear integrable equations associated with these 2D LPs. Coordinates X_i of the induced surfaces are defined as integrals over certain bilinear combinations of the wave functions ψ of these 20 LPs. General formulation as well as three concrete examples are considered. Some properties and features of such induction are discussed. Three-dimensional Riemann spaces associated with 2 + 1-dimensional nonlinear integrable equations are considered also.     

Nonlinear stochastic integration with a non-smooth family of integrators

We consider nonlinear stochastic integrals of Itô-type w.r.t. a family of semimartingales which depend on a spatial parameter. These integrals were introduced by Carmona/Nualart, Kunita, and Le Jan. The extension of the elementary nonlinear integral is based on the condition that the semimartingale kernel has nice continuity properties in the spatial parameter. We investigate the case that continuity is not available and suggest different directions of generalization. This brings us beyond the case that any integral can be approximated by integrals with integrands taking only finitely many values.     

非线性系统有理首次积分的不存在性和部分存在性

该文的目的是给出一般非线性系统存在和部分存在有理首次积分的判别准则. 作者给出系统存在有理首次积分的必要条件, 在此基础上进一步给出系统不存在其它有理首次积分(在函数独立的意义下)的判定准则.     

A unique graph of minimal elastic energy

Nonlinear functionals that appear as a product of two integrals are considered in the context of elastic curves of variable length. A technique is introduced that exploits the fact that one of the integrals has an integrand independent of the derivative of the unknown. Both the linear and the nonlinear cases are illustrated. By lengthening parameterized curves it is possible to reduce the elastic energy to zero. It is shown here that for graphs this is not the case. Specifically, there is a unique graph of minimal elastic energy among all graphs that have turned 90 degrees after traversing one unit.