钢筋混凝土结构破坏过程的近场动力学模拟

采用近场动力学(Peridynamics,PD)方法对钢筋混凝土结构破坏过程进行模拟,在"键"型近场动力学模型的基础上,考虑物质点对间的转动以突破泊松比的限制,采用能够描述混凝土材料的拉压异性和断裂特征的损伤模型,引入动态松弛、分级加载、平衡收敛准则和冲击接触等算法,建立了能准确描述钢筋混凝土结构破坏的近场动力学模型....     

近场动力学框架下的键基对应模型

传统键基近场动力学模型存在泊松比限制的问题,为了解决这一问题发展了态基近场动力学模型。其中非常规态的近场动力学模型通过定义非局部的变形梯度将近场力和传统应力关联起来,方便使用传统本构,但是态基近场动力学计算效率低于键基近场动力学。结合态基模型和键基模型的优势,提出键基对应模型,定义了基于键的变形梯度,参考连续介质力学中变形梯度的极分解过程,将键的变形分为转动部分和伸长部分。从而进一步定义了应变,通过物理方程求应力,进而计算键传递的近场力。键基对应模型解决了键基近场动力学的泊松比限制问题,也不需要进行近场动力学微观材料常数的计算。数值算例和理论推导证明了键变形梯度定义以及近场力计算方式的正确性。     

基于改进型近场动力学方法的混凝土梁破坏分析

基于非局部近场动力学(PD)理论,在常规微弹脆性(PMB)本构模型基础上,引入能够反映物质点间作用强度随物质点间距变化规律的核函数修正项,以提高PD方法的定量计算精度;并通过附加物质点转动自由度建立以双参数描述的PD微极模型,突破了常规单参数PMB本构模型的泊松比限制等缺陷。通过引入动态松弛算法和粒子系统失衡力准则等系列数值算法,构建了能够自然模拟准脆性裂纹扩展全过程的PD算法体系。经典悬臂梁挠度曲线计算结果表明,本文模型和算法的定量计算误差小于3.5%,对含切口三点弯梁的裂纹扩展过程模拟结果与试验结果吻合。通过改变加载位置和初始裂纹位置,对三点弯梁的破坏模式和承载能力进行了分析。结果表明,裂纹始终由初始裂纹位置向加载位置扩展,且初始裂纹位置和加载位置越靠近三点弯梁中部时,结构的承载能力越低。     

动载作用下复合型裂纹扩展的近场动力学模拟

构建改进的非局部近场动力学模型和粒子系统动力加载算法,开展复合型裂纹动力扩展过程模拟。在常规近场动力学微极模型中引入能反映非局部长程力尺寸效应的核函数修正项,以提高计算精度和收敛稳定性。通过模拟动载作用下含复合型裂纹混凝土三点弯梁的裂纹扩展与破坏过程并与试验结果对比,验证了本文模型和算法的可靠性。在此基础上,通过分组模拟分析了动载作用下,初始裂纹的位置、长度和方向对含复合型裂纹三点弯梁破坏模式、起裂时间与承载能力的影响规律。     

水力劈裂问题的态型近场动力学建模

将态型近场动力学理论引入水力劈裂问题的模拟。构建了能反映岩土类材料准脆性断裂特征的态型近场动力学本构模型,并在物质点间相互作用力模型中加入等效水压力项,以实现在新生裂纹面上跟踪施加水压力。同时,考虑裂纹面间的接触,引入物质点间的短程排斥力作用,并设计了相应的接触算法。通过自编程序将模型和算法应用于含初始裂纹、不含初始裂纹以及含坝基软弱结构面的混凝土重力坝在高水头作用下的水力劈裂过程模拟,并与扩展有限元等模拟结果对比,验证了本文模型和算法的可行性和准确性。     

高温断裂力学的研究进展及其应用

在石油化工、化工和电力工业中，高温下服役的构件发生断裂失效事故常有报道。失效分析表明高温构件的失效与构件中存在的裂纹状缺陷有直接的关系，而且多数由蠕变裂纹的扩展引起的失效。     

基于近场动力学的薄板弯曲大变形及断裂分析

薄板结构仅在较小的荷载下就能产生较大的位移、旋转,甚至引发结构产生裂纹并扩展,进而发生结构整体断裂,因此,建立薄板结构在大变形过程中的裂纹扩展及断裂仿真模型,具有重要的工程实际意义.文章建立了用于薄板结构几何大变形和断裂分析的近场动力学(PD)和连续介质力学(CCM)耦合模型.首先基于冯·卡门假设,采用更新的拉格朗日法得到薄板在几何大变形增量步下的虚应变能密度增量公式,并利用虚功原理和均质化假设求出几何大变形微梁键的本构模型参数;接着分别建立几何大变形薄板PD模型与CCM模型的虚应变能密度增量,并建立了薄板几何大变形PD-CCM耦合模型;最后模拟了薄板结构在横向变形作用下的渐进断裂过程,得到与实验结果高度一致的仿真结果,验证了所提出的几何非线性PD-CCM耦合模型的精度.结果表明:本文所提出的薄板PD-CCM耦合模型具有简单高效,无需考虑材料参数限制和边界效应的特点,可以很好地用于预测薄板结构在几何大变形过程中的局部损伤和结构断裂,有利于薄板结构的断裂安全评价和理论发展.     

基于近场动力学理论的单层板损伤分析方法

基于键基近场动力学理论（PD）构建复合材料的单层板模型,在本构方程中引入连续变化的键刚度,以表示复合材料中与纤维夹角相关的力学性能的变化。推导了与复合材料主方向热膨胀系数相关的任意方向的热膨胀系数,为热载荷的施加提供理论支持,将热载荷和力学载荷统一于本构方程中。最后,对预先存在裂纹的单层板进行裂纹扩展模式的仿真,得到预期的仿真结果,并与已有实验结果对比验证模型的有效性。     

混凝土复合型裂纹扩展的非局部近场动力学建模分析

基于非局部近场动力学理论,构建了修正的能反映混凝土宏观拉压异性和断裂特征的近场动力学本构模型,开发了相应的离散、加载和时间积分算法,实现典型混凝土构件中复合型裂纹扩展过程模拟。在物质点对尺度上定义局部损伤并考虑物质点对的相对转动,通过求解时空微-积分方程实现裂纹的自然萌生与扩展,避免裂尖不连续带来的求解奇异性、网格依赖性和网格重构以及常规近场动力学本构模型的泊松比限制。通过含单边和双边初始裂纹四点剪切混凝土梁裂纹扩展破坏全过程模拟,得到破坏形态、破坏荷载以及完整的荷载-裂纹开口滑移曲线,并与试验和其他数值模拟结果对比,验证了模型的精确性和算法的稳定性。     

基于态型近场动力学的淬火陶瓷破坏过程分析

基于态型近场动力学理论进行复合陶瓷板淬火破坏过程力学建模与分析。引入热膨胀项反映材料的热致变形,基于物质点对的断裂定义损伤,构建三维非局部常规态型近场动力学热弹脆性模型,结合多速率显式积分法计算热-力耦合,实现热冲击荷载作用下陶瓷板起裂和裂纹扩展全过程的模拟。通过模拟典型淬火Al₂O₃陶瓷板的破坏过程,并与实验和其他数值结果对比,验证了该模型和方法。使用该模型研究了含不同α-Al₂O₃纤维掺杂比率的Al₂O₃复合陶瓷板淬火破坏过程,结果表明,断裂韧性的提高显著减少了裂纹数量并延后起裂时间;含5%α-Al₂O₃纤维掺杂比率的复合陶瓷材料综合力学性能最优,能够有效提升构件抵抗热冲击荷载能力。     

Uniqueness in brittle fracture mechanics

It is shown that the boundary initial value problem of brittle fracture mechanics has, at most, one solution in the class of all vector fields having finite energy at each instant. No definite assumption on the elasticity tensor is made.     

三维计算断裂力学

断裂力学理论从1921年Griffith研究玻璃的脆性断裂问题开始,经历了从线弹性体系到弹塑性以及蠕变理论体系、从单参数到多参数体系和从理想的二维平面理论到实际三维含裂纹结构的三维断裂理论的发展历程。针对应力强度因子K和J积分以及C(t)积分的计算方法从理想化模型的理论计算发展到实际复杂工程结构裂纹体计算的各种商业软件平台以及专业的断裂理论分析平台。尤其是随着计算机技术的发展,对三维含裂结构的静态和扩展裂纹的计算模拟已经能够融入计算机辅助设计。结合本研究组近30年来在三维疲劳断裂理论和应用研究方面的体会,简述了三维计算断裂力学从裂纹体应力应变分析和断裂参数计算到三维蠕变断裂和疲劳裂纹扩展模拟的国内外进展,并对涉及的计算方法,包括原子尺度和跨尺度的计算模拟,以及目前面临的挑战性问题作了简要介绍和分析。     

On discrete models in fracture mechanics

In two papers published in 1969, where the foundations of the theory of brittle fracture were laid, Valentin Valentinovich Novozhilov introduced a necessary and sufficient criterion for estimating the strength of an elastic body weakened by a cut and formulated the concept of brittle fracture. The criterion is based on taking account of the body discrete structure, and the fracture process is treated as loss of stability of elastic equilibrium. These two facts, fracture discreteness and loss of stability in the deformation of the breaking bond, underlie numerous phenomena, which could not be discovered in the framework of continuum mechanics. In the present paper, the following effects of taking these facts into account are briefly discussed: an unstable leg of the stress-strain diagram and the capture of part of the fracture energy by the lattice, the role of the lattice dimension, radiation in quasi-static and dynamic crack propagation including the radiation structure, the role of the dynamic factor, irregularities in the crack growth, crack propagation under the action of high-frequency waves including steady-state modes with periodically varying speed, and cracks in continuum discrete models.     

Error analysis of photoelasticity in fracture mechanics

An error analysis of the use of photoelasticity in the study of fracture problems is attempted. In particular, it was desired to determine the optimum regions of data collection and to ascertain the sensitivity of the extractedK ₁ andK ₂ values to errors in such parameters as crack-tip position and fringe location. Experiments were performed on both Mode 1 and Mixed Mode cases and the results compared with the error analysis     

Use of three-dimensional photoelasticity in fracture mechanics

The philosophy of fracture mechanics is reviewed and utilized to formulate a simplified approach to the determination of the stress-intensity factor photoelastically for three-dimensional problems. The method involves a Taylor Series correction for the maximum in-plane shear stress (TSCM) and does not involve stress separation. The results are illustrated by applying the TSCM to surface flaws in bending fields. Other three-dimensional problems solved by the TSCM are cited.     

Formulation of problems in dynamic fracture mechanics

This note presents an analysis of the standard formulation of dynamic fracture mechanics problems. It is shown that this formulation does not correspond to the physics of such problems. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 3–9, June, 1999.     

Applications of holography to fracture mechanics

In the development of a theory of fracture mechanics for ductile metals, the role of the zone of constrained plastic deformation which forms in the region of a high stress concentration is of fundamental importance. Consequently, experimental studies of this plastic zone are of considerable interest and have attracted the attention of many investigators using many techniques. The present study represents an effort to extend the interferometric technique through the use of laser holography. In this work, a lens-less picture or hologram of each fracture specimen was exposed while the specimen was under nominal load in the testing frame. After development, the hologram was replaced and illuminated so as to superimpose the reconstructed specimen image on the actual specimen. As a result, subsequent minute deformations of the specimen produced by changes in the applied load result in the formation of readily observable fringe patterns. Theoretically, if sufficient care is taken in positioning the hologram and if the fringe distribution can be measured with sufficient accuracy, a quantitative three-dimensional determination of surface deformations could be made. The photographs taken in this study, while lacking the rigor demanded by the preceding conditions, nevertheless illustrate the nature of this technique and provide a quantitative one-dimensional measure of out-of-plane surface movement.