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| 非均匀脆性介质破坏的非平衡非线性统计演化 | |
魏宇杰
| |
| Thesis Advisor | 白以龙 |
| 2000 | |
| Degree Grantor | 中国科学院研究生院 |
| Place of Conferral | 北京 |
| Subtype | 硕士 |
| Degree Discipline | 固体力学 |
| Keyword | 系统统计 转变点 涨落 临界敏感性 Weibull Ensemble Statistics Weibull Distribution Transition Point Fluctuation Critical Sensitivity |
| Other Abstract | 在白以龙小组已有工作的基础上，利用他们提出的简化的耦合斑图模型，几种可能的应力重分配模型在该论文中得到了进一步的讨论。通过不同的应力重分配模型，我们发现了该类演化过程中的三个一般规律，这些规律对于类似的动力过程的预报（例如，非均匀介质的破坏）提供了线索。首先，我们采用系综统计的方法，对相同宏观参量的大量样本的强度分布作了考察，结果表明：宏观强度的统计结果可以非常好的拟合为Weibull分布，且其Weibull模数与系统的大小、应力重分配的方式以及细观单元的强度分布相关。其次，在模拟过程中，对演化过程中的能量释放、损伤事件的统计发现，它们存在标度行为，而且这一标度主要归因于灾变点附近的损伤事件。这一现象表明这一转变具有某种临界特征。最后，对于我们模型中的动力学过程，我们发现了灾变预报的线索。从样本演化过程 中的能量释放规律来看，我们发现有两件事是有意义的：一是辨别出主破坏的发生点（在这一时修，系统中的大部分能量得到释放）；另外，给出转变点（整体稳定转化为演化诱致灾变）的预报。对前一个问题，我们通过考察系统在GS和EIC段的应力损伤涨落特征可以给出回答，通常，在EIC段的最大应力涨落（通常出现在主破坏过程中）比在GS过程中的最大应力涨落高一个数量级，根据这一差异，可以设立一个应力涨落的警戒值来判断系统所处的演化状态。对于后者，受到地震预报中采用的加卸载响应比（LURR）的启发，我们通过对系统中的外回转应力或损伤单元施加一个微增扰动，然后，根据系统在扰动前后释放的能量和相应的扰动，就可以得到临界敏感系数，临界敏感系数在灾变点附近迅速增加，在灾变点之迅速下降到1附近-我们称这一特征为临界敏感性。不同的应力重分配模型下得到了类似的现象，由此看来，对于 类似的动力学过程，临界敏感性是一个一般的特征。这一特征可能为我们对非均匀脆性介质的破坏提供线索。; Based on the simplified coupled pattern model developed by Bai group and their works, here, several probable stress re-distribution rule (SRD) were discussed. Three generic properties were found in the simulation under different SRD models, which may provide informative clues for the rupture prediction of similar dynamics, e.g., the rupture of inhomogeneous media. Firstly, we use ensemble statistics to investigate the strengths of a large number of samples with identical macro-parameters, and found that it can be fit as Weibull distribution perfectly. The modulus of Weibull distribution varies with the size of a system, SRD models, and the mesoscopical strength distribution function. Secondly, in our simulation, the statistics of the released energy D(ΔE) and damage events D(Δ) exhibit a power law, and the power law is mainly attributed to the events near the transition point. This is an indication of criticality for the transition. Thirdly, we found the rupture prediction clues for the dynamics in our model. From the energy released phenomenon in the evolution, we found two problem are meaningful. Firstly, how can we distinguish the main rupture (where most energy will be released) in the evolution? Secondly, the prediction of the catastrophic transition point! The former question was answered based on the properties of stress fluctuation and damage fluctuation in GS and EIC. Usually, the magnitude of the maximum stress fluctuation in EIC (which usually appears in the main rupture) is one order higher than that in GS, which can be used as a warning level and give us the status of the evolution. For the latter, inspired by the LURR method used in earthquake prediction, we use a increasing perturbation of nominal stress or damage units to the system. Then, the critical sensitive coefficient can be calculated from the released energy before and behind the perturbation, together with the perturbation, which shows a rapid increasing in the vicinity of the catastrophic transition point and receding to 1.0 beyond the point-we call such a property as Critical sensitivity. Similar phenomena were exhibited under different SRD models. It seems that the critical sensitivity is a common property for those similar dynamics, and the feature might provide clues for rupture prediction of heterogeneous materials. |
| Call Number | 29900 |
| Language | 中文 |
| Document Type | 学位论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/23924 |
| Collection | 力学所知识产出(1956-2008) |
| Recommended Citation GB/T 7714 | 魏宇杰. 非均匀脆性介质破坏的非平衡非线性统计演化[D]. 北京. 中国科学院研究生院,2000. |
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