数值岩石试样破裂过程多重分形特征

采用数值分析的方法和FLAC3D软件,建立服从应变软化关系的非均质岩石试样模型。引入多重分形理论,通过盒计数法计算了单轴加载过程中峰前某一阶段单元体积应变的多重分形谱f(α)。分析了f(α)-α曲线特征参数#f和#α随加载过程的阶段特征,不同均匀程度的岩石试样在临近峰值强度前#α和f(α)max的变化规律。研究结果表明,采用多重分形理论对单元体积应变的空间分布特征进行描述,可以在较大的尺度内满足标度不变性。通过不同的参量进行概率计算得出的f(α)略有不同,但动态变化规律相近,f(α)曲线呈左钩形状,随着载荷的增加#f变大,而#α变小。当不是所有的盒子内都存在可测度的参量时,f(α)max随载荷的增加而增长。对于均匀程度不同的试样,峰前f(α)max与#α随均匀性的增加而减小,但在均匀性较高以后,逼近于某一常数。     

混凝土类材料动态压缩强度在多维应力状态下的应变率效应

对混凝土类材料动态压缩应变率效应研究的发展及问题进行了概述,对比不同应力状态下混凝土类材料动态压缩应变率效应的表现特征,揭示了不同加载路径下实测动态强度提高系数的显著差异。研究表明,在高应变率下,基于初始一维应力加载路径的试件将因横向惯性效应导致的侧向围压而演化至多维应力状态,传统霍普金森杆技术无法获得高应变率下基于真实一维应力路径的动态强度提高系数,在强度模型中直接应用实测数据将过高估计材料的动态强度。鉴于应变率效应的加载路径依赖性,将仅包含应变率的强度提高系数模型扩展至同时计及应变率和应力状态的多维应力状态模型,并结合Drucker-Prager准则在强度模型中给予了实现。针对具有自由和约束边界试件开展的数值霍普金森杆实验表明,多维应力状态下的应变率效应模型可以考虑应变率效应随应力状态改变的特点,从而准确预测该类材料的动态压缩强度。研究结果可为正确应用霍普金森杆技术确定脆性材料的动态压缩强度提供参考。     

动静组合加载作用下花岗岩破碎的分形特征

在分离式霍普金森压杆实验装置上进行了花岗岩破坏的动静组合加载实验.通过对受载后岩样破碎块度进行筛分统计,得到了该加载条件下岩石破碎的粒度分布.在此基础上,通过理论计算公式,进一步得到了相应的破碎分形维数,分别探讨了静载荷和冲击载荷对分维数的影响.结果表明,动静组合加载作用下花岗岩破碎分维值在2.0～2.8之间;相同静载不同动载下,花岗岩的破碎分维值与试样的应变率有关,随应变率增大而增大;而在相同冲击动载下,静载荷变化对分形维数的影响不大.     

不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

混凝土类材料SHPB实验中确定应变率的方法

由于混凝土类材料在SHPB实验中很难实现恒应变率加载，为了确定非恒应变率加载下的实验数据所对应的应变率，本文中针对不同强度（C20，C45，C70）和不同钢纤维含量（0%，0.75%，1.50%，4.50%）的混凝土进行了SHPB实验。对实验得到的30组恒应变率加载下的数据进行了分析总结，结果表明:实验数据所对应的恒应变率与全段平均应变率之间存在一定的比值关系，从而混凝土类材料SHPB实验数据所对应的应变率可以采用全段平均应变率的1.38倍来表征。通过对比非恒应变率加载和恒应变率加载下得到的应力应变曲线，验证了该确定应变率方法的合理性，并指出较短恒应变率加载下实验数据对应的应变率直接采用短平台段对应的应变率来表征是不合理的。     

猪后腿肌肉的冲击压缩特性实验

波形整形技术使试样满足应力均匀条件和恒定应变率加载,石英片检测试样两端的应力均匀性, 获得微弱的透射信号。对开始加载阶段径向惯性效应带来的轴向应力附加值给予了计算修正,得到了肌肉在 不同加载方向和不同应变率下的应力应变曲线。结果发现:肌肉材料的应力应变曲线呈现粘弹性材料所具有 的凹向上特征,由最小显著差数法进行统计分析,发现猪后腿肌肉的力学性能对应变率和加载方向都敏感。 沿纤维方向压缩时肌纤维易发生压缩失稳,强度比垂直纤维方向低。     

帽型试样动态绝热剪切破坏演化分析

利用分离式霍普金森压杆加载Ta2钛合金扁平闭合帽形受迫剪切试样,结合数字图像相关法和“冻结”试样的微观金相观察,研究剪切区剪切应变的演化、绝热剪切带形成条件等。结果显示：受迫剪切试样在动态加载过程,剪切区剪切应变不断集中,形成绝热剪切带,裂纹沿绝热剪切带发展;随加载率提高,绝热剪切起始临界应变减小;进一步利用数字图像相关法DIC场应变分析及金相微观观测对比,利用卸载回复特性对绝热剪切带起始临界条件进行了讨论,计算的绝热剪切带起始时温升仅为86℃。材料软化可能不是绝热剪切带起始的控制条件,相反是由于绝热剪切带形成造成的应变高度集中发展导致温度急剧升高。     

高应变率加载下材料的损伤破碎规律

对材料损伤破碎规律的分析是研究材料损伤断裂行为的一种有效途径。本文着重介绍了高应变率加载下材料损伤破碎规律的研究进展、基于损伤断裂机理的研究以及材料损伤破碎过程自相似性的分形理论研究,讨论了材料损伤破碎规律与材料自身属性和外部加载条件的相互关系。     

准噶尔盆地火成岩动态冲击破碎特征研究

针对准噶尔盆地石炭系火成岩难钻地层,利用改进的立式霍普金森压杆装置,开展了准噶尔盆地石炭系的安山岩、流纹岩、凝灰岩、玄武岩四种火成岩的动态冲击破碎实验;分析了4种冲击速度及不同应变率下火成岩的动态峰值应力、破碎特征;建立了应变率与分形维数的关系。结果显示:动态峰值应力与应变率呈较好的正相关性线性关系,玄武岩在应变率为286.7s~(-1)时,动态峰值应力达到653MPa;随着冲击速度增大,岩石应变率持续增加,所有试样的破碎程度明显增大;在冲击速度为16m/s时,岩石试样应变率在157.8s~(-1)～296.3s~(-1)之间,破碎岩屑的平均破碎块度在16mm以下。分形维数能较好地描述岩石的破碎特征,随着应变率的增大,碎屑分形维数呈增大趋势;当应变率超过157.8s-1时,火成岩试样破碎岩屑的分形维数显著增大至1.5以上;在所有冲击破碎实验中,火成岩试样碎屑没有出现粉末状态。相同冲击条件下,四种火成岩中玄武岩表现出更高的强度,动态峰值应力更高。     

混凝土一维应力层裂实验的全场DIC分析

基于74mm直径分离式Hopkinson杆(SHPB)实验平台进行了混凝土杆的一维应力层裂实验.采用超高速相机(采样频率:2 $\mu$s/frame)结合数字图像相关法(DIC),记录混凝土试件中的动态位移场实时变化情况,探讨了混凝土在拉伸断裂过程中的表面位移场及速度场演化规律.针对实验中出现的多重层裂现象,基于一维应力波传播理论,指出各个位置在发生层裂时,其最大拉应力均由透射压缩波与反射拉伸波叠加而成,各处层裂发生时均处于一维应力状态.并提出了根据层裂位置左右两点速度趋势变化判断层裂发生时刻的判据.该判据可以给出所有层裂的起裂时间,结合DIC分析直接给出了混凝土多重层裂应变.结果显示混凝土的拉伸强度具有明显的应变率效应,在30 s$^{-1}$的应变率下,其拉伸强度的动态增强因子(DIF)可以达到5.与传统的波叠加法和自由面速度回跳法相比,DIC全场分析法不受加载波形限制,可以精确给出每个层裂的位置和起裂时间,从而得到试件在高应变率加载下不同位置处的断裂应变、拉伸强度及相应应变率,提高了测量效率.      

Asymmetric multiscale multifractal detrended cross-correlation analysis for the 1999–2000 California electricity market

In order to access the asymmetric cross-correlation between two time series in a wide range of scales, the method of asymmetric multiscale multifractal detrended cross-correlation analysis (A-MMFCCA) is proposed in this study, which is an extension of the asymmetric detrended fluctuation analysis and the multifractal cross-correlation analysis. Multiscale multifractal detrended cross-correlation analysis enables us to find that the price and the load series of California electricity market exhibit long-range persistent multifractal cross-correlation at different scale ranges during 1999–2000, and the scale range has an important impact on the fractal properties of cross-correlation. Furthermore, the asymmetric cross-correlation between the price and the load series is detected by means of our proposed A-MMFCCA method. Through comparing the local Hurst surfaces with the uptrends and downtrends, we further find that the asymmetric cross-correlation between the price and the load series in 2000 is more significant than that in 1999; the contribution of asymmetric cross-correlation in 1999–2000 mainly depends on different directional trends at different scale ranges. The findings help to interpret the power crisis phenomenon and develop effective and prospective market policy recommendations.     

Weighted multifractal analysis of financial time series

In this paper, we propose the weighted multifractal analysis based on variance-weighted partition function (WMA), to evaluate the fractals of nonlinear time series containing amplitude information. The reliability of the proposed WMA is supported by simulations on generated and real-world financial volatility data. Numerical simulations with synthesized data show that WMA is comparative to the classic partition function-based standard multifractal analysis (SMA) and the multifractal detrending moving average analysis. More importantly, empirical analyses of Chinese stock indices illustrate that WMA outperforms SMA in distinguishing Hang Seng Index form SSE Composite Index and SZSE Component Index qualitatively and quantitatively, showing the power of WMA in discriminating series with distinctive amplitudes.     

Cross-correlations between the CSI 300 spot and futures markets

Financial markets are complex dynamical systems. One of the important features of market dynamics is the existence of cross-correlations between financial variables. Based on the high-frequency transaction prices (every 5 min) data, in this study, we investigate the cross-correlations between China Securities Index 300 (CSI 300) spot and futures markets. Qualitatively, employing a statistical test in analogy to the Ljung-Box test, we find that the cross-correlations are significant at the 1 % level. Quantitatively, using the multifractal detrending moving-average cross-correlation analysis (MF-XDMA) method, we find that the cross-correlations are strongly multifractal. An interesting finding is that the cross-correlation exponent is larger than the averaged generalized scaling exponent for different q, which is different from the general conclusion. Using the method of rolling windows, we find that the cross-correlations are positive over time, which suggests that China’s securities markets are not mature and efficient markets at present.     

MULTIFRACTAL ANALYSIS OF PARTICLE-FLUID SYSTEM IN A CIRCULATING FLUIDIZED BED

In this paper, multifractal analysis together with wavelet transform modulus maxima (WTMM) method is used to analyze the fluctuating signals of circulating fluidized bed (CFB). Singularity spectrum shows that the gas-particle flow in CFB has multifractal character. Motion behavior of the particle-fluid system of CFB can be described by singularity spectrum. Intermittency index can be used to determine the transition of flow regime from fast fluidization to pneumatic conveying.     

Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses

Nonlinear Dynamics - The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of...     

Intermittency and multiscale dynamics in milling of fiber reinforced composites

We have analyzed the variations in cutting force during milling of a fiber-reinforced composite material. In particular, we have investigated the multiscale dynamics of the cutting force measured at different spindle speeds using multifractals and wavelets. The multifractal analysis revealed the changes in complexity with varying spindle speeds. The wavelet analysis identified the coexistence of important periodicities related to the natural frequency of the system and its multiple harmonics. Their nonlinear superposition leads to the specific intermittent behavior. The workpiece used in the experiment was prepared from an epoxy-polymer matrix composite reinforced by carbon fibers.     

Analysis of Cross Correlations Between Well Logs of Hydrocarbon Reservoirs

We carry out a series of cross-correlation analysis of raw well-log data, in order to study the possible connection between natural gamma ray (GR) logs and other types of well logs, such as neutron porosity (NPHI), sonic transient time (denoted usually by DT), and bulk density (RHOB) of oil and gas reservoirs. Three distinct, but complementary, methods are used to analyze the cross correlations, namely, the multifractal detrended cross-correlation analysis (MF-DXA), the so-called Q _cc(m) test in conjunction with the statistical test—the χ ²(m) distribution—and the cross-wavelet transform (XWT) and wavelet coherency. The Q _cc(m) test and MF-DXA are used to identify and quantify the strength of long-range cross correlations between the porosities derived based on the NPHI, DT, and RHOB logs on the one hand, and the GR log that is indicative of the presence of clay minerals in reservoir rocks, on the other hand. The Q _cc(m) test describes qualitatively the presence of such cross correlations between the porosity and GR logs. Analysis by the MF-DXA method also indicates that the various porosity logs, the GR log, and the cross correlations between them are multifractal, hence confirming the long-range nature of the correlations. The results are confirmed further by the XWT, and indicate that the porosities estimated based on the NPHI logs are only weakly, if at all, affected by the natural GR radioactivity of reservoir rock and are, therefore, most reliable. The effect of length scale on the correlations and cross correlations was studied in detail. It is shown that such correlations exist at all length scales, and that they are of multifractal type that must be characterized by a spectrum of exponents.     

铝-铝爆炸焊接界面剪切行为与断口形貌关系研究

为了研究爆炸焊接界面的剪切损伤行为,本文对铝-铝复合材料开展剪切试验,并基于分形理论对试件剪切断口界面进行表征,尝试建立界面剪切强度与断口轮廓分维值及其多重分形谱关系。结果表明,焊接界面剪切强度随加载速率升高而降低,异于通常金属剪切行为;但从断口形貌及其轮廓分形维可认识界面剪切强度变化原因。此外,多重分形谱起点与终点间的高度差和跨度差值反映了界面的峰、谷落差及分布特征,是界面形貌特征的立体反映,并在数值上也与剪切强度正相关。     

Le modèle des peaux entropiques en turbulence développée

A geometry called entropic skins has been recently proposed to describe and interpret the phenomenon of intermittency in fully developed turbulence. It is shown that the entropic skins model represents the geometrical counterpart of the She–Lévêque's model but with a different interpretation for the main parameters. The comparison with the multifractal approach shows that this is a new geometrical framework of intermittency.