共查询到20条相似文献，搜索用时 890 毫秒
1.
If the particle paths are known for deforming continuous media such as rocks, the strain is determined at all stages of the deformation. The particle paths are studied for various types of simultaneous combinations of pure shear and simple shear. Any kind of progressive plane homogeneous strain can be expressed as a simultaneous superposition of pure shear and simple shear by selecting the proper ratio between the two strain rates and the proper angle between the slide direction of the simple-shear part and the principal axes of the pure-shear part. In the cases studied — except one — the angle between the slide direction of the simple-shear part and the principal strain rate
of the pure-shear part is 45°. Several combinations of the simple-shear rate, γ, and the pure-shear rate,
, are tested. These combinations give particle paths varying from sets of straight parallel lines to orthogonal hyperbolas. Distorted hyperbolas, ellipses and circles constitute the particle paths at intermediate
ratios. From the particle-path equations — which are found by integration of the rate-of-deformation equations — the strain ellipse is readily determined at any stage of the deformation. One particularly intriguing result is the rotating and pulsating strain ellipse found in the cases when the particle paths are closed curves (ellipses). Application of the results to various fold-, thrust- and inclusion structures is suggested. In an appendix the treatment of rotational deformation as a superposition of irrttational strain and rigid rotation is considered for comparison. 相似文献
2.
The deformation matrix and the deformation ellipsoid 总被引：1，自引：0，他引：1
Derek Flinn 《Journal of Structural Geology》1979,1(4):299-307
Homogeneous strain can be computed most easily by the methods of matrix algebra. Lines, planes and ellipsoids represented in matrix form can be homogeneously deformed by simple matrix multiplication by linear transformation matrices, the elements of which are the coefficients of the transformation equations. Deformation matrices or linear transformation matrices which cause geological-type homogeneous strain are divided into four classes based on the presence or absence of symmetry and/or orthogonality. The nature of the homogeneous strain caused by each class of deformation matrix is examined. Orthogonal-symmetrical and orthogonal matrices cause rotation. Symmetrical matrices cause irrotational strain with co-axial strain as a special case. Matrices which are neither orthogonal nor symmetrical cause many different types of rotational strain, some of which are examined. 相似文献
3.
Juan Ignacio Soto 《Mathematical Geology》1997,29(1):93-130
A deformation that is obtained by any simultaneous combination of two steady-state progressive deformations: simple shearing
and a coaxial progressive deformation, involving or not a volume change, can be expressed by a single transformation, or deformation
matrix. In the general situation of simple shearing in a direction non-orthogonal with the principal strains of the coaxial
progressive deformation, this deformation matrix is a function of the strain components and the orientation of shearing. In
this example, two coordinate systems are defined: one for the coaxial progressive deformation (xi system), where the principal and intermediate strains are two horizontal coordinate axes, and another for the simple shear
(x
i
t’
system), with any orientation in space. For steady-state progressive deformations, from the direction cosines matrix that
defines the orientation of shear strains in the xi coordinate system, an asymmetric finite-deformation matrix is derived. From this deformation matrix, the orientation and
ellipticity of the strain ellipse, or the strain ellipsoid for three-dimensional deformations, can be determined. This deformation
matrix also can be described as a combination of a rigid-body rotation and a stretching represented by a general coaxial progressive
deformation. The kinematic vorticity number (W
k is derived for the general deformation matrix to characterize the non-coaxiality of the three-dimensional deformation. An
application of the deformation matrix concept is given as an example, analyzing the changes in orientation and stretching
that variously-oriented passive linear markers undergo after a general two-dimensional deformation. The influence of the kinematic
vorticity number, the simple and pure shear strains, and the obliquity between the two deformation components, on the linear
marker distribution after deformation is discussed. 相似文献
4.
5.
V.K. Gairola 《Tectonophysics》1977,41(4):291-319
Experiments have been carried out to study the orientation and values of the three principal extensions during folding, and to investigate the nature of the deformation paths of the strain ellipsoids at the fold hinges. Single layers embedded in a matrix were deformed by plane strain pure shear with the layers obliquely inclined to the axes of the bulk strain. The strains on the outer and inner arcs of the fold hinges were measured by means of grids on the layer surfaces. The orientation and values of three principal strains during folding depend on the layer orientation and the degree of deformation, and may be different on the outer and the inner arcs. The deformation paths in the outer arc are generally in the constriction field and those in the inner arc lie in the flattening field. The deformation paths have been computed by analyzing the manner by which components of layer shortening, tangential longitudinal strain and elongation parallel to the fold-hinge line combine to give the finite strain. 相似文献
6.
Performance-based design demands accurate prediction of soil deformation under a working load condition. The nonlinear stress–strain behavior needs to be analyzed quantitatively to advance the understanding of complex soil behavior in the pre-failure condition. The singular value decomposition technique is introduced to quantitatively analyze the compliance matrix representing the strain response envelope (SRE). The rotation of the ellipse of the SRE relates to the anisotropic response of the soil deformation. The off-centered SRE provides evidence of the kinematic hardening plasticity. Quantitative data on the movement of SREs provide us with crucial information to investigate the effect of stress history and the evolution of stiffness anisotropy in soil deformation. 相似文献
7.
被动椭圆形标志物应变分析的计算机模拟 总被引：1，自引：0，他引：1
本文采用计算机数学模拟的方法更深入地探讨了椭圆形标志物应变分析技术(R_f/Φ去应变法、Shimamoto等提出的代数法、调和平均值法和算术平均值法)的适用条件。一共形成了十一组有代表性的应变前数组,四种变形路径:纯剪、单剪、纯剪加单剪和体变。当应变前数组在(-90°,90°)内均匀分布或随机分布时,无论变形路径是哪一种(共轴的还是非共轴的),上述的所有方法都是适用有,且以代数法最佳。当应变前数组具有优选方位(单峰分布)且变形路径为共轴递进变形时,在一定条件下,R_f/Φ法能用来估计应变。经分析发现当应变足够大时,调和平均值法是一种简单快速的应变计算法。 相似文献
8.
Numerical simulations have been performed to investigate the strain-dependent behaviour of rheological and kinematical responses to flow of two-phase rocks using the commercial finite-difference program FLAC2D. It was assumed that the two phases have Maxwell rheology. Plane strain and velocity boundary condition, which produces a simple shear deformation, were also assumed. Two types of geometries were considered: strong phase supported (SPS) and weak phase supported (WPS). We calculated strain-dependent variations of effective viscosity and partitioning of strain rate, vorticity and kinematic vorticity number during deformation in both SPS and WPS structure models.The results show that the strain-dependent behaviour is largely influenced by the geometry of the composite. SPS models show both strain hardening and strain softening during the simulations, with strain hardening preceding strain softening. A critical shear strain is necessary to begin the strain softening behaviour. Strain hardening and strain softening are accompanied by a reduction and an increase of the partition of strain rate into the weak phase, respectively. On the other hand, WPS models show only weak strain hardening and strain softening, being the strain-dependent behaviour close to a steady state flow. In addition, the following results are obtained on vorticity and kinematic vorticity number; (1) in both SPS and WPS models the partition of vorticity into weak phase increases with progressive shear strain, i.e. the strong phase becomes less rotational, (2) in SPS models weak inclusions changes from sub-simple shear to super-simple shear with progressive strain, whereas the strong matrix changes from super-simple shear to sub-simple shear, (3) in WPS models the strong inclusions with high viscosity contrasts are less rotational but can be in super-simple shear condition to high strains.The observed strain-dependent behaviours have been compared with previous proposed analytical models. The degree of agreement is variable. Balshin and Ryshkewitch–Duckworth models are only applicable to SPS models. Ji-generalized mixture rule model is applicable to both models.The results suggest that polyphase rocks with SPS structure during ductile shear deformation respond as strain softening materials, after an initial strain hardening stage that may drive to the strain localization into the material. 相似文献
9.
本文讨论了一种新的数学工具,即惯量投影椭球（和椭圆）,在具有任意形状构造变形体的变形描述与应变分析中的意义。论证了在均匀的递进变形过程中,构造标志体惯量投影椭球的变形与其自身的变形保持一致,两者遵循同样的均匀变形方程。在进行构造变形描述和分析时,构造标志体形状与其惯量投影椭球是等效的。惯量投影椭球具有有限应变椭球相同的性质,可以用来描述任意形状构造标志体的变形,并可以替代具有任意形状构造标志体进行变形分析。先前适用于椭圆形标志体变形分析的方法均可应用于具有任意形状的构造标志体。这将为我们对具有任意形状的构造标志体变形的描述和分析提供方便和有用的数学工具。 相似文献
10.
岩石有限应变测量反向轮法的计算机CSD软件设计 总被引：4，自引：0，他引：4
用计算机实现反向轮法测岩石有限应变的过程, 可提高有限应变测量的准确性和效率.开发出了用Visual Basic 5.0编写的CSD软件, 利用岩石薄片图像或者矿物颗粒轮廓图测出岩石有限应变的大小及应变椭圆长轴方向, 同时测出矿物颗粒分布的优选方位.其操作相当简便, 首先统计出图像中0°~180°各方向上矿物颗粒的边界数目; 然后在方位-边界坐标系中投点, 并利用最小二乘法进行数据点的多项式曲线拟合; 最后求出曲线的极值点坐标, 并根据坐标绘制相应的应变椭圆.软件运行中, 统计出的边界数据和拟合曲线以及应变椭圆图形都是可视的, 并能进行相应的保存. 相似文献
11.
A. Beach 《Journal of Structural Geology》1979,1(2):127-135
Deformed belemnites are important strain markers because they allow calculation of actual length changes in deformed rocks. They have been studied in the deformed Lower Lias sequence of part of the French Alps by measuring the orientation of about 100 belemnites at each locality, recording the amount of extension of as many as possible, and locating the sector of arc on the bedding plane occupied by extended belemnites. For comparison, studies on a similar but undeformed Lower Lias sequence in southern England show that dispersed belemnites have no strong initial preferred orientation, and that a proportion of undeformed belemnites show cross-fractures that would allow extension of the rostra from the onset of deformation.Graphs of frequency vs orientation for belemnites at locations deformed by irrotational strain lead directly to an estimate of two-dimensional strain ratio and orientation. Non-random initial distributions and rotational strain produce more complex graphs, which are treated only qualitatively. Extension-orientation graphs show that many deformed belemnites lie within the sector of extension of the strain ellipse. These graphs provide estimates of 1 + e1 and 1 + e2, which can be cross-checked using the orientation of the lines of no finite longitudinal strain derived from measuring the maximum sector of arc occupied by extended belemnites.Examples from the French Alps show how the rotational and irrotational strain of initially random samples may be distinguished, and how the more complex case of deformation of non-random samples differs from these. The direction of rotation of the strain ellipse can be derived from the geometry of the graphs of frequency and elongation. 相似文献
12.
The subjectivity of ellipse fitting in many strain techniques has hindered the determination of fabric anisotropy and tectonic strain. However, many sets of x, y co-ordinates can be approximated as an ellipse using a least-squares algorithm to calculate a best-fit ellipse and associated average radial error. For instance, the two dimensional shape of many objects can be approximated as an ellipse by entering digitized co-ordinates of the object margin into the ellipse algorithm.The rim of maximum point density in a normalized Fry diagram is defined by normalized center-to-center distances between touching or nearly touching objects. The enhanced normalized Fry (ENFry) method automates ellipse fitting by entering center-to-center distances between these “touching” objects into the least-squares ellipse algorithm. For homogeneously deformed populations of 200 objects, the ENFry method gives an accurate and precise measure of whole-rock fabric anisotropy, particularly for low ellipticities. When matrix strain exceeds clast strain, manual ellipse fitting of normalized Fry plots gives more accurate matrix anisotropies.The mean object ellipse (MOE) method calculates the best-fit ellipse from the geometry of the objects. Three points from the margin of each object ellipse, centered at the origin and expanded or reduced to unit volume, are used to calculate the best-fit fabric ellipse. The MOE method is very precise for small data sets, making it a good method for mapping heterogenous object strain. However, least-squares calculations maximize the influence of distal and spurious ellipticities, causing the MOE method to overestimate the fabric ellipticity of most aggregates. 相似文献
13.
14.
David J. Sanderson 《Tectonophysics》1976,30(1-2)
The coaxial and non-coaxial superposition of tectonic (biaxial or plane) strain on compactional (uniaxial) strain is examined and total finite strains and deformation paths calculated. Both prolate and oblate strains may result, depending on the relative orientations of the two strains. The implications of superposed strain are discussed in relation to naturally occurring strains in rocks, and various patterns of finite strain and deformation fields recognized. 相似文献
15.
A scale free representation of a general non-isochoric 2D deformation is presented which is amenable to mathematical analysis. By describing deformation in 2D in terms of polar coordinates the stretching and rotational histories of linear elements separate and are easily analysed both qualitatively and quantitatively. An analysis of finite strain combined with dynamical considerations allows the derivation of equations which may be used to estimate finite strain, area change and kinematic vorticity number. Numerical investigation of method developed here was carried out and it was found to perform well unless large area changes occur in combination with large components of simple shear. A re-analysis of natural data indicates the method is consistent. 相似文献
16.
INTRODUCTIONThe mechanical responses of soils are more com-plicated compared with metals.By comparing thephysical and mechanical properties of the metals withsoils,Lade(1988)found that there are17differentpoints between the metals and soils,which differfrom metals inthree basic mechanical characteristics:pressure sensitivity,dilatancy,and dependence ofstress path.Wang(2004)proposed a principle of theinteraction between plastic volume and shear strains,that is,there are two relatively inde… 相似文献
17.
P-T paths for a simple situation appropriate to many low- P , high- T (LPHT) terranes in which metamorphism and deformation are localized by advection of heat in magmas, has been modelled assuming a medium with a power-law rheology with an inverse exponential dependence of stress and temperature and capable of sustaining deviatoric stress, τ, in the order of 100 MPa at 400 C and strain rates of up to 10-13 s-1 . Numerical simulations and analytical approximations for P-T histories appropriate for simple convergent deformation histories show that the destruction of the deviatoric stress field around large intrusions may result in significant decompression near the metamorphic temperature peak. Moreover, for a specified strain rate and temperature evolution, P-T paths may vary from clockwise to anticlockwise merely as a function of vertical distance from the heat source. Inasmuch as mounting independent evidence suggests that the crust can support deviatoric stresses of up to about 100 MPa at temperatures of 400-500 C, and that the shear strength of the crust is strongly temperature-dependent in the range 400-800 C, these results suggest that caution should be taken in the tectonic interpretation of P-T paths involving decompression of the order of 100 MPa or less in LPHT terranes. The results illustrate a plausible mechanism for the close spatial association of both clockwise and anticlockwise P-T paths documented in some LPHT terranes. 相似文献
18.
鄂东南铁山不对称骨节状石香肠构造基质层中的应变测量与分析 总被引：1，自引：1，他引：0
鄂东南铁山是亚洲首个发现骨节状石香肠构造的地区。以该区不对称骨节状石香肠构造为研究对象,利用惯量椭圆法对其基质层进行有限应变测量,获得真应变差、运动学涡度等相关参数及有限应变椭圆长轴展布方位的分布图。对所获数据资料研究表明:该不对称骨节状石香肠构造基质层的应变受其能干层控制,有限应变值与其离能干层的距离趋于负相关,且与其矿物颗粒粒径呈负相关,在平行于石香肠构造伸展方向上基质层有限应变分布不均;石香肠体附近与之相近规模的变形构造可使其相应基质中的应变分布紊乱;该不对称骨节状石香肠构造是由早期平行于层面简单剪切叠加晚期平行层面伸长、垂直层面压缩的纯剪切作用形成。与不对称鱼嘴状石香肠构造对比研究表明,两者基质层中简单剪切与纯剪切的分布均分别与其相对增厚与减薄区段对应,而两者形态的不同主要与石香肠体不连续处充填物的能干性不同有关,再次表明两者均是较好的岩石流变学标志。 相似文献
19.
The behaviour of quartz during metamorphism is studied based on two case studies from the Barrovian terrains of Sulitjelma in arctic Scandinavia and Loch Tay in the Central Highlands Dalradian of Scotland. Both terrains preserve evidence for metamorphism in pelites involving nucleation and growth of garnet at different times in the deformation history. Data are presented on the size, shape and crystallographic orientation of quartz preserved as inclusions in garnet and as grains in the surrounding matrix. While quartz-grains remain small and dispersed between mica grains, deformation appears to be dominated by grain-boundary sliding accommodated by dissolution–precipitation. At amphibolite facies, textural coarsening occurs by dissolution of small quartz grains and growth of larger quartz grains, coupled with segregation of quartz from mica. As a result, quartz deforms by dislocation creep, developing crystallographic preferred orientations (CPO) consistent with both coaxial and non-coaxial strain. Quartz CPOs with <0001> axes lying parallel to foliation and stretching direction are commonly developed, and best explained by mechanical rotation of inequant (detrital?) quartz grains. There is no evidence for selective entrapment of quartz inclusions in garnet on the basis of quartz crystallographic orientation. 相似文献
20.
杨新岳 《大地构造与成矿学》1993,17(1):82-92
本文运用 Apple Macitonsh 计算机对无应变的均匀离散点分布进行系列平面应变模拟,应变叠加模式分别采用具普遍意义的成岩压实+顺层缩短(LPS)+压溶作用和成岩压实+简单剪切+压溶作用。对各应变阶段的变形点分布进行相应的 Fry 法应变测量,并配合低变形砂岩样品的 Fry 法应变分析实例.证实 Fry 法应变测量方法为一非常有用的应变测量方法,其结果不仅能较好地揭示全岩总应变特征,而且能揭示出许多应变叠加的信息,Fry 法揭示的全岩有限应变椭球主面的方位也较为真实可靠。而 Fry 法运用于应变分布不均匀的劈理化岩石中时,能揭示不同变形域的应变特征,从而达到应变分解的目的。 相似文献