急折褶皺是種具有急劇轉折形貌的褶皺，並具有尖銳的樞紐和筆直且不對稱的翼部，通常會由一較短之翼連接兩長翼，此短翼稱為急折帶。常於劈理面發達的變質岩中出現，如：板岩、片岩與千枚岩，亦可在部分呈薄層狀的沉積岩中發現。急折褶皺形成的機制與曲滑褶皺作用類似，但滑動僅限於急折帶內。本研究以邊界元素法，模擬複層受外力作用下的褶曲變形，模型中的複層層面得以變化摩擦強度與凝聚強度，藉此探討急折褶皺形成的條件。研究結果顯示摩擦強度（摩擦角）、凝聚強度（凝聚力）和初始應力之比R_σ^0對於形成急折褶皺具有相當重要的影響。急折褶皺無法在複層層面只具有摩擦強度的情況下形成。在只具有凝聚力的條件下，形成急折褶皺所需之凝聚力需大於楊氏係數的0.004到0.005倍。對於共軛急折褶皺的形成，若在沒有凝聚強度的情況下，則摩擦角必須介於13˚到38˚，且R_σ^0需大於0.2，才能形成急折褶皺；對於單斜急折褶皺，則R_σ^0需大於0.75。考慮三參數之關係，於摩擦角小於35˚的模型中，若其初始垂直應力較大時，形成急折褶皺所需的層面凝聚力與摩擦角相對下調；於摩擦角大於35˚的模型中，則形成急折褶皺的條件範圍變廣，取代了部分原先為複雜褶皺之區域以急折褶皺取而代之。以上研究結果得自於水平縮短量為35.9%，層面數為16的複層模型。

The features of kink folds are sharp hinges and straight asymmetric limbs; a shorter limb, which is called kink band, connects two longer limbs. Strongly foliated rocks like slates, schists, phyllites, and thin-bedded sedimentary rocks, commonly display kink folds. The properties of kink folds resemble flexural slip folds, but the slip between the layers is highly localized within shorter limbs, also known as kink bands. I use boundary element method to develop multilayer models, consisting of interface-slip in an elastic medium with possibly different parameters on interfaces of adjacent layers. The results show that the properties of interfaces (i.e., cohesion and friction) and initial differential stress play important roles in finite forms of folds. I find out that a multilayer with stand-alone friction on its interfaces cannot produce kink folds; and the lower limit of stand-alone cohesion divided by Young’s modulus ranges from 0.004 to 0.005. Friction can produce kink folds if the ratio of the vertical initial remote stress to horizontal initial remote stress (initial differential stress) is larger than 0.2, under the condition that the compression parallel to the interface, and equals to 0.75 when compression incline to the interface at 1˚ without cohesion by friction angle from 13˚ to 38˚. Considering the relation of three parameters, lower friction and cohesion can produce kink folds if the ratio of the initial differential stress is larger by friction angle is less than 35˚; kink folds replace the parts of original complex folds if the ratio of the initial differential stress is larger by friction angle is greater than 35˚.
The results of this study are attain from models under the shortening of 35.9% with an incremental far-field strain of 0.02 for multilayer models of 16 interfaces.

Anderson, T. B., 1964, Kink-bands and related geological structures: Nature, v. 202, p. 272-274.
-, 1974, The relationship between kink–bands and shear fractures in the experimental deformation of slate: Journal of the Geological Society, v. 130, no. 4, p. 367-382.
Byerlee, J., 1978, Friction of rocks: Pure and applied Geophysics, v. 116, no. 4, p. 615-626.
Camerlo, R. H., and Benson, E. F., 2006, Geometric and seismic interpretation of the Perdido fold belt: Northwestern deep-water Gulf of Mexico: AAPG bulletin, v. 90, no. 3, p. 363-386.
Clifford, P., Kink band development in the Lake St. Joseph area, northwestern Ontario1968, Volume 68, p. 52.
Clough, C., 1897, The geology of Cowal: Mem. Geol. Surv. Scotland.
Crouch, S. L., and Starfield, A. M., 1983, Boundary element methods in solid mechanics: Journal of Applied Mechanics, v. 50, p. 704.
Davis, G. H., Reynolds, S. J., and Kluth, C. F., 2011, Structural Geology of Rocks and Regions.
De Sitter, L. U., 1956, Structural Geology., McGraw Hill, London.
Dewey, J., 1965, Nature and origin of kink-bands: Tectonophysics, v. 1, no. 6, p. 459-494.
Donath, F. A., 1964, Strength variation and deformational behavior in anisotropic rock: State of the earth in the earth's crust. New York: Elsevier, p. 281-298.
-, 1968a, The development of kink bands in brittle anisotropic rock: Igneous and Metamorphic Petrology. Geol. Soc. Am. Mem, v. 115, p. 453-493.
-, Experimental study of kink band development in Martinsburg Slate, in Proceedings Kink bands and Brittle Deformation 1968b, Volume 68-52, Geological Survey of Canada Paper, p. 255-287.
Flinn, D., 1952, A tectonic analysis of the Muness phyllite block of Unst and Uyea, Shetland: Geological Magazine, v. 89, no. 04, p. 263-272.
Fossen, H., 2010, Structural Geology, Cambridge University Press.
Frehner, M., and Schmalholz, S. M., 2006, Numerical simulations of parasitic folding in multilayers: Journal of Structural Geology, v. 28, no. 9, p. 1647-1657.
Ghosh, S. K., 1968, Experiments of buckling of multilayers which permit interlayer gliding: Tectonophysics, v. 6, no. 3, p. 207-249.
Hills, E. S., 1963, Elements of Structural Geology, Wiley.
Honea, E., and Johnson, A. M., 1976, A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers:: IV. Development of sinusoidal and kink folds in multilayers confined by rigid boundaries: Tectonophysics, v. 30, no. 3-4, p. 197-239.
Johnson, A. M., 1970, Physical Processes in Geology, Freeman, Cooper & Company.
Kirschner, D., and Teixell, A., 1996, Three-dimensional geometry of kink bands in slates and its relationship with finite strain: Tectonophysics, v. 262, no. 1-4, p. 195-211.
Kleinsmiede, W. F. J., 1960, Geology of the Valle de Arán (Central Pyrenees): Leidse Geologische Mededelingen, v. 25, p. 129-245.
Knill, J., 1961, Joint-drags in Mid-Argyllshire: Proceedings of the Geologists' Association, v. 72, no. 1, p. 13-19.
Kulhawy, F. H., 1975, Stress deformation properties of rock and rock discontinuities: Engineering geology, v. 9, no. 4, p. 327-350.
Lundborg, N., Triaxial shear strength of some Swedish rocks and ores, in Proceedings 1st ISRM Congress1966, Volume 1, p. 251-255.
Okada, Y., 1985, Surface deformation due to shear and tensile faults in a half-space: Geological Society of America Bulletin, v. 75, no. 4, p. 1135-1154.
Orowan, E., 1942, A type of plastic deformation new in metals: Nature, v. 149, no. 3788, p. 643-644.
Paterson, M. S., and Weiss, L. E., 1962, Experimental folding in rocks: Nature, v. 195, p. 1046-1048.
-, 1966, Experimental deformation and folding in phyllite: Geological Society of America Bulletin, v. 77, no. 4, p. 343.
Pfaff, V. J., and Johnson, A. M., 1989, Opposite senses of fold asymmetry: Engineering geology, v. 27, no. 1-4, p. 3-38.
Pimenta, S., Gutkin, R., Pinho, S., and Robinson, P., 2009, A micromechanical model for kink-band formation: Part I--Experimental study and numerical modelling: Composites Science and Technology, v. 69, no. 7-8, p. 948-955.
Reches, Z., and Johnson, A. M., 1976, A theory of concentric, kink and sinusoidal folding and of monoclinal flexuring of compressible, elastic multilayers: VI. Asymmetric folding and monoclinal kinking: Tectonophysics, v. 35, no. 4, p. 295-334.
Scharer, K., Burbank, D., Chen, J., and Weldon II, R., 2006, Kinematic models of fluvial terraces over active detachment folds: Constraints on the growth mechanism of the Kashi-Atushi fold system, Chinese Tian Shan: Geological Society of America Bulletin, v. 118, no. 7-8, p. 1006-1021.
Stewart, K. G., and Alvarez, W., 1991, Mobile-hinge kinking in layered rocks and models: Journal of Structural Geology, v. 13, no. 3, p. 243-259.
Turner, F. J., and Weiss, L. E., 1963, Structural analysis of metamorphic tectonites.
Twiss, R. J., and Moores, E. M., 1992, Structural geology, WH Freeman.
Verbeek, E. R., 1978, Kink bands in the Somport slates, west-central Pyrenees, France and Spain: Geological Society of America Bulletin, v. 89, no. 6, p. 814-824.
Vogler, T., and Kyriakides, S., 2001, On the initiation and growth of kink bands in fiber composites: Part I. experiments: International journal of solids and structures, v. 38, no. 15, p. 2639-2651.
Wadee, M. A., and Edmunds, R., 2005, Kink band propagation in layered structures: Journal of the Mechanics and Physics of Solids, v. 53, no. 9, p. 2017-2035.
Wadee, M. A., Völlmecke, C., Haley, J. F., and Yiatros, S., 2011, Geometric modelling of kink banding in laminated structures: Arxiv preprint arXiv:1105.5768.
Weiss, L. E., 1980, Nucleation and growth of kink bands: Tectonophysics, v. 65, no. 1, p. 1-38.
Zandvliet, J., 1960, The Geology of the Upper Salat and Pallaresa Valleys: Central Pyrenees, France-Spain, Eduard Ijdo NV.
張波, 李生福, 張進江, 鄭亞東, and 張仲培, 2010, 膝褶, 膝褶帶, 共軛膝褶帶——一種可能的新型油氣構造樣式: 中國天然氣工業期刊, v. 30, no. 2, p. 32-39.
黃文正, and 凱強生, 2010, 結合斷層滑移與岩層拱彎機制的斷層居中型褶皺之增長: 經濟部中央地質調查所特刊, v. 24, p. 95-132.