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Journal of Structural Geology, 2003
Two methods have been developed in this paper to model the strain state and the layer geometry of folds. These methods analyse the superposition of strain patterns due to layer shortening, tangential longitudinal strain, flexural-flow and fold flattening. The first method multiplies the deformation gradients of these strain patterns to model the successive superposition of mechanisms. The second method is more general and is based on the transformation of points from the initial configuration to deformed points according to the geometrical properties of the folding mechanisms involved. This method simulates the simultaneous and successive superposition of strain patterns. Both methods generate graphic outputs that describe the strain variation through the folded layer. Another application of these methods is to attempt to find theoretical folds that fit natural or experimental folds and to perform a geometric and kinematical analysis of these folds. Knowledge of the shape of the folded layer and the cleavage pattern is the most common basic information available in natural folds that can be used to perform the analysis. Additional strain data from the folded rocks are valuable for improving knowledge of the kinematical mechanisms involved in the folding. q
Journal of Structural Geology, 2006
This paper deals with some problems with the concept and properties of the folding mechanism named tangential longitudinal strain. A general two-dimensional mathematical description of this mechanism in terms of displacements and finite strains is presented. In the analysis of this mechanism of folding, two geologically reasonable variants are considered. The first of these, referred to as parallel tangential longitudinal strain folding, involves no finite elongation of lines perpendicular to the layer and produces class 1B (parallel) folds. The second variant is characterized by the conservation of area across the fold profile and is therefore termed equiareal tangential longitudinal strain folding; it produces folds ranging from class 1B to more complex shapes with the development of a bulge in the hinge zone inner arc when amplitude and curvature are high. Using the computer program ''FoldModeler'' which incorporates the derived equations for displacements and finite strains, the geometrical features of idealized folds produced by these two variants have been studied, together with those arising from their successive or simultaneous combination. The implications of the operation of these two deformation mechanisms in natural folds are then considered and a discussion is presented about the features that can be diagnostic of their operation in nature. It is suggested that the two mechanisms operate together in the formation of natural folds, in a way that deformation probably begins with equiareal tangential longitudinal strain, but subsequently gives way to parallel tangential longitudinal strain when strain concentration in some parts of the folded layer makes area change probable.
This paper deals with some problems with the concept and properties of the folding mechanism named tangential longitudinal strain. A general two-dimensional mathematical description of this mechanism in terms of displacements and finite strains is presented. In the analysis of this mechanism of folding, two geologically reasonable variants are considered. The first of these, referred to as parallel tangential longitudinal strain folding, involves no finite elongation of lines perpendicular to the layer and produces class 1B (parallel) folds. The second variant is characterized by the conservation of area across the fold profile and is therefore termed equiareal tangential longitudinal strain folding; it produces folds ranging from class 1B to more complex shapes with the development of a bulge in the hinge zone inner arc when amplitude and curvature are high. Using the computer program ''FoldModeler'' which incorporates the derived equations for displacements and finite strains, the geometrical features of idealized folds produced by these two variants have been studied, together with those arising from their successive or simultaneous combination. The implications of the operation of these two deformation mechanisms in natural folds are then considered and a discussion is presented about the features that can be diagnostic of their operation in nature. It is suggested that the two mechanisms operate together in the formation of natural folds, in a way that deformation probably begins with equiareal tangential longitudinal strain, but subsequently gives way to parallel tangential longitudinal strain when strain concentration in some parts of the folded layer makes area change probable.
Journal of Structural Geology, 2018
A new mechanism, named "heterogeneous rotation shear", is defined to explain the development of similar folds. It is based on the heterogeneous distribution of a type of deformation in which a line rotates without length change and another maintains constant its direction and length (pure rotation shear) or undergo a constant stretching through the rock (rotation shear with area correction). With these constraints, a kinematical numerical model of similar folds is developed. The mechanism produces a divergent pattern of the major axis directions of the strain ellipses throughout the fold, which does not agree with the usual axial plane cleavage of natural similar folds. The operation of layer parallel shortening is necessary to solve this problem; this shortening agrees with the incompetent character of the rocks where similar folds develop. Eventually fold flattening can modify the fold shape whilst maintaining the similar geometry. The model is applied to explain the development of a natural similar fold, indicating that this could be formed by a combination of layer parallel shortening and heterogeneous rotation shear. Finally, three types of similar or sub-similar folds have been distinguished: a) sub-similar folds formed by intense flattening of parallel folds; b) sub-similar folds formed by simple shear acting on previous perturbations, and c) similar folds produce by layer-parallel shortening and heterogeneous rotation shear.
Geological Society, London, Special Publications, 1999
Geology, 2013
Folded layers in rocks can be stretched again, potentially unfolding the folds back to straight layers. Little is known, however, about how to recognize partly or even entirely unfolded layers. When folded layers can unfold, what determines their mechanical behavior, and how can we recognize them in the fi eld? In order to address these questions, we present a series of numerical simulations of the stretching of previously folded single layers and multilayers in simple shear. Layers do not completely unfold when they undergo softening before or during the stretching process, or when adjacent competent layers prevent them from unfolding. Intrafolial folds and cusp-like folds adjacent to straight layers as well as variations in fold amplitudes and limb lengths of irregular folds are indicative of stretching of a fold train.
Journal of Structural Geology, 1993
Sedimentary rocks deformed at shallow crustal depth can show a wide variety of planar, linear and mixed planar-linear fabrics depending on their structural position within folds. A model has been developed which tries to explain this variation in fabric development in terms of the strain states that it represents. We analyse the finite strain states that may develop during compaction and subsequent buckle folding of sedimentary multilayers composed of a regular alternation of competent and incompetent beds. The geometric properties of the multilayer during buckling have been analysed from a finite element model characterized by: linear viscous material properties, a viscosity contrast/~t//~2 = 40, and a ratio of incompetent to competent layer thickness d2/d I = 1. Sequential matrix multiplication allows the determination of the finite strain states for all stages of fold development.
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