Folding and necking across the scales: a review of theoretical and experimental results and their applications

Abstract

Abstract. The shortening and extension of mechanically layered ductile rock generates folds and pinch-and-swell structures (also referred to as necks or continuous boudins), which result from mechanical instabilities termed folding and necking, respectively. Folding and necking are the preferred deformation modes in layered rock because the corresponding mechanical work involved is less than that associated with a homogeneous deformation. The effective viscosity of a layered rock decreases during folding and necking, even when all material parameters remain constant. This mechanical softening due to viscosity decrease is solely the result of fold and pinch-and-swell structure development and is hence termed structural softening (or geometric weakening). Folding and necking occur over the whole range of geological scales, from microscopic up to the size of lithospheric plates. Lithospheric folding and necking are evidence for significant deformation of continental plates, which contradicts the rigid-plate paradigm of plate tectonics. We review here some theoretical and experimental results on folding and necking, including the lithospheric scale, together with a short historical overview of research on folding and necking. We focus on theoretical studies and analytical solutions that provide the best insight into the fundamental parameters controlling folding and necking, although they invariably involve simplifications. To first order, the two essential parameters to quantify folding and necking are the dominant wavelength and the corresponding maximal amplification rate. This review also includes a short overview of experimental studies, a discussion of recent developments involving mainly numerical models, a presentation of some practical applications of theoretical results, and a summary of similarities and differences between folding and necking.

Necking of the Lithosphere: A Reappraisal of Basic Concepts With Thermo‐Mechanical Numerical Modeling

“…The width of necking zones ranges between 65 and 105 km in Model Series 1 (decoupled models) and between 50 and 70 km in Model Series 3 (coupled models). These ranges are consistent with both the predictions from analytical studies (14-83 km according to Schmalholz & Mancktelow, 2016; see also Appendix A2) and the width observed at natural rift systems/margins (10-100 km according to Chenin et al, 2017; see Figure 1b). The generally narrower width of necking zones in the coupled models with respect to decoupled models is consistent with the results of previous studies, which predict wider rift zones for weaker lithospheres (for instance, Bassi, 1991;Buck, 1991).…”

“…According to the compilation of rift domains measurements by Chenin et al (2017), the width of necking zones in natural rift systems ranges from 10 to 100 km. Recently, Schmalholz and Mancktelow (2016) showed that the application of the analytical solution of Fletcher and Hallet (1983) to crustal necking predicts a comparable range of widths for necking zones (14-83 km) and thus argued that the formation of crustal necking zones may be primarily controlled by a viscoplastic necking instability (see Appendix A2). A goal of this study is to compare the width of necking zones from natural rift systems with both necking zones widths predicted by analytical studies and formed in thermo-mechanical numerical simulations of lithosphere extension.…”

Tectonic inheritance controls nappe detachment, transport and stacking in the Helvetic nappe system, Switzerland: insights from thermomechanical simulations

“…The governing system of partial differential equations is solved numerically. The applied equations are described in detail in Schmalholz et al (2019). The applied numerical algorithm is based on the finite-difference/marker-in-cell method (e.g., Gerya and Yuen, 2003).…”

Crustal versus mantle core complexes

“…Folding of layered systems that results from a buckling instability provides a well-known illustration of this (e.g. Schmalholz and Mancktelow, 2016). The large variety of fold shapes is primarily controlled by the variety of geological layering (i.e.…”

“…Among these structures, those who lead to the exhumation of deep ductile rocks from either crust or mantle all result from a necking instability (Schmalholz and Mancktelow, 2016) of the brittle or high-strength layer lying above the ductile layer to be exhumed: i) the upper brittle crust for MCCs, ii) the whole crust plus the sub-Moho high strength mantle for non-volcanic passive margins and iii) an upper brittle layer of the oceanic lithosphere for OCCs. Therefore, beyond the geological differences and tectonic signatures that result from the three different types of lithosphere rheological layering, the involved process is similar.…”