Boudinage and folding as an energy instability in ductile deformation

Abstract

We present a theory for the onset of localization in layered rate‐ and temperature‐sensitive rocks, in which energy‐related mechanical bifurcations lead to localized dissipation patterns in the transient deformation regime. The implementation of the coupled thermomechanical 2‐D finite element model comprises an elastic and rate‐dependent von Mises plastic rheology. The underlying system of equations is solved in a three‐layer pure shear box, for constant velocity and isothermal boundary conditions. To examine the transition from stable to localized creep, we study how material instabilities are related to energy bifurcations, which arise independently of the sign of the stress conditions imposed on opposite boundaries, whether in compression or extension. The onset of localization is controlled by a critical amount of dissipation, termed Gruntfest number, when dissipative work by temperature‐sensitive creep translated into heat overcomes the diffusive capacity of the layer. Through an additional mathematical bifurcation analysis using constant stress boundary conditions, we verify that boudinage and folding develop at the same critical Gruntfest number. Since the critical material parameters and boundary conditions for both structures to develop are found to coincide, the initiation of localized deformation in strong layered media within a weaker matrix can be captured by a unified theory for localization in ductile materials. In this energy framework, neither intrinsic nor extrinsic material weaknesses are required, because the nucleation process of strain localization arises out of steady state conditions. This finding allows us to describe boudinage and folding structures as the same energy attractor of ductile deformation.

Contributions of Grain Damage, Thermal Weakening, and Necking to Slab Detachment

“…The same applies to the thermal damage number S, which can be considered as the ratio between the specific deformation energy available for thermal damage, (1 − λ I )τ 0 , and the specific thermal energy, ρcT 0 . Due to our choice of non-dimensionalization, this ratio is then additionally scaled by the factor Q dis /T 0 , also known as the Arrhenius number (e.g., Peters et al, 2016), which is in itself a measure of the ratio between activation energy and thermal energy. A large value of S thus requires that (1) the system is highly temperature dependent (represented by large values of the Arrhenius number) and (2) the available deformation energy is much larger than the thermal energy.…”

Boudinage and the rheology of syntectonic migmatites in the high-strain Taili deformation zone, NE China

“…A great many geological strain and viscosity indicators have been described in detail in the literature (e.g., Ramsay and Huber, 1983;Passchier, 1988;Treagus and Lan, 2004;Passchier and Trouw, 2005;Bürgmann and Dresen, 2008). A variety of relationships between geometry, effective viscosity, and strain of boudins is already inferred from previous field and modeling work (e.g., Ramberg, 1955;Smith, 1975Smith, , 1977Passchier and Druguet, 2002;Goscombe et al, 2004;Treagus and Lan, 2004;Mandal et al, 1992Mandal et al, , 2001Mandal et al, , 2007Schmalholz et al, 2008;Marques et al, 2012;Schmalholz and Maeder, 2012;Gardner et al, 2015;Peters et al, 2015Peters et al, , 2016Samanta et al, 2017;Dabrowski and Grasemann, 2019). Generally, the geometric type of boudinaged structures is largely controlled by the contrast in viscosity between the boudinaged layers and the embedding matrix, the flow type (kinematic vorticity number), the angular relationships between the layer and the deformation (kinematic) axes, and the shear strain (Goldstein, 1988;Abe and Urai, 2012;Rodrigues and Pamplona, 2018).…”

“…Generally, the geometric type of boudinaged structures is largely controlled by the contrast in viscosity between the boudinaged layers and the embedding matrix, the flow type (kinematic vorticity number), the angular relationships between the layer and the deformation (kinematic) axes, and the shear strain (Goldstein, 1988;Abe and Urai, 2012;Rodrigues and Pamplona, 2018). For example, when embedded in an identical matrix, boudin that is angular in shape is mechanically stronger than a lensoid-shaped boudin (Abe and Urai, 2012;Peters et al, 2015Peters et al, , 2016Samanta et al, 2017). In this same matrix, the most competent layers formed the most rectangular boudins, whereas the less competent layers developed pinch-and-swell structures (Ramberg, 1955).…”

“…Boudinage of outcrop-scale migmatites has been observed in the Tolstik Peninsula, Russia (Brown, 2001); the southern Eyre Peninsula, South Australia (Pawley et al, 2013); the Aus granulite terrain, southern Namibia (Diener and Fagereng, 2014); the Karakoram Shear Zone, NW India (Weinberg and Mark, 2008); the Chotanagpur Gneissic Complex, East India (Ghosh and Sengupta, 1999;Samanta and Deb, 2014); and the Espinho Branco anatexites of southeastern Brazil (Cavalcante et al, 2016). The common occurrence of boudinage in these and other migmatites indicates that significant strain partitioning commonly occurs during migmatization and suggests that principles established from the study of boudinage (Ramberg, 1955;Sen and Mukherjee, 1975;Mandal et al, 1992Mandal et al, , 2000Mandal et al, , 2001Mandal et al, , 2007Passchier and Druguet, 2002;Treagus and Lan, 2004;Goscombe et al, 2004;Arslan et al, 2008;Schmalholz et al, 2008;Marques et al, 2012;Abe and Urai, 2012;Samanta and Deb, 2014;Dabrowski and Grasemann, 2014;Duretz and Schmalholz, 2015;Peters et al, 2015Peters et al, , 2016) may be usefully applied to understand the rheological evolution of rocks undergoing anatexis. In general, field observations of migmatites indicate that the melanosome is stronger than the leucosome during progressive anataxis, and that the leucosome becomes more competent than the melanosome once the leucosome has fully crystallized during retrogression (Ghosh and Sengupta, 1999;Diener and Fagereng, 2014;Cavalcante et al, 2016).…”

The Earth's Dissipative Structures

“…Over the last 10 years since The Earth's Dissipative Structures-Fundamental Wave Properties of Substance had been published, the following papers were devoted to studying the wave structuring of natural systems: Shvartsev (2007), Chengzhi et al (2008), Kopylov (2018), Nazimko and Zakharova (2017), Peters et al (2016) and Shuman (2016). These publications revealed high significance of the investigations' results, connected with fundamental wave properties of natural systems, provided in the book.…”