Analysis of bookshelf mechanisms using the mechanics of Cosserat generalized continua

Abstract

Bookshelf type mechanisms are commonly used to explain antithetic accommodation of deformations caused by direct shear. Stress analysis of such mechanisms have been proposed, mainly through the use of classic Mohr circle graphical constructions. The present work introduces an alternative framework for analysis, the mechanics of generalized Cosserat continua, although maintaining the same tools (Mohr circle construction). In this type of mechanics, kinematics of the material points incorporates independent rotational degrees of freedom besides the classic translational ones. In the equilibrium equations, quantities involving moments are generated and the stress tensor is in the general case non-symmetric. Such characteristics of generalized Cosserat continua make it suitable for the analysis of bookshelf mechanisms, as these are, in essence, rotational antithetic mechanisms induced by shear stresses having different magnitudes in perpendicular planes. The paper applies the mechanics of generalized continua to the analysis of a specific bookshelf mechanism, related to crustal extension. In the Appendices, a review of the generalized Cosserat continua and details of the graphical Mohr circle representation of stresses for such media are presented.

Geodynamic evolution of the SW Europe Variscides

“…The transpressive regime is a consequence of the nature of convergent triple junctions in the southern tips of Urals and northern tip of Southern Appalachians, which are connected by a transpressive transform through the European Variscides [ Arthaud and Matte , 1977]. Therefore the complete mechanical interpretation of domino style of distributed deformation must be addressed through generalized continua theory (such as Cosserat Continua [ Figueiredo et al , 2004]), or continuum micropolar theory [ Twiss and Moores , 1992]; both are more appropriate than classical continua theory to describe the schizosphere behavior [ Ribeiro , 2002] in presence of significant instability.…”

Sliding and rolling dissipation in Cosserat plasticity

“…As shown by Satake [33] and presented in more detail by other authors [10,19,13], the locus of the normal and shear components of the stress vector for all possible orientations is a (Mohr) circle whose centre does not lie on the axis of zero shear stress. This is shown in Figure 3, where it can be shown that AM = r, MC = q, OA = −p, so that the yield surface can be written as…”

Neotectonics of the Western Suleiman Fold Belt, Pakistan: Evidence for Bookshelf Faulting

“…The bookshelf model, proposed initially by Mandl [46], is the behavior of parallel faults that relate to a horizontal stack of books being displaced and consequently named 'bookshelf faulting' [46][47][48]. Mandl [46] described two basic modes of mechanism: the "dilational" mode and the "domino" mode.…”