Brittle fracture during folding of rocks: A finite element study

Abstract

The goal of the present work is the development of a novel computational analysis tool to elaborate folding-induced fracture of geological structures. Discrete failure of brittle rocks is characterised by three sets of governing equations: the bulk problem, the interface problem and the crack problem. The former two sets which define the deformation field are highly nonlinear and strongly coupled. They are solved iteratively within a Hansbo-type finite element setting. The latter set defines the crack kinematics. It is linear and solved in a single post-processing step. To elaborate the features of the computational algorithm, we define a unique benchmark problem of a single, geometrically nonlinear plate, which is subjected to layer-parallel in-plane compression combined with different levels of superposed in-plane shear. The resulting folding, or buckling, induces brittle failure in the tensile regime. By systematically increasing the shear strain at constant compression, we develop crack deviation angle versus shear-to-compression ratio tables. We determine the corresponding damage zones, analyse the folding modes and elaborate the force versus amplification diagrams. The proposed two-field folding-induced fracture algorithm can ultimately be applied to interpret natural folded rocks and understand their evolution, structural development and histology.

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture

“…value to the element center point. This procedure uniquely ensures C 0 continuity, for all possible crack surfaces and is more general than the one reported by [63], where root elements are predefined. Although this approach seems to be the most general one, an essential drawback remains: By using finite elements as the root of crack propagation, it is obviously that the number of cracks will inherently depend on the number of elements.…”

“…In the present formulation we only use a set of initial boundary conditions since we validated our algorithm in terms of experiments and benchmarks from the literature and we therefore wanted to restrict the possible number of cracks. However, the incorporation of root elements which allow for an arbitrary number of cracks is straightforward, see, e.g., [3,5,63]. In the sequel we categorize the choice of boundary conditions first addressing the initial boundary conditions and focusing on the onset boundary conditions or so-called root elements.…”

Forming Europa’s folds: Strain requirements for the production of large-amplitude deformation

“…First, any realistic lithospheric rheology must include plastic (i.e., brittle) deformation (e.g., McAdoo and Sandwell (1985)), a rheology not always considered in models of small-scale folding (though see, e.g., Johnson, 1980;Jager et al, 2008). Second, rather than being a layer fully embedded in a matrix with constant material properties, the lithosphere overlies a substrate whose viscosity decreases as a function of depth (i.e., is thermally controlled) (cf.…”

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

“…These equations are useful to describe continuous deformation and strain localisation by shear bands (with no loss of velocity continuity). Elaborated numerical algorithms based on continuum mechanics, the so-called extended finite element method or XFEM (Belytschko et al, 2001), are additionally able to model discontinuous fracture, for example due to 3-D folding (Jäger et al, 2008). In geological studies it is more common to apply so-called discrete element methods to study brittle deformation and fracturing.…”