Abstract
We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see MORESI et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios. Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength. Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.
Highlights
A common feature of mechanical systems producing infrequent, catastrophic releases of free energy such as earthquakes or rockbursts is a shared capacity to store energy over prolonged periods
We have presented a simple formulation for the consideration of viscoelasticity in deforming layered systems
The combination of the basic model with a large deformation, particle-in-cell finite element method allows the simulation of a diverse range of crustal deformation problems
Summary
A common feature of mechanical systems producing infrequent, catastrophic releases of free energy such as earthquakes or rockbursts is a shared capacity to store energy over prolonged periods. We develop a mechanical model including a large deformation formulation for viscoelastic, multi-layered rock. The formulation is devised with the goal of describing materials with fine internal layering, which can be described by a single director orientation This constitutive model is new; designed for geological deformation problems involving very large deformations. One of the most enduring tenets of geology is the existence of an organized stratigraphy in the rock record Another generalization we might make about the mechanical origins of geological formations is that deformation is almost certain to involve very high strain. It turns out that the characteristic length scale of the emerging folding pattern tends to zero with increasing relaxation time
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