Louise Olsen-Kettle

Bottlenecks in granular flow: when does an obstacle increase the flow rate in an hourglass?

Bottlenecks occur in a wide range of situations from pedestrians, ants, cattle, and traffic flow to the transport of granular materials. We examine granular flow across a bottleneck using simulations of monodisperse disks. Contrary to expectations but consistent with previous work, we find that the flow rate across a bottleneck actually increases if an obstacle is optimally placed before it. Using the hourglass theory and a velocity-density relation, we show that the peak flow rate corresponds to a transition from free flow to congested flow, similar to the phase transition in traffic flow.

Analysis of slip-weakening frictional laws with static restrengthening and their implications on the scaling, asymmetry, and mode of dynamic rupture on homogeneous and bimaterial interfaces

Dynamic simulations of homogeneous, heterogeneous and bimaterial fault rupture using modified slip-weakening frictional laws with static restrengthening are presented giving rise to both crack-like and pulse-like rupture. We demonstrate that pulse-like rupture is possible by making a modification of classical slip-weakening friction to include static restrengthening. We employ various slip-weakening frictional laws to examine their effect on the resulting earthquake rupture speed, size and mode. More complex rupture characteristics were produced with more strongly slip-weakening frictional laws, and the degree of slip-weakening had to be finely tuned to reproduce realistic earthquake rupture characteristics. Rupture propagation on a fault is controlled by the constitutive properties of the fault. We provide benchmark tests of our method against other reported solutions in the literature. We demonstrate the applicability of our elastoplastic fault model for modeling dynamic rupture and wave propagation in fault systems, and the rich array of dynamic properties produced by our elastoplastic finite element fault model. These are governed by a number of model parameters including: the spatial heterogeneity and material contrast across the fault, the fault strength, and not least of all the frictional law employed. Asymmetric bilateral fault rupture was produced for the bimaterial case, where the degree of material contrast influenced the rupture speed in the different propagation directions.

Bridging the macro to mesoscale: Evaluating the fourth-order anisotropic damage tensor parameters from ultrasonic measurements of an isotropic solid under triaxial stress loading:

One of the most challenging problems which arises in continuum damage mechanics is the selection of variables to describe the internal damage. Many theories have been proposed and various types of damage variables ranging from scalar to vector to tensor quantities have been used. In this paper we consider anisotropic damage and the most general form for damage by using a fourth-order tensor for the damage variables. We demonstrate how experimentally measured quantities can be related to the internal tensorial damage variables. We apply this analysis to experiments of an initially isotropic solid becoming transverse isotropic under triaxial or uniaxial stress loading.

Modelling of Non-coaxial Viscoplastic Deformation in Geodynamics

The formation of shear bands for time and length scales appropriate for deformation processes in the upper Lithosphere is investigated in plane strain finite element simulations under predominantly uniaxial extension and compression, respectively. The direction of gravity is assumed orthogonal to the extension/compression axis. Mathematically, the formation of shear zones may be explained as a consequence of changes in the type of the governing model equations. Such changes or bifurcations depend strongly on the details of the constitutive relationships such as strain softening, thermal or chemical effects, associated or non-associated—coaxial or non-coaxial flow rules. Here we focus on strain softening and coaxial and non-coaxial flow rules. In the simulations, we consider an initially rectangular domain with the dimensions L0, H0 in the horizontal, vertical directions, respectively. The domain is extended or compressed by prescribing a uniform, horizontal velocity field along one of the vertical boundaries while keeping the opposite boundary fixed. An important global descriptor of the deformation process is the relationship between the horizontal stress resultant (average horizontal stress) and the strain ln(L/L0), where L is the deformed length of the domain. The main goal of this paper is to investigate key factors influencing the phenomenology of the localization process such as flow rule, coaxial, non-coaxial and strain softening. Different origins of the mesh sensitivity of deformations involving localization are also investigated.

Scale Effects in Simple Models for the Dynamics of Faults

Although the evidence for complexity is overwhelming, the dynamics of faulting is still poorly understood. Whilst it has long been known that discreteness in numerical earthquake models produces complexity, the mathematical structure and form of this complexity has never been fully established. Using a simple 1D nonlinear fault model we show how complexity can arise in discrete models through the presence of nonlinear, scale-dependent (or mesh-dependent) terms. We show that scale-dependencies may be a significant factor in the generation of slip complexity and pulse-like rupture over multiple earthquake cycles. We demonstrate that the introduction of length scales in discrete earthquake models implies that both strongly weakening friction and scale-dependent processes may be necessary in generating the pulse-like rupture mode and earthquake complexity over multiple earthquake cycles.

An advanced geophysical software tool for seismic modeling based on the finite element method

We demonstrate an application of an advanced geophysical software tool to simulate seismic wave propagation and generate shot records. Simulation of seismic wave propagation was performed using eScript, a partial differential equation solver based on the finite element method. We solved the 2D acoustic wave equation for P-wave propagation by applying the partial differential equation to eScript. A traditional absorbing boundary condition was applied to reducing artificial wave reflections at the boundary. We tested several different models by employing meshes for layered media and other complex geological structures. Seismometers were placed equidistantly on the surface to record the wave field and generate shot records. Model tests prove that eScript is a user-friendly software platform which allows rapid development of numerical seismic modeling using python and XML. Keyworlds- Finite Element Method; Wave Equation; Numerical Simulation; Shot Records; Wave Propagation

Large scale shear banding in extension

In this paper, we will explore the role of non-coaxiality on shear banding in pure shear. We first outline the consitituve relations. The deformation and localization process is illustrated by results of large deformation finite element simulations on a rectangular domain in extension for different constitutive models. We also show the variation of the average horizontal stress (stress resultant) conjugate to the prescribed boundary velocity with a strain measure for the horizontal extension. We assume incompressible deformations since the emphasis in this study is on large deformations. The equations of motion are integrated using an updated Lagrangian scheme.

A study of localization limiters and mesh dependency in earthquake rupture.

No complete physically consistent model of earthquake rupture exists that can fully describe the rich hierarchy of scale dependencies and nonlinearities associated with earthquakes. We study mesh sensitivity in numerical models of earthquake rupture and demonstrate that this mesh sensitivity may provide hidden clues to the underlying physics generating the rich dynamics associated with earthquake rupture. We focus on unstable slip events that occur in earthquakes when rupture is associated with frictional weakening of the fault. Attempts to simulate these phenomena directly by introducing the relevant constitutive behaviour leads to mesh-dependent results, where the deformation localizes in one element, irrespective of size. Interestingly, earthquake models with oversized mesh elements that are ill-posed in the continuum limit display more complex and realistic physics. Until now, the mesh-dependency problem has been regarded as a red herring—but have we overlooked an important clue arising from the mesh sensitivity? We analyse spatial discretization errors introduced into models with oversized meshes to show how the governing equations may change because of these error terms and give rise to more interesting physics.