Related papers: Dislocations in a layered elastic medium with appl…
We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity…
This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lam\'e system in a bounded domain with a mixed homogeneous…
This paper investigates an elastic dislocation problem within a bounded and multi-layered solid governed by the Lam\'e system. We address the simultaneous reconstruction of the faults, the jumps in displacement and traction fields across…
We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…
We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a…
Approximation of problems in linear elasticity having small shear modulus in a thin region is considered. Problems of this type arise when modeling ground motion due to earthquakes where rupture occurs in a thin fault. It is shown that,…
Many recent studies have tried to determine the influence of geometry of faults in earthquake mechanics. In this paper, we suggest a new interpretation of the effect of geometry on the stress on a fault. Starting from the representation…
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
Seeing the Earth crust as crisscrossed by faults filled with fluid at close to lithostatic pressures, we develop a model in which its elastic modulii are different in net tension versus compression. In constrast with standard nonlinear…
By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are…
A comparison of the displacements of the earth's surface after an earthquake was made, calculating with the analytical expressions coming from an infinite flat slab approximation and compared with these numerically considering the…
In this article we present the numerical simulation of a dislocation incorporated into a Cosserat plate. The simulation is based on the mathematical model for bending of Cosserat elastic plates recently developed by the authors. The…
The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…
In Geosciences a class of phenomena that is widely studied given its real impact on human life are the tectonic faults slip. These landslides have different ways to manifest, ranging from aseismic events of slow displacement (slow slips) to…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an…
Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of…
Plastic deformation of crystals is a physical phenomenon, which has immensely driven the development of human civilisation since the onset of the Chalcolithic period. This process is primarily governed by the motion of line defects, called…
Dislocations in soft condensed matter systems such as lamellar systems of polymers, liquid crystals and ternary mixtures of oil, water and surfactant (amphiphilic systems) are described in the framework of continuum elastic theory. These…