A slip wave solution in anti-plane elasticity
It is shown that a slip wave solution exists for anti-plane sliding of an elastic layer on an elastic half-space. It is a companion solution to the well-known Love wave solution.
physics.geo-ph↗
arXiv subjects
K. Ranjith
Publications and source records attributed to K. Ranjith.
Spectral Formulation of the Elastodynamic Boundary Integral Equations for Bi-material Interfaces
A spectral formulation of the plane-strain boundary integral equations for an interface between dissimilar elastic solids is presented. The boundary integral equations can be written in two equivalent forms: (a) The tractions can be written as a space-time convolution of the displacement continuities at the interface (Budiansky and Rice, 1979) (b) The displacement discontinuities can be written as a space-time convolution of the tractions at the interface (Kostrov, 1966). Prior work on spectral formulation of the boundary integral equations has adopted the former as the starting point. The present work has for its basis the latter form based on a space-time convolution of the tractions. Tractions and displacement components are given a spectral representation in the spatial coordinate along the interface. The radiation damping term is then explicitly extracted to avoid singularities in the convolution kernels. With the spectral forms introduced, the space-time convolutions reduce to convolutions in time for each Fourier mode. Due to continuity of tractions at the interface, this leads to a simpler formulation and form of the convolution kernels in comparison to the formulation involving convolutions over the slip and opening history at the bi-material interface. The convolution kernels are validated by studying some model problems to which analytical solutions are known. When coupled with a cohesive law or a friction law at the interface, the formulation proposed here is of wide applicability for studying spontaneous rupture propagation.
cond-mat.mtrl-sci↗
Destabilization of long-wavelength Love and Stoneley waves in slow sliding
Love waves are dispersive interfacial waves that are a mode of response for anti-plane motions of an elastic layer bonded to an elastic half-space. Similarly, Stoneley waves are interfacial waves in bonded contact of dissimilar elastic half-spaces, when the displacements are in the plane of the solids. It is shown that in slow sliding, long wavelength Love and Stoneley waves are destabilized by friction. Friction is assumed to have a positive instantaneous logarithmic dependence on slip rate and a logarithmic rate weakening behavior at steady-state. Long wavelength instabilities occur generically in sliding with rate- and state-dependent friction, even when an interfacial wave does not exist. For slip at low rates, such instabilities are quasi-static in nature, i.e., the phase velocity is negligibly small in comparison to a shear wave speed. The existence of an interfacial wave in bonded contact permits an instability to propagate with a speed of the order of a shear wave speed even in slow sliding, indicating that the quasi-static approximation is not a valid one in such problems.
math-ph↗
Dynamic anti-plane sliding of dissimilar anisotropic linear elastic solids
The stability of steady, dynamic, anti-plane slipping at a planar interface between two dissimilar anisotropic linear elastic solids is studied. The solids are assumed to possess a plane of symmetry normal to the slip direction, so that in-plane displacements and normal stress changes on the slip plane do not occur. Friction at the interface is assumed to follow a rate and state dependent law with velocity-weakening behavior in the steady state. The stability to spatial perturbations of the form exp(ikx_1), where k is the wavenumber and x_1 is the coordinate along the interface is studied. The critical wavenumber magnitude, |k|_cr, above which there is stability and the corresponding phase velocity, c, of the neutrally stable mode are obtained from the stability analysis. Numerical plots showing the dependence of |k|_cr and c on the unperturbed sliding velocity, V_o, are provided for various bi-material combinations of practical interest.
math-ph↗