Boundary Element Modeling of Pyroelectric Solids with Shell Inclusions

The paper presents general boundary element approach for analysis of thermoelectroelastic (pyroelectric) solids containing shell-like electricity conducting permittive inclusions. The latter are modeled with opened surfaces with certain boundary conditions on their faces. Rigid displacement and rotation, along with constant electric potential of inclusions are accounted for in these boundary conditions. Formulated boundary value problem is reduced to a system of singular boundary integral equations, which is solved numerically by the boundary element method. Special attention is paid to the field singularity at the front line of a shell-like inclusion. Special shape functions are introduced, which account for this square-root singularity and allow accurate determination of field intensity factors. Numerical examples are presented.

Could the black hole singularity be a field singularity?

In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

Stress Intensity Factors and Weight Functions for Longitudinal Semi-Elliptical Surface Cracks Inside Thick-Walled Cylinders Using Highly-Refined Finite-Element Models

Fracture mechanics and fatigue crack-growth analysis rely heavily upon accurate values of stress intensity factors. They provide a convenient, single-parameter description to characterize the amplitude of the stress-field singularity at the crack tip, and are used to correlate brittle fracture and crack growth in pressure vessel and piping applications. Mode-I stress intensity factors that have been obtained for longitudinal semi-elliptical surface flaws on the inside of thick-walled cylinders using highly-refined finite element models are investigated. Using these results, weight function solutions are constructed and selected geometries are validated.