Elastic Dislocation Theory for a Self-Gravitating Elastic Configuration with an Initial Static Stress Field

Self-gravitating elastic bodies

Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small “test” objects. In this note, I will consider models of finite self-gravitating extended objects, which make it possible to give a rigorous treatment of the initial value problem for (finite) extended objects.

Static Self-gravitating Elastic Bodies in Einstein Gravity

We prove that given a stress-free elastic body there exists, for sufficiently small values of the gravitational constant, a unique static solution of the Einstein equations coupled to the equations of relativistic elasticity. The solution constructed is a small deformation of the relaxed configuration. This result yields the first proof of existence of static solutions of the Einstein equations...

Engineering nanophase self-assembly with elastic field

A binary monolayer on an elastic substrate may separate into two phases, which self-assemble into ordered nanoscale patterns. We apply an elastic field to the substrate to guide the self-assembly process. The effect of arbitrary three-dimensional external loading is found to be characterized by a single two-dimensional parameter – a surface stain field of the substrate. A non-uniform strain fie...

Elastic criterion for dislocation nucleation

The notion of theoretical strength, the critical stress at which a perfect crystal under uniform loading becomes structurally unstable, is extended to non-uniform loading. A position-dependent defect nucleation criterion has been derived and applied in molecular dynamics (MD) and finite-element simulations of dislocation emission in single-crystal nanoindentation. The resulting measure has the ...

Multipole representation of the elastic field of dislocation ensembles