Micromorphic Continuum and Fractal Fracturing in the Lithosphere

It seems that internal structures and discontinuities in the lithosphere essentially influence the lithospheric deformation such as faulting or earthquakes. The micromorphic continuum provides a good framework to study the continuum with microstructure, such as earthquake structures. Here we briefly introduce the relation between the theory of micromorphic continuum and the rotational effects related to the internal microstructure in epicenter zones. Thereafter the equilibrium equation, in terms of the displacements (the Navier equation) in the medium with microstructure, is derived from the theory of the micromorphic continuum. This equation is the generalization of the Laplace equation in terms of displacements and can lead to Laplace equations such as the local diffusion-like conservation equations for strains. These local balance/stationary state of strains under the steady non-equilibrium strain flux through the plate boundaries bear the scale-invariant properties of fracturing in the lithospheric plate with microstructure.