Asymmetric Continuum Theory: Fracture Processes in Seismology and Extreme Fluid Dynamics

A new joint approach to deformations and motions in solids and fluids is presented. For the theory of solids, in addition to the shear and rotation strains, we define the molecular transport, while for fluids we consider the transport motions and the shear and rotation molecular strains. In this way we arrive at a common asymmetric theory for solids and fluids. Thus, for solids we present the release-rebound relations and related wave equations for strains, while for fluids we present the Navier-Stokes transport relations; moreover, for solids the included molecular transport and for fluids the molecular rotation and shear strains are considered additionally. The molecular transport in solids helps us to understand the fracture preparation processes. Of course, to each of these continua we include an influence of pressure; thus, in fluids we have both the pressure and its time derivative, that is, the molecular pressure related to sound phenomena.