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Basing on the Asymmetric Continuum Theory, we develop the thermodynamics including fragmentation spin fracture processes; applications for the earthquake source processes are considered. The fracture band model is used to describe a dislocation and disclination superlattice. The Gibbs free energy of defect formation is specified. A dynamic spin fracture criterion was formulated. Consequently, a dynamic model of rock fracture employing dislocations, disclinations, and cracks was constructed to describe slip and fragmentation fracture processes in the earthquake sources.

The Asymmetric Continuum Theory based on deformation fields includes the strain rotation as an equally important deformation part as the shear and confining strains; all these fields can be related to their origin in the fracture processes by some displacement motions in a source. Some of these motions may belong to an individual process, some to complex correlated events; in this latter case the displacements related to these strains could be shifted in phase. Moreover, we may expect an appearance of some molecular transport motions; the molecular transport may be helpful for understanding an interaction of the molecular processes and related molecular momentum flux. These correlated events should be mutually related in a source by the release-rebound mechanism. In particular, we consider the point fracture events as associated with a confining load or/and with the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves.

Asymmetric continuum theory points to the equal roles of the rotation motions and those related directly to shear or confining strains. The strain motions could be quite independent or mutually related with the eventual phase shifts, while the displacements have only a mathematical sense; a real displacement may appear along the fracture slip only. Formally, any deformation could be presented as related to the displacements; however, its origin in a fracture source should be considered either as belonging to an individual process or to complex correlated events; in these cases, the confining, shear and rotation strains can be related mathematically to the different displacement fields. Some of these related deformations could be emitted from a source with a phase shift, while the observed displacements (deduced from records) result as a sum of these independent displacements. An important influence on a source process and on the premonitory micro-events has the material defects, their distribution, and mobility. The defect arrays lead to a concentration of stresses and their local reorganization. Thus, in this paper, we consider the induced stresses and strains related to defect content and to its modification and redistribution. Moreover, an important role in understanding the complex correlated events in a source plays the release–rebound mechanism. The release–rebound mechanism in an earthquake source processes leads to a possible direct or phase-shifted correlations between the emitted motions; in this aspect, a propagation of the coupled strain and rotation waves is discussed. In particular, we consider the point fracture events as related either to a confining load or/and to the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. In some important seismic regions, we have the recording system which permits to record the strains and rotations. However, we should point that the wordwide seismological network is not adequate to record the complex strain deformations released in the fracture processes and remains quite insufficient to understand the global stress changes and related strain waves of a very low period. Consideration on a recording mechanism of the long displacement waves indicates the insufficiencies of the present global recording system and points that recording of the global strain and rotation waves is an important and urgent task.

Induced strains play an important role in mining regions and water dam areas. We consider a mechanism of reorganization of the applied stress load by some changes in rock-body defect distribution caused by human activity. A defect content increases with increasing stress load and related deformations; hence, a relationship could appear between seismic risk and deformation level. Recent progress in the Asymmetric Continuum Theory permits to consider some internal reorganization of the applied load due to internal defect content and distribution; in this paper we consider an increase of internal defect densities due to mining works and the appearance of reorganized internal stress distribution.

We present a new development in the asymmetric continuum theory with the shear oscillations (twist motions) and independent spin; these motions (displacement velocities and spin) can be shifted in phase to describe the independent rebound processes. Our approach provides an extension of the asymmetric continuum theory by including the microfragmentation processes with a double transport which may appear in an advanced fracture process under very high load. The related nonlinear equations, leading to soliton solutions, are derived.

We shortly explain why the rotations strains should be included together with the shear strains in the theory of solid continuum; the related arguments are based both on the experimental and theoretical levels. In the presented Asymmetric Continuum Theory the wave propagation mechanism appears in a logical way with the respective shear and rotation strains. In this logical approach we include, beside the shear strains, also the rotation strains and their related wave propagation with shear and rotation strain interactions.

We present a relation between stress moments and antisymmetric part of stresses and the related constitutive law joining those stresses with the particle/point rotations. Correspondence of the asymmetric continuum theory to the micromorphic theory is considered. An extension of the asymmetric continuum theory for the case of 2D anisotropy for antisymmetric stresses leads us to the problems of friction anisotropy and fracture pattern.

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.

We theoretically study spatio-temporal evolution of macroscopic stress in an elastic medium permeated by continuously distributed dislocations. We develop a system of equations governing stress evolution, taking account of growth and coalescence of dislocations. As dislocation distribution evolves, we observe the compatible evolution of stresses. Numerical calculations of these equations denote that stress evolution shows both an increase and a decrease inside the medium, which is due to dislocation interactions, for fixed-stress load on the boundary. This kind of approach will be useful to understand the preparatory process of shallow earthquakes from physical laws at the microscopic level.

We present a comparison between some experimental results on the interaction and synchronization of mechanical and electric fields; such a synchronization may appear with the phase delay by π/2, as shown in recent theoretical results. The solutions related to such a phase-shifted synchronization between some fields follow from the Asymmetric Continuum Theory. This theory concerns not only the mechanical fields, strains and rotations, but also other physical fields entering into interaction with stresses.

In the frame of the asymmetric continuum theory we present some aspects of the micro-fracture processes. An extension of this theory, accommodating for a significant increase of external load, can describe some features of a progressively granulated and fractured material. According to our theory, two kinds of motions – displacements and rotations – in some source processes, e.g., in an earthquake source, may be generated independently or with some phase shift due to the rebound release processes. The asymmetric theory includes a possible phase shift between the simultaneous solutions for the displacement and rotation motions. Equivalently, we present the solutions with the simultaneous strain and rotation motions or those with the π/2 phase shift between them. Such specific solutions can explain the synchronization action in fracture processes.

Theoretical descriptions of defect field based on differential geometry (Kroner 1981) or gauge theory (Edelen and Lagoudas 1988, Yamasaki and Nagahama 2002) are referred to as the continuum theory of defects. In the last few years, continuum theory of defects has created considerable interest in application to space and planetary sciences such as cosmic strings (e.g., Katanaev and Volovich 1999), Einstein-Cartan gravity (e.g., Hehl and Kroner 1965, Puntigam and Soleng 1997), seismicity (e.g., Teisseyre 1995c, Takeo and Ito 1997) and geodesy (Yamasaki and Nagahama 1999). In this chapter, we introduce the continuum theory of defects.