By the detailed analysis of the modern development of the mechanics of deformable media can be found the deep internal contradiction. From the one hand it is declared that the deformation and fracture are the hierarchical processes which are linked and unite several structural and scale levels. From the other hand the sequential investigation of the hierarchy of the deformation and destruction is not carried out.
The book’s aim is filling this mentioned gap and investigates the hot topic of the fracture of non-ideal media. From the microscopic point of view in the book we study the hierarchy of the processes in fractured solid in the whole diapason of practically used scales. According the multilevel hierarchical system ideology under “microscopic” we understand taking into account the processes on the level lower than relative present strata. From hierarchical point of view the conception of “microscopic fracture” can be soundly applied to the traditionally macroscopic area, namely geomechanics or main crack propagation. At the same time microscopic fracture of the nanomaterials can be well-grounded too. This ground demands the investigation on the level of inter-atomic interaction and quantum mechanical description.
The important feature of the book is the application of fibred manifolds and non-Euclidean spaces to the description of the processes of deformation and fracture in inhomogeneous and defected continua. The non-Euclidean spaces for the dislocations’ description were introduced by J.F. Nye, B.A. Bilby, E. Kröner, K. Kondo in fiftieth. In last decades this necessity was shown in geomechanics and theory of seismic signal propagation. The applications of non-Euclidean spaces to the plasticity allow us to construct the mathematically satisfying description of the processes. Taking into account this space expansion the media with microstructure are understood as Finsler space media. The bundle space technique is used for the
- Crack represent as a quasi-particle
- Finsler metric is taken as intrinsic metric of non-ideal body
- Crack is propagate along the geodesic lines
- Hierarchical nature of the fracture taking into account
- Non-Archimedian numbers are characterized the chaotic properties of hierarchical space
This book is suitable for researchers in the field of fracture mechanics, solid state physics and geomechanics. It can be used as well by the last year students wishing to become more familiar with some modern approaches to the physics of fracture and continual theory of dislocations.