Continuum theory of defects: Advanced approaches

Theoretical descriptions of defect field based on differential geometry (Kr'ner 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 Kr'ner 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.