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Differential geometry in modeling the microstructural material media

Rymarz C.

Journal of Technical Physics

2001

Vol. 42, no 1

23-32

The paper contains considerations, which concern an application of differential geometry to construction of a compatible theory of media with microstructure. Technologies of modern materials create a need for modeling the processes and phenomena occurring in such materials. Application of the differential geometry to this end is justified, since this mathematical theory is concisely and logically formulated and exhibits a high level of generality. Therefore the physical theories constructed with application of the geometry are, as usual, very effective. In this paper, a short introduction to the differential geometry is given. Further the outline of geometrical theory of defected media is presented. Main part of the considerations has been devoted to a construction of the micropolar media is a bundle space. The bundle space is a very fruitful extension of the tangent space, because it is Cartesian product of the classical (Euclidean} space and the microstructural fiber space.