Notes on the possibilities and limitations of using metrical tools in mechanical modeling of media
10.15660/AUOFMTE.2019-2.3451
G Lámer
glamer@eng.unideb.hu
Volume XXVIII, 2019/2
Changes in the size and shape of a continuous body can be described by metrical tools. The change in size is experimentally associated with relative elongation, the change of shape with the (local) angle change. Within the body, the concept of size (line length) and angle (angle between two lines) is based on the scalar product; the metric tensor is also needed to describe these relationships. When determining the relationship between size and size change as well as angle and angle change, it should be taken into account that, although both length and angle are interpreted by scalar product of metric tensor components, but in the context of relative length change there are fractional functions of radical expressions, in the context of angular change, there are fractional functions of radical expressions and partly inverse angle functions. The tensor cannot be formed directly from these two functions, but only by series expansion, and then there is a limit to the theoretical and numerical application of the introduced strain tensor: that the whole function can be approached well with the first few members of series expansion. This allows only a small strain (small relative elongation) to be described. This limit and the limitation of the use of topological tools (that is, the significant change of size and shape is not a deformation but a rearrangement) are consistent with each with other.
ISSN 1583-0691, CNCSIS "Clasa B+"