Geometrical Foundations of Mesomechanics and Lagrangian Formalism

摘要

Results of a scouting program of research in foundations of mesomechanics are presented. A special case of Weyl's geometry was employed to derive equations of thermoelasticity on pure geometrical ground; this demonstrates the potential of using Weyl's geometry as a model of the geometry of the material space. Experimental methods of finding fractal dimensions of fracture surfaces were examined (for various materials) together with a method of fracture profile simulation; the results contribute to developing experimental techniques of studying metric properties of the material space. A new dynamic crack propagation equation was derived on the basis of the least action principle; this is a first step of applying the Lagrangian formalism to deriving equations of continuous damage evolution. (KR)