Theoretical Models of Micro-cracked Continua

Discontinuity of Scalar and Vector Fields

Abstract

In order to represent discontinuities in the deformation of a material and its consequences on the energy dissipation during micro-crack kinetics, a model of micro-cracked continuum is derived. The Micro-crack density is represented in terms of the non-metric connection on a manifold. Torsion and curvature of the nonmetric connection represent a non-topological deformation and explicitly include mesoscopic discontinuities. The developed model includes both the non-equilibrium thermodynamic processes of micro-crack creation and the micro-crack growth. This approach contrasts to the empirical methodology of continuum mechanics that seeks a phenomenological description. An illustrative example of the model application is presented for the uniaxial vibration test, providing representations for wave propagation within a micro-cracked solid. The result of this example highlights the importance of rigorously revisiting the conservation laws in the framework of nonmetric connected manifolds.