Modeling of densely cracked surfaces and the Griffith energy criterion of fracture
Considering an elastic homogeneous isotropic body with a periodic family of surface microcracks, it is observed and justified rigorously that an influence of the microcracks on the far-field stress-strain state of the body can be taken into account at an appropriate asymptotic precision in a certain norm by creation of an asymptotic-variational model for an elastic dummy obtained by clipping out a thin near-surface layer of the elastic material. In other words, an abatement of a solid resistance due to the surface damage is equivalent to spalling of a subsurface flake realized in the model as a regular shift of the exterior boundary along the interior normal. The asymptotic-variational model is consistent with both, the Griffith energy criterion of fracture and spectral characteristics (e.g., eigenfrequencies) of the damaged body. At the same time, the traditional modelling through so-called "wall-laws" or singularly perturbed boundary conditions of Wentzel's type leads to ill-posed spectral problems. Numerical schemes for the asymptotic-variational model in the designed regularly perturbed domain do not differ from the ones in the original elastic body with a smooth intact surface that is without microcracks that makes the proposed approach to interpret damaged surfaces efficient.