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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.
Keywords: surface microcracks; densely cracked surfaces; the Griffith energy criterion of fracture. |
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