The spatial problem of the compression of a material along a periodic system of parallel circular cracks

Abstract

The non-axisymmetric problem of the biaxial uniform compression of a material along a periodic system of parallel circular cracks is considered. A facture criterion is used /1, 2/ within the framework of linearized stability theory according to which the beginning of fracture of the material under compression along the cracks is characterized by local buckling near the cracks. Within the framework of this approach, axisymmetric and plane problems were considered earlier for different material models (highly-elastic, composite and plastic) for one or two internal cracks, near-surface cracks and a periodic system of cracks /1–13/★★ Proceeding of the Eleventh Scientic Conf. of Young Scientists. Inst. Mechanics, Ukraine Academy of Sciences, Kiev, 1986. 154–161, Dep. VINITI 5507-86, July 28, 1986 Nazarenko, V.M. and Starodubtsev, I.P., On material fracture under compression along two parallel cracks in the case of plane strain. Non-classical and Mixed Problems of the Mechanics of a Deformable Body: Materials of a Seminar of Young Scientists, Kiev, 1985, 142–145, Dep. 5531-85 in VINITI, July 29, 1985.) The investigation is performed in general form for an arbitrary kind of elastic potential for compressible and incompressible materials, the theory of large and modifications of small sub-critical strains, and can be extended to other models of a deformable body (composites, plastic bodies, etc.).