title: On the effective elastic properties of a material with mutually perpendicular systems of parallel cracks
metadata.name: dc.contributor.author
metadata.value: Abakarov, Abdulla M.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Pronina, Yulia G.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-06-23T13:55:27Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-06-23T13:55:27Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Abakarov A. M., Pronina Yu. G. On the effective elastic properties of a material with mutually perpendicular systems of parallel cracks. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 1, pp. 111–119.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2022.109
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/36936
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The effective properties of cracked solids are often expressed in terms of the crack density
  parameter or its tensor generalization, using the approximation of noninteracting cracks. This
  approximation remains accurate at sufficiently high crack densities, provided the location
  of cracks are random. The presented analysis confirms that the effective elastic moduli of
  a material with ordered fracture structures strongly depend on the linear dimensions of
  cracks and their mutual arrangement even at a constant crack density. A change in these
  parameters can cause a noticeable anisotropy of the effective properties of the material
  even when the eigenvalues of the crack density tensor are equal to each other. The effective
  elastic characteristics of a material with one doubly periodic system of parallel cracks are
  compared with those for a material with two mutually perpendicular systems of such cracks
  in a two-dimensional formulation. The calculations are carried out using the approximate
  method of M. Kachanov for determining the mean stresses at the cracks edges, applicable
  for large systems of interacting cracks. Analysis of the obtained results showed that the
  effective compliance of the material in a certain direction is largely determined by the effects
  of interaction (shielding and amplification) within a system of parallel cracks perpendicular
  to this direction. The interaction of this system of cracks with the perpendicular system has
  a weak effect on the indicated properties in the case of rectangular symmetry of the system.
  In this case, the interaction of mutually perpendicular systems of cracks leads to a violation
  of the symmetry of the tensor of effective elastic constants.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by the Russian Science Foundation (grant N 21-19-00100).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 18; Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: crack density
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: crack interaction
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: effective elastic properties
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the effective elastic properties of a material with mutually perpendicular systems of parallel cracks
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 111-119.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/36936/1/111-119.pdf
resources.format: Adobe PDF
resources.size: 358,57 kB