TY - JOUR

T1 - Об эффективных упругих свойствах материала со взаимно перпендикулярными системами параллельных трещин

AU - Абакаров, Абдулла Мурадович

AU - Пронина, Юлия Григорьевна

N1 - Funding Information: This work was supported by the Russian Science Foundation (grant N 21-19-00100). Publisher Copyright: © 2022 Saint Petersburg State University. All rights reserved.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - crack density

KW - crack interaction

KW - effective elastic properties

UR - http://www.scopus.com/inward/record.url?scp=85134183291&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/de8afe4e-2fac-3a49-b25e-b081d6d42293/

U2 - 10.21638/11701/SPBU10.2022.109

DO - 10.21638/11701/SPBU10.2022.109

M3 - статья

AN - SCOPUS:85134183291

VL - 18

SP - 111

EP - 119

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 1

ER -