PSI - Issue 28

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ScienceDirect

Procedia Structural Integrity 28 (2020) 2245–2252 Structural Integrity Procedia 00 (2020) 000–000 Structural Integrity Procedia 0 (20 0) 000–000

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© 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo © 2020 The Authors. Published by Elsevier B.V. his is an open access article under the CC BY-NC-ND license (http: // creativec mmons.org / licenses / by-nc-nd / 4.0 / ) r-review under responsibility of the European Structural Integrity Society (ESIS) ExCo. Keywords: stress singularity; finite element method; cracks; singularity exponent Abstract In problems of the theory of elasticity, there are singular solutions associated with the presence of infinite values of stresses at separate points (or lines), which are called singular. The great interest due to practical importance is those singular points that define the vertices of plane or spatial cracks. The algorithm for the numerical analysis of singular solutions in two-dimensional and three-dimensional problems of elasticity theory is considered. The numerical algorithm is based on extracting from the finite element solution the power law dependence of stresses near the singular points of the considered region, where singular solutions are possible. Based on the found power-law dependences, a conclusion about the absence or presence of a stress singularity and its nature is made. This algorithm is verified for two-dimensional and three-di ensional problems of the theory of elasticity by co paring the stress singularity exponents found by the proposed numerical method and obtained from known analytical and numerical solutions. The considered algorithm is applicable for variants in which the stress behavior in the vicinity of singular points is described by one power law dependence. One of the purposes of the article is to study the stress behavior near the common vertex of several radial spatial cracks in an isotropic material. In this case, the evaluation of stress behavior in the vicinity of the singular points is based on the construction of a correct stress field pattern by the finite element method when approaching the singular points. The results of numerical studies have shown that the highest stress level near the common vertex is observed for configurations with the equal angles between radial cracks. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo. Keywords: stress singularity; finite element method; cracks; singularity exponent 1st Virtual European Conference on Fracture Numerical analysis of stresses near the vertices of a single and several radial spatial cracks Andrey Fedorov ∗ Institute of Continuous Media Mechanics UB RAS, 1 Academician Korolev Street, Perm 614018, Russian Federation Abstract In problems of the theory of elasticity, there are singular solutions associated with the presence of infinite values of stresses at separate points (or lines), which are called singular. The great interest due to practical importance is those singular points that define the vertices of plane or spatial cracks. The algorithm for the numerical analysis of singular solutions in two-dimensional and three-dimensional problems of elasticity theory is considered. The numerical algorithm is based on extracting from the finite element solution the power law dependence of stresses near the singular points of the considered region, where singular solutions are possible. Based on the found power-law dependences, a conclusion about the absence or presence of a stress singularity and its nature is made. This algorithm is verified for two-dimensional and three-dimensional problems of the theory of elasticity by comparing the stress singularity exponents found by the proposed numerical method and obtained from known analytical and numerical solutions. The considered algorithm is applicable for variants in which the stress behavior in the vicinity of singular points is described by one power law dependence. One of the purposes of the article is to study the stress behavior near the common vertex of several radial spatial cracks in an isotropic material. In this case, the evaluation of stress behavior in the vicinity of the singular points is based on the construction of a correct stress field pattern by the finite element method when approaching the singular points. The results of numerical studies have shown that the highest stress level near the common vertex is observed for configurations with the equal angles between radial cracks. 1st Virtual European Conference on Fracture Numerical analysis of stresses near the vertices of a single and several radial spatial cracks Andrey Fedorov ∗ Institute of Continuous Media Mechanics UB RAS, 1 Academician Korolev Street, Perm 614018, Russian Federation

1. Introduction 1. Introduction

It is known from the theory of elliptic equations that the violation of surface smoothness or smoothness of coef ficients entering into the equations may lead to singular solutions. It will be recalled that the equilibrium equations of elasticity or Lame equations belong to the class of elliptic equations. In the theory of elasticity, the existence of singular solutions is associated with the appearance of infinite stresses at the points or lines, which are called singular. It is known from the theory of elliptic equations that the violation of surface smoothness or smoothness of coef ficients entering into the equations may lead to singular solutions. It will be recalled that the equilibrium equations of elasticity or Lame equations belong to the class of elliptic equations. In the theory of elasticity, the existence of singular solutions is associated with the appearance of infinite stresses at the points or lines, which are called singular.

∗ Corresponding author. Tel.: + 7-342-273-8330 ; fax: + 7-342-237-84-87. E-mail address: fedorov@icmm.ru ∗ Corresponding author. Tel.: + 7-342-273-8330 ; fax: + 7-342-237-84-87. E-mail address: fedorov@icmm.ru

2452-3216 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 10.1016/j.prostr.2020.11.054 2210-7843 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo. 2210-7843 © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http: // creativecommons.org / licenses / by-nc-nd / 4.0 / ) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo.