PSI - Issue 72

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ScienceDirect

Procedia Structural Integrity 72 (2025) 113–119

12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Axially loaded bars having two-dimensional material inhomogeneity: a lengthwise fracture study with considering the deflection velocity Victor Rizov a, * a Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria Abstract The paper considers how lengthwise fracture behavior is influenced by deflection velocity. Bars with continuous two-dimensional material inhomogeneity are investigated. The parameters of the non-linear stress-strain relationship applied in the current analysis vary continuously along the width and thickness of the bar. There is a lengthwise vertical crack in the bar. The external influence on the bar represents axial displacements that change at a constant velocity. These displacements are applied on the two ends of the bar. In fact, due to the two-dimensional material inhomogeneity, the bar is subjected to eccentric tension. The mechanical behavior of the bar is analyzed. For this purpose, the bar curvatures and the strain in the center of the bar cross-section are studied. Then these curvatures and strains are used to derive the strain energy release rate for the lengthwise crack. Verification is carried out by analyzing the complementary strain energy in the bar. A parametric study is performed. © 2026 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 Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs,

Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia Keywords: Lengthwise fracture; Axial displacement; Inhomogeneous bars; Velocity

1. Introduction More frequent use of continuously inhomogeneous structural materials in a variety of applications in different segments of the modern engineering is a clearly expressed tendency in the recent years (El-Galy et al. (2019), Hirai and Chen (1999), Yan Li et al. (2020)). One of the basic peculiarities of these advanced and highly effective composite

* Corresponding author. Tel.: + (359-2) 963 52 45 / 664; fax: + (359-2) 86 56 863 E-mail address: v_rizov_fhe@uacg.bg

2452-3216 © 2026 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 Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.081