PSI - Issue 77

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2026) 000–000

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 77 (2026) 382–388

© 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 ICSI organizers Abstract The present paper studies theoretically how the longitudinal fracture in functionally graded beam constructions is affected by the time. The beam explored has non-linear viscoelastic mechanical behaviour under static loading. Furthermore, the beam is functionally graded in the direction of thickness. To treat the viscoelastic deformation of the structure, a theoretical model representing a combination of linear and nonlinear dampers and springs is applied. This model has two parameters, namely the modulus of elasticity of the non-linear spring and the coefficient of viscosity of the non-linear dashpot which change with time. The time-dependent strain energy release rate is derived. A significant influence of the time factor on the strain energy release rate is detected. For example, it is found that the strain energy release rate – time graph has an upward slop. The question of the influence of the elastic modulus and the viscosity coefficient on the time-dependent behavior of the strain energy release rate is also clarified. © 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 ICSI organizers Keywords: Beam construction; Time; Longitudinal fracture; Static load; Non-linear viscoelastic behaviour 1. Introduction As known, there is a clear tendency of increasing the usage of functionally graded materials in various spheres of engineering (Hirai and Chen (1999), Marae Djouda et al. (2019), Zhou and Yan (2002)). This can be explained International Conference on Structural Integrity Effect of time on longitudinal fracture in functionally graded beam constructions Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria

* 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 ICSI organizers

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 ICSI organizers 10.1016/j.prostr.2026.01.049