PSI - Issue 51

ScienceDirect Structural Integrity Procedia 00 (2022) 000–000 Structural Integrity Procedia 00 (2022) 000–000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 51 (2023) 206–212

© 2023 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 scientific committee of the ICSID 2022 Organizers Abstract Delamination in a multilayered inhomogeneous viscoelastic beam structure under relaxation is analyzed. The moduli of elasticity of beam layers change with time. A linear viscoelastic model with two springs and a dashpot is used for describing the relaxation behaviour. The response of the model is obtained by considering the equilibrium of its components. The material properties vary continuously along the width of layers. Besides, the modulus of elasticity of one of the springs changes with time. Time-dependent strain energy release rate (TDSERR) for the delamination is found by using the time-dependent strain energy (TDSE) in the beam. The TDSERR is found also by analyzing the compliance. The results are identical. The influence of different factors and parameters on the delamination is evaluated. © 2023 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 scientific committee of the ICSID 2022 Organizers Keywords: Multilayered material; relaxation; inhomogeneous beam; viscoelastic behaviour; delamination; time-dependent behaviour 1. Introduction The attention to continuously inhomogeneous materials paid from international academic community in the recent decades is due to functionally graded materials (FGM) (Gururaja Udupa et al. (2014), Hirai and Chen (1999), Reichardt et al. (2020)). FGM are a kind of continuously inhomogeneous composites which have been frequently used in engineering (Chikh (2019), Kou et al. (2012), Mahamood and Akinlabi (2017)). In fact, the advance in such areas as aeronautics, nuclear fusion, aerospace, electronics and biomedicine is closely related to application of FGM. Multilayered inhomogeneous structures consist of layers of different inhomogeneous materials. Multilayered materials are excellent for reducing the weight of structures. Delamination fracture, or separation of layers, threatens 6th International Conference on Structural Integrity and Durability (ICSID 2022) Multilayered inhomogeneous beam under relaxation: an analytical delamination investigation Victor Rizov* Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria Abstract Delamination in a multilayered inhomogeneous viscoelastic beam structure under relaxation is analyzed. The moduli of elasticity of beam layers change with time. A linear viscoelastic model with two springs and a dashpot is used for describing the relaxation behaviour. The response of the model is obtained by considering the equilibrium of its components. The material properties vary continuously along the width of layers. Besides, the modulus of elasticity of one of the springs changes with time. Time-dependent strain energy release rate (TDSERR) for the delamination is found by using the time-dependent strain energy (TDSE) in the beam. The TDSERR is found also by analyzing the compliance. The results are identical. The influence of different factors and parameters on the delamination is evaluated. © 2023 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 scientific committee of the ICSID 2022 Organizers Keywords: Multilayered material; relaxation; inhomogeneous beam; viscoelastic behaviour; delamination; time-dependent behaviour 1. Introduction The attention to continuously inhomogeneous materials paid from international academic community in the recent decades is due to functionally graded materials (FGM) (Gururaja Udupa et al. (2014), Hirai and Chen (1999), Reichardt et al. (2020)). FGM are a kind of continuously inhomogeneous composites which have been frequently used in engineering (Chikh (2019), Kou et al. (2012), Mahamood and Akinlabi (2017)). In fact, the advance in such areas as aeronautics, nuclear fusion, aerospace, electronics and biomedicine is closely related to application of FGM. Multilayered inhomogeneous structures consist of layers of different inhomogeneous materials. Multilayered materials are excellent for reducing the weight of structures. Delamination fracture, or separation of layers, threatens 6th International Conference on Structural Integrity and Durability (ICSID 2022) Multilayered inhomogeneous beam under relaxation: an analytical delamination investigation 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 * 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 © 2023 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 scientific committee of the ICSID 2022 Organizers 2452-3216 © 2023 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 scientific committee of the ICSID 2022 Organizers

2452-3216 © 2023 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 scientific committee of the ICSID 2022 Organizers 10.1016/j.prostr.2023.10.090