Issue 73

Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Table of Contents

S.B. Sapozhnikov, E.A. Dubovikov https://youtu.be/eD0grzUcAcg

The assessment of the severity of local impact on a pro-bionic composite lattice shell by the use of fiber-optic sensors ....………………………………………………………….………. 1-11 V.M.S. Bomfim, S.L.S. Nunes, G.M. Santos Júnior, C.S. Vieira, D.L.N.F. Amorim https://youtu.be/kwfzIxqwjK0 A simplified nonlinear model for bamboo-reinforced concrete beams based on lumped damage mechanics ................................................................................................................................... 12-22 H. S. Vishwanatha, S. Muralidhara, B. K. Raghu Prasad https://youtu.be/nnlBzAAGGHI Size effect in concrete beams: a numerical investigation based on the size effect law ……………. 23-40 A. Masmoudi, A. Khechai, A. Bouaziz, G. Belhi, A. Zeroual, Y. Adimi https://youtu.be/IinfxOwQT7w Experimental investigation on mechanical behavior of sandwich structures using Digital Image Correlation (DIC) …...………………...……………………………….……….......... 41-58 U. De Maio, F. Greco, P. Lonetti, P. Nevone Blasi, G. Sgambitterra https://youtu.be/VtOUz0cKwyk Flood-induced load effects on real-scale structures: a 3D multilevel dynamic analysis ………….. 59-73 R. K. Singh, K. Verma, G. C. Mohan Kumar https://youtu.be/XYHBDOMHrN0 Predictive modeling of PMMA-based polymer composites reinforced with hydroxyapatite: a machine learning and FEM approach ......................................................................................... 74-87 N. Laouche, A. Saimi, I. Bensaid, M. Dahmane, H. Ait Atmane https://youtu.be/O-xYF0nAA-8 A study on the crack presence effect on dynamical behavior of higher-order Quasi-3D composite steel-polymer concrete box section beams via DQFEM …………………………………… 88-107 V. Pisarev, S. Eleonsky, Y. Matvienko, G. Gvozdeva https://youtu.be/Wam5eEwVE70 Influence of contact interaction character on residual stresses arising over damaged area in composite plate …..……………………………………………...………….……...… 108-130

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Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

L. Malíková, P. Miarka https://youtu.be/jRUyzMQXats Parametric study on the effect of anchor’s geometry on the stress distribution and crack initiation direction in a concrete body …………………………………………………………..... 131-138 J. M. Parente, L. M. Ferreira, P. N.B. Reis https://youtu.be/L7OlqK8ZKos Damage mechanisms in hybrid composites: experimental characterisation and energy-based numerical analysis ………………………………..………………………......………. 139-152 C. F. Popa, S. V. Galatanu, L. Marsavina https://youtu.be/loejiXdV-m0 Prediction of the tensile strength of FDM specimens based on Tsai Hill criteria …..................… 153-165 B.-T. Vu, X.-L. Nguyen, D.-D. Nguyen, T.-T. Tran, D.-N. Tran, N.-L. Nguyen, T.- T. Bui https://youtu.be/6NVw8ZMgAHQ Phase-field modeling for investigating the effect of rebar positioning and uniform versus non uniform corrosion on concrete fracture ………………………………………………….... 166-180 V. Tomei, E. Grande, M. Imbimbo https://youtu.be/qxJNUF8az8s Experimental test on 3D-printing components for Architectural Restoration ................................ 181-199 S. Mara ş , Ç. Bolat https://youtu.be/uApt_r5KCWA An investigation on the free vibration behaviors of additively manufactured PA6 layered plates: influences of stacking sequence, infill ratio, and boundary conditions ……………………….... 200-218 M. Ravikumar https://youtu.be/RY_LuR68KDg Investigation on the tensile strength, hardness and wear properties in n-B4C reinforced Al7075 composites ……………………………………………………………….………….. 219-235 H. Taoufik, A. H. Fouad, M. Fatima https://youtu.be/KClr-ARpM0k Damage of additively manufactured polymer materials: experimental and probabilistic analysis .... 236-255 D. Leonetti, B. van Schuppen, M. Jahanian, S. Mobder, H.H. Snijder https://youtu.be/cPjZ4VqYq_k An experimental study into the net cross-sectional failure of damaged plates with holes for different steel grades and temperatures ………......................................................................................... 256-266 Z. Xiong, D. Di, H. Wang, Z. Pan, M Feldmann https://youtu.be/xOR0yYAkk3c Integral bridge abutment with composite dowels: structural scheme and failure patterns …............. 267-284

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Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Editorial Team

Editor-in-Chief Francesco Iacoviello Sabrina Vantadori

(Università di Cassino e del Lazio Meridionale, Italy)

(Università di Parma, Italy)

Co-Editor in Chief Filippo Berto

(Università di Roma “Sapienza”, Italy)

Jianying He Oleg Plekhov

(Norwegian University of Science and Technology (NTNU), Trondheim, Norway)

(Perm Federal Research Center of the Ural, Perm, Russia)

Section Editors Sara Bagherifard Vittorio Di Cocco Stavros Kourkoulis

(Politecnico di Milano, Italy)

(Università di Cassino e del Lazio Meridionale, Italy) (National Technical University of Athens, Greece) (National Technical University of Athens, Greece)

Ermioni Pasiou

(Perm federal research center Ural Branch Russian Academy of Sciences, Russian Federation)

Oleg Plekhov

Ł ukasz Sadowski Daniela Scorza

(Wroclaw University of Science and Technology, Poland)

(Università di Parma, Italy)

Advisory Editorial Board Harm Askes

(University of Sheffield, Italy) (Tel Aviv University, Israel) (Politecnico di Torino, Italy) (Università di Parma, Italy) (Politecnico di Torino, Italy) (Politecnico di Torino, Italy)

Leslie Banks-Sills Alberto Carpinteri Andrea Carpinteri Giuseppe Ferro Youshi Hong M. Neil James Gary Marquis Liviu Marsavina Thierry Palin-Luc Robert O. Ritchie Yu Shou-Wen Darrell F. Socie Ramesh Talreja David Taylor Cetin Morris Sonsino Donato Firrao Emmanuel Gdoutos Ashok Saxena Aleksandar Sedmak

(Democritus University of Thrace, Greece) (Chinese Academy of Sciences, China)

(University of Plymouth, UK)

(Helsinki University of Technology, Finland)

(University Politehnica Timisoara, Department of Mechanics and Strength of Materials, Romania) (Ecole Nationale Supérieure d'Arts et Métiers | ENSAM · Institute of Mechanics and Mechanical Engineering (I2M) – Bordeaux, France)

(University of California, USA)

(Galgotias University, Greater Noida, UP, India; University of Arkansas, USA)

(University of Belgrade, Serbia)

(Department of Engineering Mechanics, Tsinghua University, China)

(University of Illinois at Urbana-Champaign, USA)

(Fraunhofer LBF, Germany) (Texas A&M University, USA) (University of Dublin, Ireland)

John Yates

(The Engineering Integrity Society; Sheffield Fracture Mechanics, UK)

Regional Editorial Board Nicola Bonora

(Università di Cassino e del Lazio Meridionale, Italy)

Raj Das

(RMIT University, Aerospace and Aviation department, Australia)

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Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Dorota Koca ń da Stavros Kourkoulis Carlo Mapelli Liviu Marsavina

(Military University of Technology, Poland) (National Technical University of Athens, Greece)

(Politecnico di Milano, Italy)

(University of Timisoara, Romania) (Tecnun Universidad de Navarra, Spain)

Antonio Martin-Meizoso Mohammed Hadj Meliani

(LPTPM , Hassiba Benbouali University of Chlef. Algeria) (Indian Institute of Technology/Madras in Chennai, India)

Raghu Prakash

Luis Reis Elio Sacco

(Instituto Superior Técnico, Portugal) (Università di Napoli "Federico II", Italy) (University of Belgrade, Serbia) (Tel-Aviv University, Tel-Aviv, Israel)

Aleksandar Sedmak

Dov Sherman Karel Sláme č ka

(Brno University of Technology, Brno, Czech Republic) (Middle East Technical University (METU), Turkey)

Tuncay Yalcinkaya

Editorial Board Jafar Albinmousa Mohammad Azadi Nagamani Jaya Balila

(King Fahd University of Petroleum & Minerals, Saudi Arabia) ( Faculty of Mechanical Engineering, Semnan University, Iran) (Indian Institute of Technology Bombay, India) (Università di Cassino e del Lazio Meridionale, Italy) (Institute of sciences, Tipaza University center, Algeria) (GM Institute of Technology, Dept. Of Mechanical Engg., India)

Costanzo Bellini

Oussama Benaimeche

K. N. Bharath

Alfonso Fernández-Canteli

(University of Oviedo, Spain) (University of Mascara, Algeria)

Bahri Ould Chikh

Angélica Bordin Colpo

(Federal University of Rio Grande do Sul (UFRGS), Brazil)

Mauro Corrado

(Politecnico di Torino, Italy)

Dan Mihai Constantinescu

(University Politehnica of Bucharest, Romania)

Abílio de Jesus

(University of Porto, Portugal) (Università della Calabria, Italy) (University of Belgrade, Serbia)

Umberto De Maio

Milos Djukic

Andrei Dumitrescu

(Petroleum-Gas University of Ploiesti, Romania)

Devid Falliano

(Dipartimento di Ingegneria Strutturale, Edile e Geotecnica, Politecnico di Torino, Italy)

(Federal University of Pampa (UNIPAMPA), Brazil)

Leandro Ferreira Friedrich

Parsa Ghannadi Eugenio Giner

(Islamic Azad university, Iran)

(Universitat Politècnica de València, Spain) (Université-MCM- Souk Ahras, Algeria) (Middle East Technical University, Turkey) (Hassiba Benbouali University of Chlef, Algeria) (Università di Roma “La Sapienza”, Italy)

Abdelmoumene Guedri

Ercan Gürses

Abdelkader Hocine Daniela Iacoviello

Ali Javili

(Bilkent University, Turkey) (Southeast University, China) (University of Piraeus, Greece) (Federal University of Pampa, Brazil)

Cai Jingming

Dimitris Karalekas

Luis Eduardo Kosteski

Sergiy Kotrechko Grzegorz Lesiuk

(G.V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine, Ukraine)

(Wroclaw University of Science and Technology, Poland)

Qingchao Li Paolo Lonetti

(Henan Polytechnic University, China)

(Università della Calabria, Italy)

Tomasz Machniewicz

(AGH University of Science and Technology) (Università Politecnica delle Marche, Italy)

Erica Magagnini Carmine Maletta

(Università della Calabria, Italy) (Università Roma Tre, Italy) (University of Porto, Portugal) (University of Porto, Portugal)

Sonia Marfia

Lucas Filipe Martins da Silva

Pedro Moreira

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Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Mahmoud Mostafavi Madeva Nagaral Vasile Nastasescu

(University of Bristol, UK)

(Aircraft Research and Design Centre, Hindustan Aeronautics Limited Bangalore, India) (Military Technical Academy, Bucharest; Technical Science Academy of Romania)

Stefano Natali Pavlos Nomikos

(Università di Roma “La Sapienza”, Italy) (National Technical University of Athens, Greece)

(Karpenko Physico-Mechanical Institute of the National Academy of Sciences of Ukraine, Ukraine)

Hryhoriy Nykyforchyn

Marco Paggi

(IMT Institute for Advanced Studies Lucca, Italy) (Università di Cassino e del Lazio Meridionale, Italy)

Gianluca Parodo Arturo Pascuzzo

(Università della Calabria, Italy)

Hiralal Patil

(GIDC Degree Engineering College, Abrama-Navsari, Gujarat, India)

Alessandro Pirondi Andrea Pranno Zoran Radakovi ć D. Mallikarjuna Reddy

(Università di Parma, Italy) (Università della Calabria)

(University of Belgrade, Faculty of Mechanical Engineering, Serbia) (School of Mechanical Engineering, Vellore Institute of Technology, India)

Luciana Restuccia

(Politecnico di Torino, Italy) (Università di Padova, Italy) (Università di Messina, Italy) (Università di Parma, Italy)

Mauro Ricotta

Giacomo Risitano Camilla Ronchei

Hossam El-Din M. Sallam

(Jazan University, Kingdom of Saudi Arabia) (Università di Roma "Tor Vergata", Italy)

Pietro Salvini Mauro Sassu Raffaele Sepe

(Università di Cagliari, Italy) (Università di Salerno, Italy)

Abdul Aabid Shaikh

(Prince Sultan University, Saudi Arabia)

Dariusz Skibicki Marta S ł owik Luca Sorrentino Andrea Spagnoli Cihan Teko ğ lu Dimos Triantis Andrea Tridello

(UTP University of Science and Technology, Poland)

(Lublin University of Technology, Poland)

(Università di Cassino e del Lazio Meridionale, Italy)

(Università di Parma, Italy)

(TOBB University of Economics and Technology, Ankara, Turkey)

(University of West Attica, Greece) (Politecnico di Torino, Italy) (Università di Pisa, Italy) (Universidade de Brasília, Brasilia) (Kettering University, Michigan,USA)

Paolo Sebastiano Valvo Cristian Vendittozzi

Charles V. White Andrea Zanichelli Shun-Peng Zhu

(Università di Parma, Italy)

(University of Electronic Science and Technology of China, China)

Special Issue Vittorio Di Cocco Camilla Ronchei

Crack Paths - CP2024

(Università di Cassino e del Lazio Meridionale, Italy)

(Università di Parma, Italy) (Università di Parma, Italy) (Università di Parma, Italy)

Daniela Scorza

Sabrina Vantadori

Special Issue

Modeling in Structural Integrity

Bartlomiej Blachowski

(IPPT PAN, Poland)

Martin Krejsa Petr Lehner

(VSB-Technical University of Ostrava, Czech Republic) (VSB-Technical University of Ostrava, Czech Republic)

Majid Movahedi Rad

(Széchenyi István University, Hungary) (California State University Fullerton, USA)

Ghosh Pratanu

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Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Alexander Sedmak

(University of Belgrade, Serbia)

Special Issue

Russian mechanics contributions for Structural Integrity

(Mechanical Engineering Research Institute of the Russian Academy of Sciences, Russia) (Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Russia)

Valerii Pavlovich Matveenko

Oleg Plekhov

Special Issue

Damage mechanics of materials and structures

Shahrum Abdullah

(Universiti Kebangsaan Malaysia) (Universiti Kebangsaan Malaysia)

Salvinder Singh

VI

Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Fracture and Structural Integrity (Frattura ed Integrità Strutturale) is an Open Access journal affiliated with ESIS

Sister Associations help the journal managing Algeria: Algerian Association on Fracture Mechanics and Energy -AGFME Australia: Australian Fracture Group – AFG Czech Rep.: Asociace Strojních Inženýr ů (Association of Mechanical Engineers) Greece: Greek Society of Experimental Mechanics of Materials - GSEMM India: Indian Structural Integrity Society - InSIS Israel: Israel Structural Integrity Group - ISIG Italy: Associazione Italiana di Metallurgia - AIM Italy: Associazione Italiana di Meccanica Teorica ed Applicata - AIMETA Italy:

Società Scientifica Italiana di Progettazione Meccanica e Costruzione di Macchine - AIAS Group of Fatigue and Fracture Mechanics of Materials and Structures

Poland: Portugal:

Portuguese Structural Integrity Society - APFIE Romania: Asociatia Romana de Mecanica Ruperii - ARMR Serbia:

Structural Integrity and Life Society "Prof. Stojan Sedmak" - DIVK Grupo Espanol de Fractura - Sociedad Espanola de Integridad Estructural – GEF

Spain: Turkey: Ukraine:

Turkish Solid Mechanics Group

Ukrainian Society on Fracture Mechanics of Materials (USFMM)

VII

Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Journal description and aims Fracture and Structural Integrity (Frattura ed Integrità Strutturale) is the official Journal of the Italian Group of Fracture. It is an open-access Journal published on-line every three months (January, April, July, October). Fracture and Structural Integrity encompasses the broad topic of structural integrity, which is based on the mechanics of fatigue and fracture and is concerned with the reliability and effectiveness of structural components. The aim of the Journal is to promote works and researches on fracture phenomena, as well as the development of new materials and new standards for structural integrity assessment. The Journal is interdisciplinary and accepts contributions from engineers, metallurgists, materials scientists, physicists, chemists, and mathematicians. Contributions Fracture and Structural Integrity is a medium for rapid dissemination of original analytical, numerical and experimental contributions on fracture mechanics and structural integrity. Research works which provide improved understanding of the fracture behaviour of conventional and innovative engineering material systems are welcome. Technical notes, letters and review papers may also be accepted depending on their quality. Special issues containing full-length papers presented during selected conferences or symposia are also solicited by the Editorial Board. Manuscript submission Manuscripts must be written using a standard word file without any specific format and submitted via e-mail to gruppofrattura@gmail.com. Papers should be written in English. A confirmation of reception will be sent within 48 hours. The review and the on-line publication process will be concluded within three months from the date of submission. Peer review process Fracture and Structural Integrity adopts a single blind reviewing procedure. The Editor in Chief receives the manuscript and, considering the paper’s main topics, the paper is remitted to a panel of referees involved in those research areas. They can be either external or members of the Editorial Board. Each paper is reviewed by two referees. After evaluation, the referees produce reports about the paper, by which the paper can be: a) accepted without modifications; the Editor in Chief forwards to the corresponding author the result of the reviewing process and the paper is directly submitted to the publishing procedure. b) accepted with minor modifications or corrections (a second review process of the modified paper is not mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. c) accepted with major modifications or corrections (a second review process of the modified paper is mandatory); the Editor in Chief returns the manuscript to the corresponding author, together with the referees’ reports and all the suggestions, recommendations and comments therein. d) rejected. The final decision concerning the papers publication belongs to the Editor in Chief and to the Associate Editors. The reviewing process is usually completed within three months. The paper is published in the first issue that is available after the end of the reviewing process.

Publisher Gruppo Italiano Frattura (IGF) http://www.gruppofrattura.eu ISSN 1971-8993 Reg. Trib. di Cassino n. 729/07, 30/07/2007

Fracture and Structural Integrity (Frattura ed Integrità Strutturale) is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0)

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Fracture and Structural Integrity 73 (2025); International Journal of the Italian Group of Fracture

Fracture and Structural Integrity news

D

ear friends, don’t forget the upcoming joint conference organized by IGF: IGF28 - MedFract3 (https://www.igf28 medfract3.eu/). This event combines the 28th International Conference on Fracture and Structural Integrity (IGF28) with the 3rd Mediterranean Conference on Fracture and Structural Integrity (MedFract3) . The conference will be held both in person in the beautiful setting of Aci Castello (Catania, Italy) and remotely. While remote participants will be able to fully engage in all sessions and discussions, they will unfortunately miss the opportunity to savor the delicious cuisine of Sicily! Five different thematic symposia and a Summer School entitled “ AI-Driven Innovations in Structural Integrity ”are organized during the Conference. It is important to underline that all fees collected will be entirely dedicated to::  Event organisation;  Summer School organization; Discover a new dimension of collaborative research with our shared NotebookLM presentations. These aren't just static documents; they're dynamic, interactive environments designed to foster deeper understanding and collective exploration. Imagine dissecting complex topics, contributing insights, and building upon shared knowledge in real-time. Our shared notebooks offer unparalleled opportunities for discussion, allowing you to seamlessly integrate your perspectives and questions directly within the research context. This innovative approach breaks down barriers, making scientific inquiry a truly collaborative endeavor. Elevate your research experience by engaging with data, analyses, and ideas in a uniquely interactive and shared space. Prepare to unlock new levels of insight through collective intelligence. The first NotebookLM presentation we published is focused on our first thematic issue entitled “ Revisiting classical concepts of Linear Elastic Fracture Mechanics ”. Stay tuned! Soon, other shared NotebookLM presentations will be available in the journal website. Ciao  Publication of the dedicated Procedia Structural Integrity issue;  Publication of the IGF journal Fracture and Structural Integrity ;  All other IGF activities (e.g., website publication). With this issue we activated a new service in the Fracture and Structural Integrity website: Ask to AI.

Francesco Iacoviello Fracture and Structural Integrity Editor in Chief

IX

S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

The assessment of the severity of local impact on a pro-bionic composite lattice shell by the use of fiber-optic sensors

S.B. Sapozhnikov South Ural State University (National research university), Chelyabinsk, Russia Central aerohydrodynamic institute (TsAGI), Zhukovsky, Russia sapozhnikovsb@susu.ru, https://orcid.org/0000-0002-7022-4865 E.A. Dubovikov Central aerohydrodynamic institute (TsAGI), Zhukovsky, Russia evgeny.dubovikov@tsagi.ru, https://orcid.org/0000-0001-9402-3649

Citation: Sapozhnikov, S.B., Dubovikov E.A., The assessment of the severity of local impact on a pro-bionic composite lattice shell by the use of fiber-optic sensors, Fracture and Structural Integrity, 73 (2025) 1-11.

Received: 28.02.2025 Accepted: 27.03.2025 Published: 05.04.2025 Issue: 07.2025

Copyright: © 2025 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

K EYWORDS . Lattice shell, Local impact, Fiber optic sensor, Thermoplastic protective tab, Residual strain.

I NTRODUCTION

he health of critical composite structures is impossible without installing sensors based, for example, on fiber optic, strain gauges or piezoelectric sensors in critical areas [1-3]. A request to SCOPUS on the topic of fiber optic sensor (FOS) for aerospace revealed more than 1000 publications, demonstrating a steady growth, starting from one in 1984 to 177 publications in 2024. T

1

S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

Information from the installed FOS is recorded and processed in order to determine the place of a local impact [4,5], the size of a defect like delamination [4-7] or the approach to catastrophic failure [8,16]. The FOS item in the mechanics of composites is not complete, developing to wider strain or thermal range [20-22], to measure of magnetic fields [20,23], to solve problems of visualization of measuring results and machine learning [19,24], to fastening measurement process and miniaturization of FBG sensors [25], to getting higher accuracy by doping of nanoparticles [26]. For aircraft structures, local impacts by foreign bodies are dangerous due to the fragility of composites based on carbon-, glass- or organic fibers [9]. It forces the introduction of additional safety factor and reduces the potentially high weight efficiency of composite structures. To solve the above-mentioned problems, relatively recently pro-bionic lattice shells (PBLS) have been proposed [10-12], containing not two, but three systems of load-bearing ribs made of UD composite, protective tabs on the ribs and an outer elastic skin to take aerodynamic forces. The load-bearing ribs are located deeper in the structure and protected from external impacts by the skin lying on the protective tab, Fig. 1. In this case, the use of traditional non-destructive testing technics like ultrasound or thermal vision is impossible.

Figure 1: The PBLS and its fragment: rib (1), protective tab (2), impactor (3) and skin (4).

During a local impact, the elastic skin bends without breaking, and the tab dampens the impact, extending the contact time and reducing the contact load [11,12]. In the practice of testing of aircraft composite elements, the concept of a “standard impact” is used, i.e. a low-velocity impact by a falling body with a given energy, which should not damage the load-bearing elements [13-15]. In this work, these are the ribs of the PBLS, protected by special tabs made of thermoplastic material. According to the aim of this article, it needs to use these tabs also as sensing media of impact, carrying embedded FOS. At the same time, questions remain open: what parameters should the damping tab have, what happens to the PBLS elements after the impact, where did the impact occur, can FOS (Bragg or Brillouin) register residual strain of the load bearing rib? This paper attempts to answer these questions based on numerical modeling of the low-velocity impact process.

M ODELING

T

here are two tasks here: the first is to justify the cutting of a small enough volume from a whole shell for detailed study of the stress state and the second - correctly assign boundary conditions for that detailed volume.

Smooth shell For an estimate of the contact time, the magnitude of the loads acting in the “impactor - shell” contact, we will represent the PBLS with an isogrid mesh of ribs as a smooth shell made of a quasi-isotropic equivalent material [10,17]. Elastic modulus and Poisson's ratio of that material are calculated using the dependencies

  A A A A 2 12 ,

12

 

E A

(1)

11

22

22

Here

2

S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

n

n

1

1

 i 1 

 i 1 

4

2

2

(2)





A

i i E δ cos φ , A i

i i E δ sin φ cos φ i

11

12

i

a

a

i

i

The density of the equivalent shell material is

  n i

 i

 

(3)

 i

i a 1

Parameters of the lattice shell: a,  Е and  – distance between ribs, width, lay-up angle with the longitudinal axis of the shell, modulus of elasticity and density of the material of the rib of the i-th family. All ribs have the same height h. If the parameters of the lattice shell are known and, for example:  90  30  30  (isotropic scheme), the smooth shell should be made of a virtual material with E=5.2 GPa,  0.333,  0.15 g/cm3. Next, let’s look at the shell (wide body civil aircraft fuselage) with an outer diameter D=4 m and a length L=12 m, subjected to a local impact by a steel sphere with a diameter of 50.8 mm (weight 0.539 kg) with different energies E=5, 10, 20 and 50 J. Fig. 2 shows the scheme of the problem, in which the geometry was created in the SolidWorks software (thin shell and solid sphere). Numerical calculations were performed in the ANSYS (explicit dynamics). The total process time t=2 ms, the impactor velocities before contact V=4.33; 6.12; 8.66 and 13.7 m/s.

Figure 2: Model, FE mesh, detailed zone and deflection picture (V=4.33 m/s) of the shell at t=1 ms.

Fig. 3 shows the dependences of the impactor velocity V(t), the displacement of the shell during contact and the contact force P(t) obtained by calculation based on the FEM data using numerical differentiation of V(t)

 

dV t

 

    ,

 



P t

m a t a t

(4)

dt

The maximum contact force is about 3.2 kN, and the maximum deflection of the shell at the point of contact is 1.59 mm. The coefficient of restitution - the ratio of the rebound velocity (0.98 m/s) to the initial velocity (4.33 m/s) is 0.226. In other words, almost 80% of the energy of the falling body is converted into the energy of shell deformation.

3

S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

For other impact energies, the results are qualitatively the same. Tab. 1 shows the generalized calculation results. The contact time in all cases is about 1.51 ms.

Figure 3: Model, FE mesh, detailed zone and deflection picture (V=4.33 m/s) of the shell at t=1 ms.

Impactor velocity, m/s

Shell displacement, mm

Recovery coefficient, -

Impact energy, J

Contact force, kN

Contact time, ms

5

4.33 6.12 8.66 13.7

3.20

1.59 2.24 3.27 5.27

0.226 0.269 0.275 0.269

1.50 1.51 1.51 1.54

10 20 50

4.2

6.40

10.01

Table 1: Calculation results.

Detailed modeling of the PBLS fragment Next, we will consider quasi-static loading of a fragment of the mesh shell with the found forces. The fragment has hinged support at the edges, based on the nature of the shell bending during the impact, Fig. 4 (cross section, amplification of displacements by 50 times).

Figure 4: Deformation of the shell under local impact. Time 0.8877 ms.

Here we can see the change in the sign of the curvature - from positive to negative (see arrows), which allows us to find the correct boundary conditions - the position of the hinge supports for simplified modeling of the fragment's deformation. The fragment has two planes of symmetry, so it is rational to consider ¼ of the part, Fig. 4. It is important to note that the PBSO rib is made layered, consisting of a unidirectional composite and a polymer matrix, which reflects the technology of wet winding of a lattice shell with carbon fiber bundles.

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In [18], it was shown that the presence of layers of a polymer matrix during transverse compression of the rib creates additional tension of the composite layer across the fibers (in the plane of the layer), halving the rib's fracture stress. The protective tab is made of thermoplastic PA6 with a thickness of 5 mm, and the skin is made of 3D-woven aramid FRP with a thickness of 1.5 mm. The steel indenter has a diameter of 2 inches (50.8 mm). A force of 10.01/4=2.5 kN is applied to the indenter corresponding to the case with an impact energy of 50 J.

Figure 5: Fragment of the PBSO (total length 200 mm, left) and its ¼ part for calculations (right).

The loading program consisted of two stages: increasing the force to a value of 2.5 kN and unloading. The materials of the tab and polymer matrix were assumed isotropic elastic-plastic with a bilinear diagram. Tab. 2 shows the elasticity parameters of the models of all materials, and Tab. 3 - the strength parameters. Here  Y - yield strength, ES is the tangent modulus at the stage of plastic deformation, e* is the failure strain. Carbon fiber reinforced plastic (CFRP) and aramid fabric reinforced plastic (AFRP) are orthotropic materials (9 elasticity characteristics and 9 strength characteristics along main axis of materials).

density g/sm 3

E 1

E 2

E 3

G 12

G 23

G 13

  

  

  

Material

GPa

GPa

-

UD CFRP

1.55 1.30 1.16 1.20 7.85

200

8.6

8.6

4.7

4.7

4.7

0.27 0,04

0.40

0.27

AFRP*

10

10

5

2

2

2

0.3

0.3

Resin epoxy

3.78

- - -

0.35 0.40 0.30

PA6 Steel

2.0

200

*3D-weaving, low elastic modulus (polyurethane matrix)

Table 2: Elasticity characteristics (for evaluation only).

F 1t

F 1c

F 2t

F 2c

F 3t

F 3c

F 12

F 23

F 13

Material

MPa

UD GFRP

2000 1500

1000

60

200 800

60

200 300

70 50

60 50

70 50

AFRP*

800

1500

200

Es= 1000 MPa Es=300 MPa

e*=0.05 e*=0.20

Resin epoxy

 Y =60 MPa  Y =40 MPa

PA6 Steel

-

-

-

Table 3: Strength characteristics (for evaluation only).

Fig. 6 shows the boundary conditions and the finite element (FE) mesh. It is important to note that the share topology option (ANSYS, SpaceClaim module) was used when creating the model to have common nodes on the layer interfaces and to exclude operations with contact algorithms. It significantly decreases the calculation time for geometrically and physically nonlinear problems. Frictionless contact is established between the indenter and the skin.

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S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

Figure 6: Boundary conditions and FE mesh.

The calculations were performed in the ANSYS on a multiprocessor cluster of South Ural State University. The results of calculating the displacements and stresses in the fragment elements are shown in Figs. 7-9.

Figure 7: Displacement pictures at t=1 s (maximum load) and t=2 s (complete unloading).

Figure 8: Pictures of von Mises stresses in the tab at t=1 s (maximum load) and t=2 s (complete unloading).

In Fig. 8, the yield zone (stresses above 40 MPa) is marked in red on the left. On the right is the picture of residual stresses in the tab. Obviously, the presence of residual stresses allows asserting the possibility of recording residual deformations and localizing the impact site using the FOS. Fig. 9 shows the distribution of maximum and residual deformations in carbon fiber layers. It can be seen that after unloading, the level of strain on the lower surface of the rib is 0.03-0.04%, which is close to the detection limit of the FOS.

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S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

It follows that the sensors should be located into the body of the tab at the contact surface with the skin. Fig. 10 shows the distribution of strain in the skin.

Figure 9: Longitudinal deformations in composite layers at t=1 s (maximum load) and t=2 s (complete unloading).

Figure 10: Distribution of strain in the skin at t=1 s (maximum load) and t=2 s (complete unloading).

D ISCUSSION

T

he distribution of strain along the contact line of the skin with the tab (dotted arrow, Fig. 11) is shown in Fig. 11. Near the contact point, the strain reaches 2%, which is acceptable for the FOS. After unloading, the maximum residual strain is about 0.5%. This value can be reliably recorded by the FOS. The measurement step should be no more than 15 mm in order to record the impact point with an error of ±7.5 mm.

Figure 11: Strain along the contact line of the tab with the skin (50 J).

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S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

With an impact with less energy (20 J), the FOS will show smaller strain along the contact line of the tab with the skin, Fig. 12. Tab. 4 shows the dependences of the maximum values of longitudinal strain in the tab material upon impact and the maximum residual values as a function of the impact energy. The stress state in the UD CFRP rib layers is shown in Fig. 13. The danger is posed by the compression stresses along the fibers of the upper layer, which are close to the strength limit, as well as the stresses across the fibers, which exceed the tensile strength of the UD CFRP (Tab. 3). Analysis of these results shows that when impact has an energy of 50 J, the upper layer of CFRP cracks along the fibers and may lose stability when compressed.

Figure 12: Strain along the contact line of the tab with the skin (20 J).

Impact energy, J

5

10

20

50

Maximum strain, %

1.35

1.67

2.05

2.57

Residual strain, %

0.57

0.83

1.28

2.07

Table 4: Strain in the impact zone.

It follows that the protective tab material should not have large transverse strain to avoid cracking of the UD CFRP along the fibers. For this purpose, it is proposed to install a thin layer (0.5 mm) of fabric AFRP under the tab, Fig. 14, and reduce the thickness of the pad from 5 to 4 mm.

Figure 13: Stress state in UD CFRP layers (50 J).

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S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

Figure 14: Typical (left) and new (right) design.

The elastic moduli of fabric AFRP for the warp and weft are E1 = E2  30 GPa and this will restrain the transverse strain of the thermoplastic tab, Fig. 15.

Figure 15: Stress state in UD CFRP layers (50 J).

It can be seen that the stresses along the fibers have not changed, and across the fibers have decreased to a safe level. With this modification, the skin strain at the boundary with the thermoplastic tab have remained virtually unchanged, Fig. 16 (see also Fig. 11). A slight increase in maximum strain is observed (from 2 to 2.1%), which is not critical for the strength of the optical fiber.

Figure 16: Deformations along the contact line of the pad with the skin (50 J).

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S.B. Sapozhnikov et alii, Fracture and Structural integrity, 73 (2025) 1-11; DOI: 10.3221/IGF-ESIS.73.01

C ONCLUSIONS

I

n the paper, the finite element analysis of the overall loading of a cylindrical ribbed shell with a diameter of 2 meters under a low-velocity local impact with an energy of up to 50 J was performed. To get detailed information about state of the ribs under impact, it was offered a two-stage scheme, where the first stage was devoted to investigation of smooth shell (with a stiffness equivalent to ribbed one) under impact and determine the maximum load in dynamic contact. The second stage was devoted to detailed quasi-static loading with maximum load and unloading to assess the residual strain state of a fragment containing a layered UD CFRP rib measuring 10x20 mm, a protective tab made of PA6 thermoplastic with a thickness of 5 mm and an external skin made of AFRP with a thickness of 1.5 mm. It was found that the placement of the fiber optical sensor (FOS) for recording residual strain in the impact zone should be in the upper part of the tab at the contact with the skin. In the case of a local impact with an energy of 50 J, the maximum strain of the FOS will not exceed 2%, and the residual strain of FOS will be about 0.5%. When placing the FOS in the middle of the tab, the maximum strain will increase to 2.6% (close to failure), and the residual one will be about 2%. There is a monotonic function of the residual strain of the tab on the impact energy. When the impact energy decreases from 50 to 5 J, the residual strain in the tab decrease from 2.07 to 0.57%. It is also shown that, under an impact with an energy of 50 J, the failure of the first layer of UD CFRP in the rib can be avoided if the protective tab made of PA6 with a thickness of only 4 mm contains a fabric tape made of AFRP with a thickness of 0.5 mm at the bottom, restraining its transverse strain in the local impact zone. Moreover, to register a residual strain near the local impact place, which is not known before, it is better to use a distributed FOS (Brillouin) rather than Bragg’s one (FBG) needed to know exact place for strain measurement .

A CKNOWLEDGMENTS

T

he work was carried out as part of a major scientific project of Ministry of science and higher education of the Russian Federation (Agreement No. 075-15-2024-535 dated 23 April 2024).

R EFERENCES

[1] Rocha, H., Semprimoschnig, C., Nunes, J.P. (2021) Sensors for process and structural health monitoring of aerospace composites: A review, Engineering Structures, 237, 112231. [2] Vorathin, E., Hafizi, Z.M., Che, S.A., Ghani, K.S. (2016) Lim real-time monitoring system of composite aircraft wings utilizing Fibre Bragg Grating sensor, IOP Conference Series: Materials Science and Engineering, 152 (1), 012024. [3] Takeda, N. (2008) Fiber optic sensor-based SHM technologies for aerospace applications in Japan, Proceedings of SPIE - The International Society for Optical Engineering, 6933, 693302. [4] Goossens, S., Berghmans, F., Muñoz, K., Jiménez, M., Karachalios, E., Saenz-Castillo, D., Geernaert, T. (2021) A global assessment of barely visible impact damage for CFRP sub-components with FBG-based sensors, Composite Structures, 272, 114025. [5] Datta, A., Augustin, M.J., Gupta, N., Viswamurthy, S.R., Gaddikeri, K.M., Sundaram. R. (2019) Impact localization and severity estimation on composite structure using Fiber Bragg Grating sensors by least square support vector regression, IEEE Sensors Journal, 19 (12), pp. 4463-4470. [6] Díaz-Maroto, P.F., Fernández, A., Larrañaga, B., Guemes, A. (2016) Free-edge delamination location and growth monitoring with an embedded distributed fiber optic network, 8th European Workshop on Structural Health Monitoring, EWSHM 2016, 2, pp. 993-1001. [7] Sun, C.T., Dicken, A., Wu, H.F. (1993) Characterization of impact damage in ARALL laminates, Composites Science and Technology, 49 (2), pp. 139-144. [8] Nyman, T., Bredberg, A., Schön, J. (2000) Equivalent damage and residual strength for impact damaged composite structures,” Journal of Reinforced Plastics and Composites, 19 (6), pp. 428-448. [9] Chen, V.L., Wu, H.-Y.T., Yeh, H.-Y. (1993) A parametric study of residual strength and stiffness for impact damaged composites, Composite Structures, 25 (1-4), pp. 267-275.

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[10] Vasiliev, V.V., Barynin, V.A., Razin, A.F. (2012) Anisogrid composite lattice structures - development and aerospace applications, Composite Structures, 94 (3), pp. 1117-1127. [11] Shanygin, A., Zichenkov, M., Kondakov, I. (2014) Main benefits of pro-composite layouts for wing and fuselage primary structure units, 29th Congress of the International Council of the Aeronautical Sciences, ICAS 2014. [12] Kondakov, I.O., Chernov, A.V., Shanygin, A.N., Sapozhnikov, S.B. (2022) Protection of aircraft lattice shell made of UD CFRP ribs from Low-Velocity Impacts, Mechanics of Composite Materials, 57 (6), pp. 721-730. [13] Chaumette, D. (1985) Certification problems for composite airplane structures, Materials Science Monographs, 29, pp. 19-28. [14] Ilcewicz, L.B., Murphy, B. (2005) Safety & certification initiatives for composite airframe structure, Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2, pp. 887-898. [15] Zhuguo, Z., Yingchun, Z., Xupo, O. (2011) Study on key certification issues of composite airframe structures for commercial transport airplane, Procedia Engineering, 17, pp. 247-257. [16] Serioznov, A.N., (2016) Application of fiber optic technologies in the creation of built-in self-diagnostic systems for aircraft structures, Novosibirsk, Scientific Bulletin of NSTU, 64(3), pp. 95-105, in Russian. [17] Vasiliev, V.V. (1988) Mechanics of structures made of composite materials, Moscow, Mashinostroenie, 270 pp., in Russian. [18] Sapozhnikov, S.B., Shaburova, N.A., Ignatova, A.V., Shanygin, A.N. (2022)Analysis of the mesostructure and fracture kinetics of elements of lattice composite structures under transverse compression using stochastic FEM micromechanics, Bulletin of Perm National Research Polytechnic University. Mechanics, 4, pp. 54–66. [19] Marceddu, A.C., Aimasso, A., Bertone, M., Viscanti, L., Montrucchio, B., Maggiore, P., Dalla Vedova, M.D.L. (2024) Augmented reality visualization of fiber Bragg grating sensor data for aerospace application, IEEE International Workshop on Metrology for AeroSpace, MetroAeroSpace 2024. Proceeding, pp. 519-524. [20] Berthold III, J.W. (2024) Fiber optic sensors: an introduction for engineers and scientists, Third Edition, pp. 573 – 591. [21] Hu, C., Du, A., Yang, L., Yang, B. (2024) Research progress on health monitoring techniques for composite pressure structures, Chinese Quarterly of Mechanics, 45 (3), pp. 593-613. [22] Aimasso, A., Dalla Vedova, M.D.L., Bertone, M., Maggiore, P. (2024) Preliminary design and performance evaluation of optical fiber-based load sensor for aerospace systems, Journal of Physics: Conference Series, 2802 (1), 012010. [23] Li ,Y., Jia, X., Li, L., Hu, D. (2024) Application of FBG sensing technology in flight test strain measurement, IEEE 6th International Conference on Power, Intelligent Computing and Systems, ICPICS, pp. 1485-1489. [24] Gupta S., Kumar B., Mishra S. (2024) Machine learning enabled FBG optical sensor applications, 2nd International Conference on Advancements and Key Challenges in Green Energy and Computing, AKGEC 2024. [25] Li, C., Tong, X., Huang, W., Wang ,Y., Zeng, F., Chen, L., Shi, X., Zeng, C. (2024) Development of a fast response, high accuracy, and miniaturized fiber Bragg grating (FBG) sensor for fluid temperature measurement, IEEE Sensors Journal, 24 (6), pp. 8746-8753. [26] Wang, X., Xiao, Y., Rans, C., Benedictus, R., Groves, R.M. (2024) Enhanced strain measurement sensitivity with gold nanoparticle-doped distributed optical fibre sensing, Structural Control and Health Monitoring, 2716156.

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V. Bomfim et alii, Fracture and Structural Integrity, 73 (2025) 12-22; DOI: 10.3221/IGF-ESIS.73.02

A simplified nonlinear model for bamboo-reinforced concrete beams based on lumped damage mechanics

Vitória Maria Souza Bomfim, Sergio Luiz de Sousa Nunes, Gilberto Messias dos Santos Júnior Disaster Research Institute, Federal University of Sergipe, São Cristóvão, Brazil vitoriamaria@academico.ufs.br, http://orcid.org/0009-0006-8547-9584 snunes@academico.ufs.br, http://orcid.org/0009-0001-8051-3417 gilbertomessias@academico.ufs.br, http://orcid.org/0009-0009-5107-6148 Camila de Sousa Vieira

Campus do Sertão, Federal University of Alagoas, Delmiro Gouveia, Brazil camila.vieira@delmiro.ufal.br, http://orcid.org/0000-0002-5371-191X David Leonardo Nascimento de Figueiredo Amorim Disaster Research Institute, Federal University of Sergipe, São Cristóvão, Brazil Post-Graduate Programme in Civil Engineering, Federal University of Alagoas, Maceió, Brazil davidnf@academico.ufs.br, http://orcid.org/0000-0002-9233-3114

Citation: Bomfim, V.M.S., Nunes, S.L.S., Santos Júnior, G.M., Vieira, C.S., Amorim, D.L.N.F., A simplified nonlinear model for bamboo-reinforced concrete beams based on lumped damage mechanics, Fracture and Structural Integrity, 73 (2025) 12-22.

Received: 08.01.2025 Accepted: 05.04.2025 Published: 06.04.2025 Issue: 07.2025

Copyright: © 2025 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

K EYWORDS . Bamboo-reinforced concrete, Nonlinear model, Lumped damage mechanics.

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V. Bomfim et alii, Fracture and Structural Integrity, 73 (2025) 12-22; DOI: 10.3221/IGF-ESIS.73.02

I NTRODUCTION

B

amboo is a renewable and sustainable material with high tensile strength that has been used as an alternative to steel as reinforcement of concrete elements [1]. The study of flexural performance of bamboo-reinforced concrete (BRC) beams in terms of load capacity, deflection and failure showed its feasibility [2-3]. However, to design BRC beams, it is necessary to consider the intrinsic characteristics of bamboo, it such as its reduced bond with concrete [4]. The behaviour and strength of BRC beams depend on the bond strength between bamboo and cement, the reinforcement ratio, the application of confinement, the presence of admixtures, and the strength of concrete [5]. Ibrahim et al. [6] tested experimentally bamboo-reinforced concrete beams subjected to flexural loads. The study verified the influence of bamboo’s cross-sectional area on the beam’s load-carrying capacity and the influence of its ultimate tensile strength on deflection. Besides experiments, the behaviour of BRC elements is also analysed through numerical methods. Awoyera et al. [7] validated the experimental evaluation of flexural behaviour of large-scale BRC beams with finite element modelling performed using ABAQUS® software. They demonstrated that members reinforced with 50% bamboo, although with about 14% lesser strength but with minimal deformation and crack propagation, can also be a sustainable alternative for construction. Besides real-life experiments, Mondal et al. [8] utilised finite element numerical experiments to develop a load and resistance factor design framework for BRC beams. They showed that a strength reduction factor to consider the slippage of bamboo inside the concrete could be utilised in the design equation. These papers usually apply two- or three dimensional finite element analysis, which might require considerable computational effort. Alternatively, lumped damage mechanics (LDM) can be an interesting tool for approaching bamboo-reinforced concrete structures since it is based on key concepts of classic fracture [9-11] and damage mechanics [12]. LDM was originally developed for seismic analysis of conventional reinforced concrete frames [13]. Later, it was developed for different materials and load conditions [14-21]. Recently, LDM was extended to two-dimensional continuum media [22-23] and reinforced concrete slabs [24]. Note that other approaches might also be helpful in analysing reinforced (steel or bamboo) concrete structures, such as continuum damage and cohesive fracture approaches. Regarding continuum damage modelling, concrete damage plasticity (CDP) modelling is quite effective in analysing reinforced concrete structures under different load conditions [25-27]. Another option is to analyse complex concrete structures by cohesive fracture models [28-30]. Regardless of the accuracy of such approaches, lumped damage models may present more efficient simulations. According to Bosse et al. [31], when compared to CDP, lumped damage modelling of reinforced concrete structures demands computational resources approximately 10,000 times lower. Therefore, this paper proposes a novel lumped damage model for bamboo-reinforced concrete beams. The proposed model is easy to implement and feasible for practical applications, especially if several numerical analyses are required, e.g., Monte Carlo simulations on structural reliability.

P ROPOSED LUMPED DAMAGE MODEL FOR BAMBOO - REINFORCED CONCRETE BEAMS

F

Strain equivalence hypothesis and its application in bamboo-reinforced concrete beams rom classic damage mechanics, the first main concept to analyse is the effective stress. For the sake of simplicity, consider a uniaxial case. If the applied Cauchy stress (  ) implies in damaged material, the effective stress can be defined as:



 



(1)

 1



where  is the damage variable. Then, the strain equivalence hypothesis states that an undamaged material can replace the damaged material submitted to a Cauchy stress state with the same strain state submitted by the effective stress (Fig. 1). Therefore, the elasticity law (Hooke’s law) is rewritten using the effective stress, i.e.

          E E 1 

  e d

  E 

   

 

(2)





E

1

13