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Meccanica

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04-09-2022

The analytical and numerical solution of the problem of stretching a system of parallel elements with random strength characteristics taking into account the postcritical stage of deformation and rigidity of the loading system

Authors: Valeriy E. Wildemann, Artur I. Mugatarov, Michail P. Tretyakov

Published in: Meccanica | Issue 9/2022

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Abstract

The work studies the influence of the postcritical stage of deformation and rigidity of the loading system on the deformation of the material using the example of the system of parallel-connected elements that have the random strength characteristics and postcritical stage of deformation. In this case, by taking into account the rigidity of the loading system we predict the moment of destruction of the system of the deformable elements at the postcritical stage caused by the loss of stability of the deformation process. A new analytical solution makes it possible to calculate the systems with a large number of elements. Strength reserves are determined by taking into account the postcritical stage of deformation. A high rigidity of the loading system has a positive effect on the stable deformation process. An algorithm of the developed program that allows solving a similar problem for a finite number of elements is presented. We determine how a number of structural elements influences the form of the loading diagrams of the system of parallel elements and calculated strength values. The proposed approach makes it possible to carry out the refined calculations to predict the mechanical behavior of the systems of elements that are characterized by the manifestation of supercritical deformation with the known statistical spreads of characteristics. The solution can be applied to predict the mechanical behavior of the unidirectional composite materials, in particular, basalt plastics, and their structural elements, such as a fiber bundle or fabric. A comparison of the obtained results of the solutions with the experimental data of stretching the basalt filament samples and bundles of them is carried out. A good convergence between the developed model and experimental results is shown. We confirm the rationality of taking into account the postcritical stage of the material deformation in the considered problems of deformation and fracture.

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Fridman YB (1952) Mechanical properties of metals. Oborongiz, Moscow

Vildeman VE, Sokolkin YuV, Tashkinov AA (1997) Mechanics of inelastic deformation and fracture of composite materials. Nauka, Moscow

Bazant ZP, Di Luizo G (2004) Nonlocal microplane model with strain-softening yield limits. Intern J Solids Struct 41:7209–7240. https://doi.org/10.1016/j.ijsolstr.2004.05.065CrossRefMATH

Bazant ZP, Planas J (1997) Fracture and size effect in concrete and other quasibrittle materials. CRC Press LLC, London

Vildeman VE (2008) Mechanics of postcritical deformation and questions of strength analysis methodology. Int J Comput Civ Struct Eng 4(2):43

Struganov VV (2004) Deformation stability of plastic beam under pure bending. Phys Mesomech 7(S1–1):169

Radchenko VP, Gorbunov SV (2014) The method of solution of the elastic-plastic boundary value problem of tension of strip with stress raisers with allowance for local domains of softening plasticity of material. J Samara State Tech Univ Ser Phys Math Sci 4(37):98–110. https://doi.org/10.14498/vsgtu1366CrossRef

Wildemann VE (1998) On the solutions of elastic-plastic problems with contact-type boundary conditions for solids with loss-of-strength zones. J Appl Math Mech 62(2):281MathSciNetCrossRef

Tretyakov MP (2014) Experimental investigation of the postcritical deformation stage of materials under tension and torsion. Dissertation, Institute of Continuous Media Mechanics

10.

Faleskog J, Barsoum I (2013) Tension–torsion fracture experiments. Part I: experiments and a procedure to evaluate the equivalent plastic strain. Int J Solids Struct 50(25–26):4241–4257CrossRef

11.

Bazhenov VG, Osetrov SL, Osetrov DL (2018) Analysis of stretching of elastoplastic samples and necking with edge effects. J Appl Mech Tech Phys 59(4):693–698CrossRef

12.

Tretyakov MP, Wildemann VE, Lomakin EV (2016) Failure of materials on the postcritical deformation stage at different types of the stress-strain state. Procedia Struct Integr 2:3721–3726. https://doi.org/10.1016/j.prostr.2016.06.462CrossRef

13.

Wildemann VE, Lomakin EV, Tretyakov MP (2014) Postcritical deformation of steels in plane stress state. Mech Solids 49(1):18–26CrossRef

14.

Lomakin EV, Tretyakov MP (2016) Fracture properties of graphite materials and analysis of crack growth under bending conditions. Meccanica 51(10):2353–2364. https://doi.org/10.1007/s11012-016-0370-xMathSciNetCrossRefMATH

15.

Goldstein RV, Perelmuter MN (2009) Modeling of fracture toughness of composite materials. Comput Contin Mech 2(2):22–39. https://doi.org/10.7242/1999-6691/2009.2.2.10CrossRef

16.

Goldstein RV, Perelmuter MN (1999) Modeling of bonding at an interface crack. Int J Fract 99(1–2):53–79. https://doi.org/10.1023/A:1018382321949CrossRef

17.

Volmir AS (1967) Stability of the deformable systems. Nauka, Moscow

18.

Wildemann VE (2005) Problems of mechanics of postcritical deformation of rod systems. PSTU Bull Dyn Strength Mach 5:15–29

19.

Mullahmetov MN, Ilinih AV. Numerical simulation of the process of destruction of sequentially and parallel associated fibers. Master's J 1:9–26

20.

Adusumalli R et al (2019) Tensile testing of single fibres. Procedia Struct Integr 14:150–157. https://doi.org/10.1016/j.prostr.2019.05.020CrossRef

21.

Herrera-Ramirez JM (2012) Characterization of Kevlar-29 fibres by tensile tests and nanoindentation. J Alloys Compd 536:456–459CrossRef

22.

Revol BP, Thomassey M, Ruch F, Nardin M (2016) Influence of the sample number for the prediction of the tensile strength of high tenacity viscose fibres using a two parameters Weibull distribution. Cellulose 23:2701–2713. https://doi.org/10.1007/s10570-016-0974-2CrossRef

23.

Ilankeeran P, Mohite P, Kamle S (2012) Axial tensile testing of single fibres. Mod Mech Eng 2:151–156. https://doi.org/10.4236/mme.2012.24020CrossRef

24.

Temerova MS, Wildemann VE, Lobanov DS (2013) Quasi-static tests of threads and fabrics as reinforcing elements of composite materials. Book of abstracts. In: Russian conference applied mathematics, mechanics and control processes, vol 1, pp 119–128

25.

Sapuan SM et al (2020) Mechanical properties of longitudinal basalt/woven glass fiber reinforced unsaturated polyester-resin hybrid composites. Polymers 12(10):2211. https://doi.org/10.3390/polym12102211CrossRef

26.

Lomakin EV, Fedulov BN (2015) Nonlinear anisotropic elasticity for laminate composites. Meccanica 50(6):1527–1535MathSciNetCrossRef

27.

Protchenko K, Zayoud F, Urbanski M, Szmigiera E (2020) Tensile and shear testing of basalt fiber reinforced polymer (BFRP) and hybrid basalt/carbon fiber reinforced polymer (HFRP) bars. Materials 13(24):5839. https://doi.org/10.3390/ma13245839CrossRef

28.

Ozdemir H, Bilisik K (2021) Off-axis flexural properties of multiaxis 3d basalt fiber preform/cementitious concretes: experimental study. Materials 14:2713. https://doi.org/10.3390/ma14112713CrossRef

29.

Zhou H, Jia B, Huang H, Mou Y (2020) Experimental study on basic mechanical properties of basalt fiber reinforced concrete. Materials 13(6):1362. https://doi.org/10.3390/ma13061362CrossRef

30.

Wildemann VE, Lomakin EV, Tretyakov MP et al (2018) Experimental studies of postcritical deformation and fracture of structural materials. PNRPU Press, Perm

31.

Temerova MS, Wildemann VE (2016) Study of basalt fibers at the stage of post-critical deformation under conditions of quasi-static loading. Book of abstracts. In: International conference on mathematical modeling in natural sciences, vol 1, pp 381–383

32.

Slovikov S, Lobanov D (2020) Mechanical properties of a basalt-fiber-reinforced plastic rod used in composite high-voltage wires in torsion and three-point bending. Mech Compos Mater. https://doi.org/10.1007/s11029-020-09886-2CrossRef

33.

Lobanov D, Slovikov S (2018) Mechanical behavior of a unidirectional basalt-fiber-reinforced plastic under thermomechanical loadings. Mech Compos Mater. https://doi.org/10.1007/s11029-018-9746-4CrossRef

Title: The analytical and numerical solution of the problem of stretching a system of parallel elements with random strength characteristics taking into account the postcritical stage of deformation and rigidity of the loading system
Authors: Valeriy E. Wildemann
Artur I. Mugatarov
Michail P. Tretyakov
Publication date: 04-09-2022
Publisher: Springer Netherlands
Published in: Meccanica / Issue 9/2022
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-022-01573-x

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