Skip to main content
Top
Published in: Mechanics of Composite Materials 2/2020

22-05-2020

Method for Calculating the Near-Surface Effect in Piecewise Homogeneous Bodies at Large Deformations Based on a Two-Level Approach

Author: V. M. Akhundov

Published in: Mechanics of Composite Materials | Issue 2/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

A method is proposed for calculating the near-surface effect in piecewise homogeneous bodies under large deformations based on a combined use of one-level applied and two-level carcass theories. The applied theory is used for a macromechanical continuation of the solution of the problem, but the carcass theory is used in the final part of the loading path or directly at the final loading of the body. The implementation of the problem by the carcass theory for the body as a whole ends with solution of extreme problems using a highly gradient scheme for assemblies of structural blocks near boundary surfaces of the body. The rotation-caused development of configurations of cylinders reinforced with ring fibers is studied using this method and the model of a piecewise homogeneous medium. The results obtained by the carcass theory and the model of a piecewise homogeneous medium differed only slightly, confirming the high accuracy of the analysis using the two-level approach. A higher stability of the numerical implementation of the carcass theory, in comparison with the model of a piecewise homogeneous medium, was revealed when the macromechanical continuation was carried out within the framework of this theory itself. An even higher stability of the approach was reached by implementation of the macromechanical continuation of the applied theory. Performing calculations only for nodal blocks of the medium at the micromechanical level of the carcass theory, together with application of the applied theory for the macromechanical continuation, led to an extremely high efficiency of the two-level approach. In contrast to the piecewise homogeneous medium model, this approach made it possible to study the behavior of piecewise homogeneous cylinders considering the near-surface effect up to the configurationdetermined ultimate rotation speed.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference A. A. Rassoha and V. O Kaledin, “On the deformation of a fiber-reinforced layered composite near to a free surface,” Prikl. Mekh., 20, No. 9, 91-97 (1984). A. A. Rassoha and V. O Kaledin, “On the deformation of a fiber-reinforced layered composite near to a free surface,” Prikl. Mekh., 20, No. 9, 91-97 (1984).
2.
go back to reference V. Yu. Bojchuk, “Research of edge effects in a composite weakly reinforced with rectangular fibers,” Prikl. Mekh., 37, No. 5, 126-132 (2001). V. Yu. Bojchuk, “Research of edge effects in a composite weakly reinforced with rectangular fibers,” Prikl. Mekh., 37, No. 5, 126-132 (2001).
3.
go back to reference Yu. V. Kokhanenko and V. M. Bystrov, “Edge effect in a fibrous composite material in uniform loading of near-surface fibers,” Prikl. Mekh., 43, No. 11, 15-23 (2007). Yu. V. Kokhanenko and V. M. Bystrov, “Edge effect in a fibrous composite material in uniform loading of near-surface fibers,” Prikl. Mekh., 43, No. 11, 15-23 (2007).
4.
go back to reference Yu. V. Kokhanenko and S. V. Fesenko, “Parameters of effects as functions of the mechanical characteristics of a composite weakened by a crack on the interface of layers,” Prikl. Mekh., 39, No. 12, 93-99 (2003). Yu. V. Kokhanenko and S. V. Fesenko, “Parameters of effects as functions of the mechanical characteristics of a composite weakened by a crack on the interface of layers,” Prikl. Mekh., 39, No. 12, 93-99 (2003).
5.
go back to reference I. V. Andrianov, V. V. Danishevs’kyy, and D. Weichert, “Analytical study of the load transfer in fiber-reinforced 2D composite materials,” Int. J. of Solids and Structures., 45, Mar., 1217-1243 (2008).CrossRef I. V. Andrianov, V. V. Danishevs’kyy, and D. Weichert, “Analytical study of the load transfer in fiber-reinforced 2D composite materials,” Int. J. of Solids and Structures., 45, Mar., 1217-1243 (2008).CrossRef
6.
go back to reference J. Harich, Y. Lapusta, and W. Wagner, “3D FE-modeling of surface and anisotropy effects during microbuckling in fiber composites,” Compos. Struct., 89, Aug., 551-555 (2009).CrossRef J. Harich, Y. Lapusta, and W. Wagner, “3D FE-modeling of surface and anisotropy effects during microbuckling in fiber composites,” Compos. Struct., 89, Aug., 551-555 (2009).CrossRef
7.
go back to reference L. Banks-Sills and V. Leiderman, “Macro-mechanical material model for fiber reinforced metal matrix composites,” Composites: Part B, 30, Jan., 443-452 (1999).CrossRef L. Banks-Sills and V. Leiderman, “Macro-mechanical material model for fiber reinforced metal matrix composites,” Composites: Part B, 30, Jan., 443-452 (1999).CrossRef
8.
go back to reference J. Fish, “The s-version of the finite element method,” Computers and Structures, 43, May, 539-547 (1992).CrossRef J. Fish, “The s-version of the finite element method,” Computers and Structures, 43, May, 539-547 (1992).CrossRef
9.
go back to reference V. M. Akhundov, “Applied theory of composites with low fillings by strings at high deformations,” Mekh. Kompoz. Mater. Konstr., 7, No.1, 3-15 (2001). V. M. Akhundov, “Applied theory of composites with low fillings by strings at high deformations,” Mekh. Kompoz. Mater. Konstr., 7, No.1, 3-15 (2001).
10.
go back to reference V. M. Akhundov, “Carcass theory of fibrous media with uncurved and locally curved fibers at large deformations,” Mech. Compos. Mater., 51, No. 6, 971–990 (2015). V. M. Akhundov, “Carcass theory of fibrous media with uncurved and locally curved fibers at large deformations,” Mech. Compos. Mater., 51, No. 6, 971–990 (2015).
11.
go back to reference V. M. Akhundov, “Form changes of a toroidal body with a crossed arrangement of fibers on the basis of the two-level carcass theory,” Mech. Compos. Mater., 53, No. 2, 359-378 (2017).CrossRef V. M. Akhundov, “Form changes of a toroidal body with a crossed arrangement of fibers on the basis of the two-level carcass theory,” Mech. Compos. Mater., 53, No. 2, 359-378 (2017).CrossRef
12.
go back to reference M. P. Galanin and E. B. Savenkov, “Joint use of the method of finite elements and the method of finite superelements,” Preprity Inst. Prikl. Mekh. RAN, М., 34 p. (2004). M. P. Galanin and E. B. Savenkov, “Joint use of the method of finite elements and the method of finite superelements,” Preprity Inst. Prikl. Mekh. RAN, М., 34 p. (2004).
13.
go back to reference V. M. Akhundov and T. A. Skripochka, “Large deformations of homogeneous and fiber-reinforced cylinders under the influence of centrifugal forces,” Mech. Compos. Mater., 45, No. 3, 347-366 (2009).CrossRef V. M. Akhundov and T. A. Skripochka, “Large deformations of homogeneous and fiber-reinforced cylinders under the influence of centrifugal forces,” Mech. Compos. Mater., 45, No. 3, 347-366 (2009).CrossRef
14.
go back to reference V. M. Akhundov, “Analysis of elastomeric composites based on fiber-reinforced systems. 1. Development of design methods for composite materials,” Mech. Compos. Mater., 34, No. 6, 733-745 (1998).CrossRef V. M. Akhundov, “Analysis of elastomeric composites based on fiber-reinforced systems. 1. Development of design methods for composite materials,” Mech. Compos. Mater., 34, No. 6, 733-745 (1998).CrossRef
15.
go back to reference V. M. Akhundov and M. M. Kostrova, “Nonlinear deformation of a piecewise homogeneous cylinder under the action of rotation,” Mech. Compos. Mater., 54, No. 2, 345-360 (2018).CrossRef V. M. Akhundov and M. M. Kostrova, “Nonlinear deformation of a piecewise homogeneous cylinder under the action of rotation,” Mech. Compos. Mater., 54, No. 2, 345-360 (2018).CrossRef
16.
go back to reference R. M. Christensen, Mechanics of Composite Materials, John Wiley & Sons, New Yorc–Chichester–Brisbane–Toronto (1979). R. M. Christensen, Mechanics of Composite Materials, John Wiley & Sons, New Yorc–Chichester–Brisbane–Toronto (1979).
17.
go back to reference F. L. Chernous’ko and V. P. Banichuk, Variational Problems of Mechanics and Control [in Russian], M., Nauka (1973). F. L. Chernous’ko and V. P. Banichuk, Variational Problems of Mechanics and Control [in Russian], M., Nauka (1973).
18.
go back to reference O. K. Zenkevich and K. Morgan, Finite Elements and Approximation, M., Mir, (1986). O. K. Zenkevich and K. Morgan, Finite Elements and Approximation, M., Mir, (1986).
19.
go back to reference G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems and Formulas for Reference and Review, N.Y.: General Publ. Company (2000). G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems and Formulas for Reference and Review, N.Y.: General Publ. Company (2000).
20.
go back to reference J. Ortega and V. Reiboltd, Iteration Methods of Solution of Nonlinear Systems of Equations with Many Unknowns, M., Nauka (1975). J. Ortega and V. Reiboltd, Iteration Methods of Solution of Nonlinear Systems of Equations with Many Unknowns, M., Nauka (1975).
21.
go back to reference S. K. Gupta and K. K. Tanji, “Computer program for solution of large, sparse, unsymmetric systems of linear equations,” Int. J. for Numerical Methods in Engineering, 11, No.8, 1251-1259 (1977).CrossRef S. K. Gupta and K. K. Tanji, “Computer program for solution of large, sparse, unsymmetric systems of linear equations,” Int. J. for Numerical Methods in Engineering, 11, No.8, 1251-1259 (1977).CrossRef
22.
go back to reference K. F. Chernykh, Nonlinear Elasticity Theory of in Machine-Building Calculations [in Russian], L., Mashinostroenie (1986). K. F. Chernykh, Nonlinear Elasticity Theory of in Machine-Building Calculations [in Russian], L., Mashinostroenie (1986).
23.
go back to reference S. I. Dymnikov, E. E. Lavendel, A.-M. Pavlovskis, and M. I. Sniegs, Applied Methods of Calculation of Products from Highly Elastic Materials [in Russian], Riga, Zinatne (1980). S. I. Dymnikov, E. E. Lavendel, A.-M. Pavlovskis, and M. I. Sniegs, Applied Methods of Calculation of Products from Highly Elastic Materials [in Russian], Riga, Zinatne (1980).
Metadata
Title
Method for Calculating the Near-Surface Effect in Piecewise Homogeneous Bodies at Large Deformations Based on a Two-Level Approach
Author
V. M. Akhundov
Publication date
22-05-2020
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 2/2020
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-020-09870-w

Other articles of this Issue 2/2020

Mechanics of Composite Materials 2/2020 Go to the issue

Premium Partners