 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| D.L. Bykov, D.N. Konovalov, and V.A. Peleshko, "Constitutive Relations for Calculating the Processes of Quasistatic Deformation, Damage, and Fracture of Bodies (Including Those with Concentrators) Made of Filled Polymer Materials," Mech. Solids. 46 (6), 839-855 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
6 |
Pages |
839-855 |
| DOI |
10.3103/S0025654411060045 |
| Title |
Constitutive Relations for Calculating the Processes of Quasistatic Deformation, Damage, and Fracture of Bodies (Including Those with Concentrators) Made of Filled Polymer Materials |
| Author(s) |
D.L. Bykov (Central Scientific Research Institute for Engineering (TsNIIMash), Pionerskaya 4, Korolev, Moscow Oblast, 141070 Russia)
D.N. Konovalov (OT-Kontakt Ltd., Aviamotornaya 2, Moscow, 111020 Russia, dimconov@mtu-net.ru)
V.A. Peleshko (Central Scientific Research Institute for Engineering (TsNIIMash), Pionerskaya 4, Korolev, Moscow Oblast, 141070 Russia, peleshkobva@inbox.ru) |
| Abstract |
We study composite polymer materials with a high degree of dispersion filling (several tens of percent in volume). A tensor generalization of the previously developed variant of the gero-endochronic theory of viscoelastic materials is obtained, which allows us to pose and solve initial-boundary value problems using this model. A numerical solution algorithm is proposed, which is realized as the UMAT subroutine for the ABAQUS finite element software package.
Finite element computations are performed for the process of tensile stretching of bodies having the shape of short wide strips made of a highly filled polymer material and the results are compared with the relevant experimental data published by K. Ha and R. A. Schapery (Int. J. Solids Struct. 35 (26-27), 3497-3517 (1998)). The computational results for the deformation and fracture of solids in which a weakly inhomogeneous stress-strain state (SSS) is realized show a quite satisfactory agreement with the experiments. It has been found that, for correct strength analysis of bodies with holes and cuts, one has to consider the influence of the SSS concentration in the model. To this end, we propose to generalize the constitutive relations as follows: in the equation for the damage and fracture parameters, introduce a material function of the concentration parameter, for which we take the ratio of some state variable (the fracture parameter from the model where the concentration effect is not taken into account) at the point in question to the average value of this variable in a neighborhood of a given radius. A method is suggested for reducing the initial-boundary value problem of the proposed nonlocal theory to a problem for a piecewise-homogeneous body composed of a set of layers described by local constitutive relations. The method was successfully tested in the calculations of bodies with a hole and an sharp internal cut (stress concentrators of moderate and high level, respectively).
The obtained results show that the developed model has a high accuracy, including adequate prediction of the time and location when and where the fracture begins, which is the main objective of the strength analysis. |
| Keywords |
filled polymer materials, constitutive relations, local fracture, concentrators, finite element calculations |
| References |
| 1. | D. L. Bykov and V. A. Peleshko,
"Constitutive Relations for Strain and Failure of Filled Polymer
Materials in Dominant Axial Tension Processes under Various Barothermal Conditions,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 40-65 (2008)
[Mech. Solids (Engl. Transl.)
43 (6), 870-891 (2008)]. |
| 2. | S. W. Park and R. A. Schapery,
"A Viscoelastic Constitutive Model for Particulate Composites with Growing Damage,"
Int. J. Solids Struct.
34 (8), 931-947 (1997). |
| 3. | S. Özüpek and E. V. Becker,
"Constitutive Equations for Solid Propellants,"
J. Engng Mater. Technol.
119 (2), 125-132 (1997). |
| 4. | S. Özüpek,
Constitutive Equations for Solid Propellants,
PhD Thesis
(Univ. Texas, Austin, 1997). |
| 5. | G. D. Jung and S. K. Youn,
"A Nonlinear Viscoelastic Constitutive Model of Solid Propellant,"
Int. J. Solids Struct.
36 (25), 3755-3777 (1999). |
| 6. | F. Xu, N. Aravas, and P. Sofronis,
"Constitutive Modeling of Solid Propellant Materials
with Evolving Microstructural Damage,"
J. Mech. Phys. Solids
56 (5), 2050-2073 (2008). |
| 7. | D. L. Bykov and D. N. Konovalov,
"Endochronic Model of Mechanical Behavior
of Ageing Viscoelastic Materials at Finite Strains,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 136-148 (2006)
[Mech. Solids (Engl. Transl.)
41 (6), 110-120 (2006)]. |
| 8. | C. Truesdell,
A First Course in Rational Continuum Mechanics
(The Johns Hopkins University Press, Baltimore, Maryland, 1972; Mir, Moscow, 1975). |
| 9. | W. Sun, E. L. Chaikof, and M. E. Levenston,
"Numerical Approximation of Tangent Moduli for Finite Element Implementations
of Nonlinear Hyperelastic Material Models,"
Trans. ASME. J. Biomech. Engng
130 (6), 061003 (2008). |
| 10. | K. Ha and R. A. Schapery,
"A Three-Dimensional Viscoelastic Constitutive Model for Particulate Composites
with Growing Damage and Its Experimental Validation,"
Int. J. Solids Struct.
35 (26-27), 3497-3517 (1998). |
| 11. | D. L. Bykov and V. A. Peleshko,
"Constitutive Relations of Strain, Anisotropic Degradation, and Fracture
of Filled Polymer Materials in Prevailing-Tension Processes with Varying
Axis Direction and Relaxations,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 5, 59-67 (2009)
[Mech. Solids (Engl. Transl.)
44 (5), 705-711 (2009)]. |
| 12. | V. E. Apet'yan, D. L. Bykov, and V. A. Peleshko,
"Deformation and Fracture of a Filled Polymer Material with Anisotropic Degradation
Caused by Its Preliminary Loading: Tests and Their Modeling,"
Kosmonavtika Raketostr.,
No. 3 (60), 52-60 (2010). |
| 13. | D. L. Bykov, D. N. Konovalov, V. P. Mel'nikov, and A. N. Osavchuk,
"Method for Identification of the Filled Polymer Material Relaxation Kernel in Millisecond Time Range,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 143-154 (2010)
[Mech. Solids (Engl. Transl.)
45 (3), 427-436 (2010)]. |
|
| Received |
01 July 2011 |
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