## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### On internal stability loss of a row unidirected periodically located fibers in the Viscoelastic matrix

**ABSTRACT**

In the present paper, the microbuckling or internal stability loss in the viscoelastic composites containing unidirected fibers under compression along the fibers is studied by use of piecewise homogeneous body model. In this model, it is used the Three-Dimensional Geometrically Nonlinear Exact Equations of Viscoelasticity Theory. The composite material was considered as an infinite viscoelastic body with a row unidirected periodically located elastic fibers that have an initial infinitesimal imperfection. When the initial imperfection starts to increase and becomes indefinitely, this is taken as a stability loss criterion and co-phase microbuckling mode out of plane are taken into account. The numerical results about the influence of the interaction between the fibers on the values of the critical time are abtained and presented.

**KEYWORDS**

PAPER SUBMITTED: 2018-11-28

PAPER REVISED: 2018-12-26

PAPER ACCEPTED: 2019-01-15

PUBLISHED ONLINE: 2019-03-09

- Liu, Y.-Q., et al., Air Permeability of Nanofiber Membrane With Hierarchical Structure, Thermal Science, 22, 2018, 4, pp. 1637-1643.
- Wang, P., et al., Energy Absorption in Friction-Based Stab-Proof Fabrics and the Puncture Resis tance of Nanofiber Membrane, Thermal Science, 22, 2018, 1A, pp. 39-41.
- Liu, P. and He, J., Geometric Potential An Explanation of Nanofiber's Wettability, Thermal Science, 22, 2018, 1A, pp. 33-38..
- Akbarov, S.D., Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites, Springer, Berlin, Germany, 2012:
- 5 Akbarov, S. D., Guz, A. N., Stability of Two Fibers in an Elastic Matrix with Small Strains, Soviet Appl. Mech., 21, 1985, 1, pp. 1-7.
- Akbarov, S. D. And Guz, A.N., Statics of Laminated and Fibrous Composites With Curved Structures. Appl. Mech. Rev., 45, 1992, 2, pp. 17-35.
- Akbarov, S. D., Guz, A. N., Mechanics of curved composites, Kluwer Academic Pubishers, Dortrecht/ Boston/ London, 2000.
- Akbarov, S. D., Kosker, R., Fiber Buckling in a Viscoelastic Matrix, Mechanics of Composite Materials, 37, 2001, 4, pp. 299-306.
- Akbarov, S. D., Kosker, R., Internal Stability Loss of Two Neighbouring Fibers in a Viscoelastic Matrix, Int. J. Eng. Scien., .42, 2004, 17/18, pp.1847-1873.
- Babaev, M.S., et al., Stability of the Row of Fibers in the Elastic Matrix at Small Precritical Deformations., Soviet Appl. Mech., 21, 1985, 5, pp. 27-34.
- Babich, I., Stab. of Fiber in a Matrx with Small Str., Soviet Appl. Mech., 9, 1973, 4, pp. 29-35.
- Babich, I.Yu., Guz, A.N., Stability of Fibrous Com., Appl. Mech. Rev., 45, 1992, 2, pp. 60-80.
- Babich, I.Yu., et al., The Three-Dimensional Theory of Stability of Fibrous and Laminated Materials, Int. Appl. Mech., 37, 2001, 9, pp. 1103-1141.
- Budianski, B. and Fleck, N.A., Compressive Failure of Fibre Composites, J. Mech. Phys. Solids, 41,1993, 1, pp. 183-21.
- Greszczuk, I.B., Fracture of Composite Reinforced by Circular Fibers From Loss of Stability Of Fibers, J. AIAA, 13, 1975, 10, pp. 67-75.
- Guz, A.N., Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin, Germany, 1999.
- Guz, A. N.; Lapusta, Yu. N., Three-Dimensional Problems of the Near-Surface Instability of Fiber Composites in Compression,. Inter. Appl. Mech., 35, 1999, 7, pp. 641-671.
- Guz, A. N., Rushchitskii, Ya. Ya., Nanomaterials: on the Mechanics of Nanomaterials, Int. App. Mech., 39, 2003, 11, pp. 1271-1293.
- Rosen, B.W., Fiber composite materials. Amer. Soc. For. Metals, Met. P., Ohio, USA, 1965.
- Dow, N.F., Grunfest, I.J. Determination of Most Needed Potentially Possible Improvements in Materials for Ballistic and Space Vehicles, General Electric Co. Space Sci Lab., USA, 1960.
- Drapier S., et al., A structural approach of plastic microbuckling in long fibre composites: comparison with theoretical and exp.results. Int. J. Solids and Str., 38, 2001, 28, pp. 3877-3904.
- Chamis, C.C. Micromechanics strength theories.
- Akbarov, S.D., Three-dimensional stability loss problems of the viscoelastic composite materials and structural members. Int. Appl. Mech, .43, 2007, 10, pp. 3-27.
- Sadovsky, M.A., et al., Buckling of Microfibers, Trans ASME, 34, 1967, 4, pp. 295-302.
- Schuerch, H., Prediction of Compressive Strength in Uniaxial Boron Fibermetal Matrix Composite Materials, J. AIAA 4, 1966, 1, pp. 102-106.
- Akbarov, S.D. et al., On The Fracture of the Unidirectional Composites in Compression. Int.J.Eng. Sci. 35, 1997, 12/13, pp. 1115-1136.
- Akbarov, S.D. et al., The Theoritical Strenght Limit in Compression of Viscoelastic Layered Composite Materials. Composites Part B: Engineering, 30, 1999, 5, pp. 465-472.
- Watson, G.N., A Treatise on the Theory of Bessel functions, Cambridge University Press, England., 1944.
- Schapery, R.A., Approximate Methods of Transform Inversion for Viscoelastic Stress Analysis, Proceedings 4th US Nat. Congress on App. Mech., Berkely, USA, 1962, pp. 1075-1085.
- Guz, A.N. . et al., Plane Problems of Stability of Composite Materials with a Finite Size Filler. Mechan. Comp. Materials., 36, 2000, 1, pp 77-86.