METHODOLOGY FOR EVALUATING CHANGES IN PERFORMANCE CHARACTERISTICS OF FOAM MATERIALS
Abstract
An analytical-numerical approach for studying the dynamic stress state of foam materials (auxetics) with negative Poisson’s coefficients is developed in the article. Auxetics have the property of expanding during axial stretching. This effect results from the unique structure of these materials, which are formed by combining different types of nanotubes. Special interest in auxetics arises during the development of methods for increasing the operational characteristics of classical materials by creating structures that have adaptive mechanical reactions to external influences. To model the dynamic stress state, the Cosserat moment continuum model with compressed rotation – the couple stress elasticity – was used. The development of the analytical-numerical approach was carried out with the simultaneous use of the Fourier transform in the time variable and the method of integral equations. The use of such an approach made it possible to reduce the solution of a non-stationary problem to a finite system of the issues written in the form of a system of integral equations with established singular features. Analytical equations for determining radial stresses in the medium in integral form were obtained in the article. Numerical modelling was carried out for the case of an infinite structural-inhomogeneous medium weakened with tunnel cavities. The numerical analysis was carried out for the case under the action of an impulse load applied to the boundary of the tunnel cavity in the radial direction. Based on the developed approach, the distribution of dynamic radial stresses in foam materials with a positive and negative Poisson’s ratio was studied. The impact of the impulse duration on the stress state of the bodies made with classical and auxetic foam was studied. The developed approach makes it possible to evaluate the influence of the change in the microstructure of the material on the propagation of non-stationary processes in foam materials with a positive and negative Poisson’s ratio.
References
Bonnet, М. (1995). Integral equations and boundary elements. Mechanical application of solids and fluids. (Équations intégrales et éléments de frontière. Application en mécanique des solider et des fluids). Paris, CNRS Éditions / Éditions EYROLLES.
Brandel, B., & Lakes, R. S. (2001). Negative Poisson’s ratio polyethylene foams. Journal of Material Science, 36, 5885-5893.
Chen, C. P., & Lakes, R. S. (1989). Dynamic wave dispersion and loss properties of conventional and negative Poisson’s ratio polymeric cellular materials. Journal of Cellular Polymers, 8, 343-359.
Evans, K. E. (1991). Auxetic polymers: a new range of materials. Endeavour, 15(4), 170-174.
Friis, E. A., Lakes, R. S., & Park, J. B. (1988). Negative Poisson’s ratio polymeric and metallic materials. Journal of Material Science, 23, 4406-4414.
Kurashige, M., Sato, M., & Imai, K. (2005). Mandel and Cryer problems of fluid-saturated foams with negative poisson’s ratio. Acta Mechanica, 175(1-4), 25-43.
Lakes, R. S. (1991). Experimental micro mechanics methods for conventional and negative Poisson’s ratio cellular solids as Cosserat continua. Journal of Engineering Materials and Technology, 113, 148-155.
Lakes, R. S. (2016). Physical meaning of elastic constants in Cosserat, void, and microstretch elasticity. Journal of Mechanics of Materials and Structues, 11(3), 217-229.
Lakes, R. S., & Lowe, A. (2000). Negative Poisson’s ratio foam as seat cushion material. Cellular
Polymers, 19, 157-167.
Ostash, O. P., Kiva, D. S., Uchanin, V. M, Semenets’, O. I., Andreiko, I. M., & Golovatyuk, Yu. V. (2013). Diagnostics of technical condition of aircraft structures after long-term service. Technical Diagnostics and Non-Destructive Testing, 2, 15-22.
Ostash, O. P., Vol’demarov, O. V., & Hladysh, P. V. (2014). Diagnostics of the structural-mechanical state of steels of steam pipelines by the coercimetric method and prediction of their service life. Materials Science, 49(5), 667-680.
Ramamohan, K., Kim, D., & Hwang, J. (2010). Fast Fourier transform: algorithms and applications. New York, Springer.
Rueger, Z., & Lakes, R. S. (2016). Cosserat elasticity of negative Poisson’s ratio foam: experiment. Smart Materials and Structures, 25, 100-108.
Savin, G. N., & Shulga, N. A. (1967). Dynamic plane problem of the moment theory of elasticity. Applied Mechanics, 3(6), 216-221.
Shvabyuk, V., Sulym, H., & Mikulich, O. (2015) Stress state of plate with incisions under the action of oscillating concentrated forces. Acta Mechanica et Automatica, 9(3), 140-144.
Skalsky, V., Nazarchuk, Z., Hirnyj, S., & Dobrovolska, L. (2014). Acoustic emission during crack propagation in nuclear RPV steels. International Journal of Innovative and Information Manufacturing Technologies, 1, 45-48.
Куриляк, Д. Б., & Назарчук, З. Т. (2011). Розвиток методів аналітичної регуляризації в теорії дифракції (Development of analytical regularization methods in diffraction theory). Фізико-хімічна механіка матеріалів, 47(2), 42-55.
Мікуліч, О. А. (2017). Розрахунок напруженого стану пінистих матеріалів за динамічних навантажень (Calculation of the stress state of foam materials under dynamic loads). Наукові нотатки, 58, 243-247.
