caa a22 4500 463163990 CHVBK 20180406164756.0 cr unu---uuuuu 170326e20070601xx s 000 0 eng 10.1007/s10778-007-0062-2 doi (NATIONALLICENCE)springer-10.1007/s10778-007-0062-2 Modeling cylindrical waves in nonlinear elastic composites [Elektronische Daten] [J. Rushchitsky, Ya. Simchuk] A procedure of deriving nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves in composite materials modeled by a mixture with two elastic constituents is outlined. Nonlinearity is introduced by metric coefficients, Cauchy-Green strain tensor, and Murnaghan potential. It is the quadratic nonlinearity of all governing relations. For a configuration (state) dependent on the radial coordinate and independent of the angular and axial coordinates, quadratically nonlinear wave equations for stresses are derived and a relationship between the components of the stress tensor and partial strain gradient is established. Four combinations of physical and geometrical nonlinearities in systems of wave equations are examined. Nonlinear wave equations are explicitly written for three of the combinations Springer Science+Business Media, Inc., 2007 nonlinear theory of elastic mixtures nationallicence nonlinear hyperelastic cylindrical waves nationallicence quadratically nonlinear wave equations nationallicence geometrical and physical nonlinearities nationallicence Rushchitsky J. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv aut Simchuk Ya S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv aut International Applied Mechanics Springer US 43/6(2007-06-01), 638-646 1063-7095 43:6<638 2007 43 10778 https://doi.org/10.1007/s10778-007-0062-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10778-007-0062-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Rushchitsky J. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv aut NATIONALLICENCE 700 1- Simchuk Ya S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv aut NATIONALLICENCE 773 0- International Applied Mechanics Springer US 43/6(2007-06-01), 638-646 1063-7095 43:6<638 2007 43 10778 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer