caa a22 4500 475840062 CHVBK 20180406123859.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1023/A:1004713707083 doi (NATIONALLICENCE)springer-10.1023/A:1004713707083 Hill J. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia aut Finite elastic eversion of a thick-walled incompressible spherical cap [Elektronische Daten] [J. Hill] For perfectly elastic rubber-like materials, which are capable of undergoing extremely large deformations, the number of exact solutions remains limited, especially in the context of fully three-dimensional deformations. Here a simple exact solution describing the finite elastic eversion of a sector of a thick-walled incompressible spherical shell is determined for the modified Varga elastic material. This new solution, which describes a portion of a spherical shell being turned inside out, is deduced from a known simplified system and it is shown, by solving the full equilibrium equations, that no further solutions of this type can be deduced for this particular material. Further, a general family of response functions is considered, which involves an arbitrary index n, and which incorporates standard materials such as the neo-Hookean and Varga strain-energy functions. It is established that other than n=1 (namely the Varga material) only the special case n=2 admits nontrivial solutions to the eversion problem, but the resulting second-order highly nonlinear ordinary differential equation appears not to admit any simple analytical solutions. Finally, the new solution is examined as a potential solution of the 'snap-buckling' problem of a spherical cap. Unfortunately, the solution appears not to be applicable to this problem and instead it is presented in the specific context of the eversion of a thick-walled spherical cap, with no applied forces acting on one of the surfaces of the deformed configuration. Kluwer Academic Publishers, 2000 perfectly elastic nationallicence incompressible nationallicence Varga strain-energy nationallicence spherical eversion nationallicence exact solution nationallicence Journal of Engineering Mathematics Kluwer Academic Publishers 37/1-3(2000-02-01), 93-109 0022-0833 37:1-3<93 2000 37 10665 https://doi.org/10.1023/A:1004713707083 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004713707083 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hill J. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 37/1-3(2000-02-01), 93-109 0022-0833 37:1-3<93 2000 37 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer