Asymptotic modelling of viscoelastic von Kármán membrane shells

Abstract The objective of this work is to study the asymptotic justification of the two-dimensional model of viscoelastic von Kármán membrane shells. More precisely, we consider a three-dimensional model for a nonlinearly viscoelastic membrane shell with a specific class of boundary conditions of von Kármán type. Using techniques from formal asymptotic analysis with the thickness of the shell as a small parameter, we show that the scaled three-dimensional solution still leads to the two-dimensional model of viscoelastic von Kármán membrane shells.