An isogeometric collocation formulation for finite-strain visco-hyperelastic geometrically exact beams

Most of the existing computational models for the analysis of beam structures undergoing large deformations are based on the hypothesis of small strains. In this paper, we present a finite-strain, geometrically-exact beam formulation suitable for visco-hyperelastic materials. Three-dimensional constitutive equations are expressed starting from the stored energy function, which is split into hyperelastic and dissipative contributions. We employ a linearized evolution law that permits expressing the rate-dependent strains in terms of the one-dimensional geometrically exact strain measures. High efficiency is pursued discretizing the governing equations using the isogeometric collocation (IGA-C) method. Numerical examples demonstrate the distinctive ability of the proposed model to reproduce the beam rate-dependent response in a context where large deformations and finite-strains coexist.