Isogeometric analysis for nonlinear planar pantographic lattice: discrete and continuum models

Pantographic sheets are metamaterials constituted by two interconnected layers of straight fibers. One of the great features of these structures is that they are extremely elastically compliant toward large nonlinear deformations. To model pantographic lattices, Kirchhoff rods based on Euler–Bernoulli assumptions can be used. Otherwise, if the fibers are sufficiently dense, homogenization of the microstructure results in a two-dimensional second-order gradient continuum model. The discrete and continuum models have in common the fact that their energy terms depend on the second-order derivatives of the displacement field, such that the classical finite element method cannot be directly employed. We propose instead the use of the isogeometric analysis where the basis functions are endowed with a higher inter-element continuity, allowing the rotation-free discretization of these problems. The discrete and continuum models are compared to existing benchmarks and are found in excellent agreement, validating the proposed approach.status: publishe