A review on models for the 3D statics and 2D dynamics of pantographic fabrics

A review on models for the statics of out-of-plane deformable pantographic fabrics is presented, along with a model describing the dynamics of in-plane only deformable pantographic fabrics. We discuss those models able to describe the mechanical exotic properties conferred by the peculiar microstructure possessed by pantographic metamaterials, when three-dimensional deformations and in-plane dynamics are separately involved. For each approach, model formulation and modelling assumptions are discussed along with the presentation of numerical solutions in exemplary cases, and no attempt is made to model damage and failure phenomena.