Numerical simulations of folding mechanics in nonlinear plates using discontinuous rotations

A wide range of modern and advanced structural applications includes self-folding materials and origami metamaterials. Simulation tools capable of modelling creases in continuum media have become desirable to keep up with such technological advancements. We present an approach to simulate folding as sharp discontinuities in the Euler rotations of nonlinear plates. We used large deformations and large rotations within a first-order shear plate theory. The novel finding is a set of constraints that the rotation jumps must satisfy on a crease. We used a meshfree method to implement such conditions and check their effectiveness. We verified the numerical solutions against available analytical and semi-analytical solutions. We show that the proposed idea works well also for more complicated configurations, such as rigid origami motions with multiple folding lines and crumpled sheets with random creases.