Multi-Body Dynamical Modeling and Prediction of Flexible Origami/Kirigami Metamaterials by Affine Transformation

An original multi-body dynamical modeling method of Origami/Kirigami metamaterials considering flexibility both on surfaces and creases is proposed. The surfaces are discretized by combining triangle and rectangle reduced elements based on the absolute nodal coordinate formulation (ANCF), while the creases are described by time-varying torque constraints, which depend on dihedral angles. To solve the problem that reduced elements cannot give the relationship of the crease force and gradients, an affine transformation principle is proposed. Due to the topological invariance of configurations and characteristics of generalized forces, the complexity of modeling and calculating are effectively decreased, which also results the successful dynamic prediction and design on Origami/Kirigami metamaterials. Two numerical examples (an open Origami plates system with different external force field, an enclosed Yoshimura Origami system with different elasticity modulus) are simulated to validate the modeling feasibility. Then, the method is employed to study the dynamic behaviors and design principle of a Kirigami metamaterials for multi-stability. Comparisons between theoretical results from modeling and experiments demonstrate the effectiveness of the modeling method, which induces more precision on structural and dynamical designs.