Origami‐based designs refer to the application of the ancient art of origami to solve engineering problems of different nature. Despite being implemented at dimensions that range from the nano to the meter scale, origami‐based designs are always defined by the laws that govern their geometrical properties at any scale. It is thus not surprising to notice that the study of their applications has become of cross‐disciplinary interest. This article aims to review recent origami‐based applications in engineering, design methods and tools, with a focus on research outcomes from 2015 to 2020. First, an introduction to origami history, mathematical background and terminology is given. Origami‐based applications in engineering are reviewed largely in the following fields: biomedical engineering, architecture, robotics, space structures, biomimetic engineering, fold‐cores, and metamaterials. Second, design methods, design tools, and related manufacturing constraints are discussed. Finally, the article concludes with open questions and future challenges.

The deployment of a cylinder based on origami with Kresling pattern, whose basic mechanisms are formed by the buckling of a thin cylindrical shell under torsional loading, is studied in this paper. The model consists of identical triangular panels with cyclic symmetry and has a small displacement internal inextensional mechanism. First, geometric formulation of the design problem is presented. Then, assuming that the deployment and folding process is uniform, the bistable behavior of the cylinder is discussed. It can be found that, during the deployment, the dimensionless strain energy increases first and then reduces to zero but followed by another sharp increase. Moreover, the limit condition of geometry parameters for the bistable phenomenon is also discussed. Finally, the bistable behavior is also studied by using numerical simulations for simple and more complex case of the cylinder with multistory. The numerical results agree well with the analytical predictions. Therefore, comparisons with finite element predictions have shown that the analytical solutions given in this paper are accurate and have validated the assumptions made in the derivations.

The folding and deployment of a cylinder with Miura origami patterns are studied in this paper. First, the geometric formulation of the design problem is discussed. Then the loading case of the axial strains and corresponding external nodal loads applied on the vertices of the top polygon during the motion is investigated analytically. The influence of the angle between the diagonal and horizontal fold lines α and β and the number of Miura origami elements n on the dynamic behavior of the basic segment is also discussed. Then the dynamic behavior is analyzed using numerical simulations. Finally, the deployment process of a cylinder with multi-stories is discussed. The numerical results agree well with the analytical predictions. The results show that the range of motion, i.e. the maximal displacement of top nodes, will also increase with the increase of angles α and β . This cylinder, with a smaller n , may have a bistable behavior. When n is larger, the influence of n on the axial strains and external nodal loads is slight. The numerical results agree well with the analytical predictions. Moreover, the deployment of the cylinder with multi-stories is non-uniform, which deploys from the upper story to the lower story.

In recent decades, origami has transitioned from a traditional art form into a systematic field of scientific inquiry, characterized by attributes such as high foldability, lightweight frameworks, diverse deformation modes, and limited degrees-of-freedom. Despite the abundant literature on smart materials, actuation methods, design principles, and manufacturing techniques, comprehensive reviews focusing on the mechanical properties of origami-inspired structures are relatively rare and unsystematic. This review aims to fill this void by analyzing and summarizing the significant studies conducted on the mechanical properties of origami-inspired structures from 2013 to 2023. We begin with an overview that includes essential definitions of origami, classical origami patterns, and their associated tessellated or stacked structures. Following this, we delve into the principal dynamic modeling method for origami and conduct an in-depth analysis of the key mechanical properties of origami-inspired structures. These properties include tunable stiffness, bistability and multistability, metamechanical properties demonstrated by origami-based metamaterials, and bio-inspired mechanical properties. Finally, we conclude with a comprehensive summary that discusses the current challenges and future directions in the field of origami-inspired structures. Our review provides a thorough synthesis of both the mechanical properties and practical applications of origami-inspired structures, aiming to serve as a reference and stimulate further research.

The folding behavior of a prismatic mast based on Kresling origami pattern is studied in this paper. The mast consists of identical triangles with cyclic symmetry. Bar stresses and necessary external nodal loads of the mast during the motion are studied analytically. The results show that the mechanical behaviors are different when the initial height of the mast is different. Then the numerical analysis is used to prove the accuracy of the analytical results. The influence of the geometry and the number of sides of the polygon on the folding behavior of the basic segment is also investigated. The folding process of the mast with multistories was discussed. The effect of the imperfection based on the eigenvalue buckling modes on the folding behavior is also studied. It can be found that when the number of sides of the polygon is small, the imperfection in the axial direction affects the energy seriously by changing the folding sequence of the mast. When the number of sides of the polygon is larger, the imperfection in the horizontal plane has significant effect on the folding pattern, which leads to the sudden change of energy curve.

This article proposes a numerical method for the kinematic path modeling of retractable roof structures based on the concept of kirigami. The kinematics of origami structures have been studied by many researchers. However, the singular point in the kinematic path which will crucially affect the overall performance of the structure has not been investigated. In this article, the method to detect the singular point in the kinematic path is first introduced. Then, a prediction‐correction algorithm is developed to simulate the motion along a uniquely determined path. A second‐order program is used to select kinematic paths deviating from a singular point. After that, the proposed method is applied in the kinematic modeling of a kirigami structure to show its accuracy.