Glaucio H. Paulino’s research while affiliated with Princeton University and other places

The concepts of origami and kirigami have often been presented separately. Here, we put forth a synergistic approach—the folded kirigami—in which kirigami assemblies are complemented by means of folding, typical of origami patterns. Besides the emerging patterns themselves, the synergistic approach also leads to topological mechanical metamaterials. While kirigami metamaterials have been fabricated by various methods, such as 3D printing, cutting, casting, and assemblage of building blocks, the “folded kirigami” claim their distinctive properties from the universal folding protocols. For a target kirigami pattern, we design an extended high-genus pattern with appropriate sets of creases and cuts, and proceed to fold it sequentially to yield the cellular structure of a 2D lattice endowed with finite out-of-plane thickness. The strategy combines two features that are generally mutually exclusive in canonical methods: fabrication involving a single piece of material and realization of nearly ideal intercell hinges. We test the approach against a diverse portfolio of triangular and quadrilateral kirigami configurations. We demonstrate a plethora of emerging metamaterial functionalities, including topological phase-switching reconfigurability between polarized and nonpolarized states in kagome kirigami, and availability of nonreciprocal mechanical response in square-rhombus kirigami.

Traditional topology optimization methods only consider a limited number of loads in the optimization procedure, neglecting load variations common in real-world scenarios. To incorporate real load scenarios, robust topology optimization considers uncertainties in load directions while minimizing compliance, generating structures capable of withstanding variations in the load. This paper incorporates the angles of the load directions as parameters into the optimization formulation to design structures that perform well under a range of load directions. Additionally, the formulation is extended to incorporate local volume constraints to balance the solution distribution throughout a domain, achieving more complex designs with proper material distribution as the angle of the loads and the number of sub-regions increases while maintaining consistency in the worst-case scenario. Two and three-dimensional examples demonstrate that topology-optimized designs are susceptible to loads that vary in direction and magnitude, and by considering realistic loading conditions, this formulation yields robust, reliable designs, markedly enhancing their suitability for actual engineering applications.

Investigations of origami tessellations as effective media reveal the ability to program the components of their elasticity tensor. However, existing efforts focus on crease patterns that are composed of parallelogram faces where the parallel lines constrain the quasi-static elastic response. In this work, crease patterns composed of more general trapezoid faces are considered and their low-energy linear response is explored. Deformations of such origami tessellations are modeled as linear isometries that do not stretch individual panels at the small scale yet map to non-isometric changes of coarse-grained fundamental forms that quantify how the effective medium strains and curves at the large scale. Two distinct mode shapes, a rigid breathing mode and a nonrigid shearing mode, are identified in the continuum model. A specific example, called Morph-derivative trapezoid-based origami, is presented with analytical expressions for its deformations in both the discrete and continuous models. A developable specimen is fabricated and tested to validate the analytical predictions. This work advances the continuum modeling of origami tessellations as effective media with the incorporation of more generic faces and ground states, thereby enabling the investigation of novel designs and applications.

Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.

Origami structures have been receiving a lot of attention from engineering and scientific researchers owing to their unique properties such as deployability, multi-stability, negative stiffness, etc. However, dynamic properties of origami structures have not been explored much due to a lack of validated analytical dynamic modeling approaches. Given the range of interesting properties and applications of origami structures, it is important to study the dynamic behavior of origami structures. In this study, a dynamic modeling approach for origami structures is presented considering distributed mass modeling, which has the potential to be a generalizable approach. In the proposed approach, stiffness is modeled using the bar and hinge modeling approach while the mass is modeled using the mass distribution approach. Various candidate mass distribution approaches were investigated by comparing their responses to the finite element method responses for various geometric conditions, loading and boundary conditions, and deformation modes. It was observed that a dynamic modeling approach with triangle circumcenter mass distribution was able to capture most of the dynamics satisfactorily consistently. Subsequently, a Miura-ori specimen was manufactured and its free vibration response was determined experimentally and then compared to the prediction of the analytical model. The comparison demonstrated that the analytical model was able to capture most of the dynamics in the longitudinal direction.

A robust ground structure topology optimization framework is presented to handle the uncertainty of load direction and design for the worst case compliance scenario. The deterministic optimization framework is formulated by a min-max compliance objective to first determine the critical load angle corresponding to the worst case compliance and then to design the topology for compliance minimization. The first optimization problem, based on our load definition, is shown to be equivalent to a maximum eigenvalue function, thus causing significant drawbacks in gradient-based optimization approaches in the case of eigenvalue coalescence. Here, we propose a method to treat the non-differentiability of the maximum eigenvalue optimization problem by a smooth maximum regularization function; hence, presenting a framework for optimizing ground structure networks considering an infinite number of load directions. The results achieved demonstrate that the proposed framework provides solutions with low compliance in all possible loading directions leading to robust structural designs.

Soft robots often draw inspiration from nature to navigate different environments. Although the inching motion and crawling motion of caterpillars have been widely studied in the design of soft robots, the steering motion with local bending control remains challenging. To address this challenge, we explore modular origami units which constitute building blocks for mimicking the segmented caterpillar body. Based on this concept, we report a modular soft Kresling origami crawling robot enabled by electrothermal actuation. A compact and lightweight Kresling structure is designed, fabricated, and characterized with integrated thermal bimorph actuators consisting of liquid crystal elastomer and polyimide layers. With the modular design and reprogrammable actuation, a multiunit caterpillar-inspired soft robot composed of both active units and passive units is developed for bidirectional locomotion and steering locomotion with precise curvature control. We demonstrate the modular design of the Kresling origami robot with an active robotic module picking up cargo and assembling with another robotic module to achieve a steering function. The concept of modular soft robots can provide insight into future soft robots that can grow, repair, and enhance functionality.

Origami foldcores, especially the blockfold cores, have emerged as promising components of high-performance sandwich composites. Inspired by the blockfold origami, we propose the axisymmetric blockfold origami (ABO), which is composed of both rectangular and trapezoidal panels. The ABO inherits the non-flat-foldability of the blockfold origami, and furthermore, displays self-locking mechanisms and enhanced stiffness. The geometry and folding kinematics of the ABO are formulated with respect to the geometric parameters and the folding angle of the assembly. The mathematical conditions are derived for the existence of self-locking mechanisms. We perform compression test simulations to demonstrate enhanced stiffness and increased load-bearing capacity. We find that the existence of rectangular panels not only dominates the non-flat-foldability of the ABO, but also contributes to the enhancement of the stiffness. Our results suggest the potential applications of the ABO for building load-bearing structures with rotational symmetry. Moreover, we discuss the prospects of designing tightly assembled multi-layered origami structures with prestress induced by the mismatch of successive layers to enlighten future research.