Reduced-order modeling of a sliding ring on an elastic rod with incremental potential formulation

Mechanical interactions between rigid rings and flexible cables are widespread in both daily life (hanging clothes) and engineering system (closing a tether net). A reduced-order method for the dynamic analysis of sliding rings on a deformable one-dimensional (1D) rod-like object is proposed. In contrast to discretize the joint rings into multiple nodes and edges for contact detection and numerical simulation, a single point is used to reduce the order of the numerical model. In order to achieve the non-deviation condition between sliding ring and flexible rod, a novel barrier functional is derived based on incremental potential theory, and the tangent frictional interplay is later procured by a lagged dissipative formulation. The proposed barrier functional and the associated frictional functional are $C^{2}$ continuous, hence the nonlinear elastodynamic system can be solved variationally by an implicit time-stepping scheme. The numerical framework is first applied to simple examples where the analytical solutions are available for validation. Then, multiple complex practical engineering examples are considered to showcase the effectiveness of the proposed method. The simplified ring-to-rod interaction model can provide lifelike visual effect for picture animations, and also can support the optimal design for space debris removal system.Comment: 15 pages, 9 figure

Automated generation of flat tileable patterns and 3D reduced model simulation

The computational fabrication community is developing an increasing interest in the use of patterned surfaces, which can be designed to show ornamental and unconventional aesthetics or to perform as a proper structural material with a wide range of features. Geometrically designing and controlling the deformation capabilities of these patterns in response to external stimuli is a complex task due to the large number of variables involved. This paper introduces a method for generating sets of tileable and exchangeable flat patterns as well as a model-reduction strategy that enables their mechanical simulation at interactive rates. This method is included in a design pipeline that aims to turn any general flat surface into a pattern tessellation, which is able to deform under a given loading scenario. To validate our approach, we apply it to different contexts, including real-scale 3D printed specimens, for which we compare our results with the ones provided by a ground-truth solver

Modeling of Flexible Beam Networks and Morphing Structures by Geometrically Exact Discrete Beams

Abstract We demonstrate how a geometrically exact formulation of discrete slender beams can be generalized for the efficient simulation of complex networks of flexible beams by introducing rigid connections through special junction elements. The numerical framework, which is based on discrete differential geometry of framed curves in a time-discrete setting for time- and history-dependent constitutive models, is applicable to elastic and inelastic beams undergoing large rotations with and without natural curvature and actuation. Especially, the latter two aspects make our approach a versatile and efficient alternative to higher-dimensional finite element techniques frequently used, e.g., for the simulation of active, shape-morphing, and reconfigurable structures, as demonstrated by a suite of examples.</jats:p

ACM Transactions on Graphics

We present an interactive design system to create functional mechanical objects. Our computational approach allows novice users to retarget an existing mechanical template to a user-specified input shape. Our proposed representation for a mechanical template encodes a parameterized mechanism, mechanical constraints that ensure a physically valid configuration, spatial relationships of mechanical parts to the user-provided shape, and functional constraints that specify an intended functionality. We provide an intuitive interface and optimization-in-the-loop approach for finding a valid configuration of the mechanism and the shape to ensure that higher-level functional goals are met. Our algorithm interactively optimizes the mechanism while the user manipulates the placement of mechanical components and the shape. Our system allows users to efficiently explore various design choices and to synthesize customized mechanical objects that can be fabricated with rapid prototyping technologies. We demonstrate the efficacy of our approach by retargeting various mechanical templates to different shapes and fabricating the resulting functional mechanical objects

Analysis of a Reduced-Order Model for the Simulation of Elastic Geometric Zigzag-Spring Meta-Materials

We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d and bent elastically such that they approximate doubly-curved 2-manifold surfaces in 3d space. They obtain their elasticity attributes mainly from the geometry of their cellular elements and their connections. In this paper we focus on cells build from so-called zigzag springs. The physical properties of the base material (i.e., the physical substance) influence the behavior as well, but we essentially factor them out by keeping them constant. The simulation of such complex geometric structures comes with a high computational cost, thus we propose an approach to reduce it by abstracting the zigzag cells by a simpler model and by learning the properties of their elastic deformation behavior. In particular, we analyze the influence of the sampling of the full parameter space and the expressiveness of the reduced model compared to the full model. Based on these observations, we draw conclusions on how to simulate such complex meso-structures with simpler models.Comment: 14 pages, 12 figures, published in Computers & Graphics, extended version of arXiv:2010.0807