Geodesy

Abstract

Thermoplastic and Fused Deposition Modeling (FDM) based 4D printing are rapidly expanding to allow for space-and material-saving 2D printed sheets morphing into 3D shapes when heated. However, to our knowledge, all the known examples are either origami-based models with obvious folding hinges, or beam-based models with holes on the morphing surfaces. Morphing continuous double-curvature surfaces remains a challenge, both in terms of a tailored toolpathplanning strategy and a computational model that simulates it. Additionally, neither approach takes surface texture as a design parameter in its computational pipeline. To extend the design space of FDM-based 4D printing, in Geodesy, we focus on the morphing of continuous doublecurvature surfaces or surface textures. We suggest a unique tool path-printing thermoplastics along 2D closed geodesic paths to form a surface with one raised continuous doublecurvature tiles when exposed to heat. The design space is further extended to more complex geometries composed of a network of rising tiles (i.e., surface textures). Both design components and the computational pipeline are explained in the paper, followed by several printed geometric examples. CCS CONCEPTS • Computer-aided manufacturing, Interactive systems and tools;

SimuLearn

“…In relatively small scales, Thermorph [1], Printed Paper Actuator [39], A-line [40], and bioLogic [46] combined parametric geometries with forward kinematics to simulate tree-topological patterns, but this approach is incompatible with more complex or larger patterns like 4DMesh [41] due to their omission of physical forces. To tackle more complex patterns, [32] and Geodesy [12,32] used linear mass-spring models to approximate the materials' transformation. Still, this approach requires taking small time steps to avoid divergence, leading to long simulation rollout (i.e., a trial of simulation) time and cannot afford real-time CAD interactions and iterations.…”

“…While this work is adapted to a specific material system, SimuLearn's algorithm is also adaptable to other material systems by exchanging the FEA model and/or the feature representation. E.g., SimuLearn can adapt to Geodesy [12] by describing the continuous shells as aggregations of rectangular patches, which are then represented by their corner points, or it can further adapt to Transformative Appetite [42] by swapping the FEA model from stressrelease PLA to swelling gel. Existing works have also validated the viability of ML-based physics in various engineering and design contexts [49].…”

“…While they are fast to compute, these methods often take few if any physical parameters into account, and thus are not physically accurate. Alternatively, mass-spring models [12] seek to incorporate some physical factors present in the actuation environment, but they cannot account for the complex, nonlinear physics inherent to morphing materials and are prone to diverge. Advanced methods such as elastic rods [5,31] are also restricted to certain material properties and shapes, thus having a limited morphing materials design space.…”

Pop-up Print

“…Furthermore, to simplify the transformation process, 4D printing methods are intensively studied by many researchers. They print the object in a compact form, such as sheets [2,9,8,5,38,1,39,28] or linear elements [37], and cause self-assembling transformation by environmental stimuli, such as water [2,9,8,38,39,28], humidity [5], or heat [1].…”

“…object into a target 3D form by changing the environmental conditions [34] (e.g., by exposing them to hot water [37,38,9,2]). These methods are attracting a great deal of attention for their capability to print objects in a compact state and simultaneously transform them to the final artifact.…”