Abstract Maintaining the maximum stiffness of components with as little material as possible is an overarching objective in computational design and engineering. It is well‐established that in stiffness‐optimal designs, material is aligned with orthogonal principal stress directions. In the limit of material volume, this alignment forms micro‐structures resembling quads or hexahedra. Achieving a globally consistent layout of such orthogonal micro‐structures presents a significant challenge, particularly in three‐dimensional settings. In this paper, we propose a novel geometric algorithm for compiling stress‐aligned hexahedral lattice structures. Our method involves deforming an input mesh under load to align the resulting stress field along an orthogonal basis. The deformed object is filled with a hexahedral grid, and the deformation is reverted to recover the original shape. The resulting stress‐aligned mesh is used as basis for a final hollowing procedure, generating a volume‐reduced stiff infill composed of hexahedral micro‐structures. We perform quantitative comparisons with structural optimization and hexahedral meshing approaches and demonstrate the superior mechanical performance of our designs with finite element simulation experiments.

We introduce the Stress-Guided Lightweight Design Benchmark (SGLDBench), a comprehensive benchmark suite for applying and evaluating material layout strategies to generate stiff, lightweight designs in 3D domains. SGLDBench provides a seamlessly integrated simulation and analysis framework, including six reference strategies and a scalable multigrid elasticity solver to efficiently execute these strategies and validate the stiffness of their results. This facilitates the systematic analysis and comparison of design strategies based on the mechanical properties they achieve. SGLDBench enables the evaluation of diverse load conditions and, through the tight integration of the solver, supports high-resolution designs and stiffness analysis. Additionally, SGLDBench emphasizes visual analysis to explore the relationship between the geometric structure of a design and the distribution of stresses, offering insights into the specific properties and behaviors of different design strategies. SGLDBench's specific features are highlighted through several experiments, comparing the results of reference strategies with respect to geometric and mechanical properties.

Shape-changing textile interfaces have the potential to create unique functions, expressions, and interactions in everyday artifacts. However, the technical expertise required to fabricate and interact with these interfaces limits designers from rapidly iterating through diverse textile expressions. This pictorial presents TEX(alive), a low-cost and open-source physical-digital toolkit to facilitate the creation of temporal expressions in textile interfaces. TEX(alive) comprises pneumatic actuators that can be interactively configured across a 3d printed grid structure on the textile. Creative sessions with seven designers show that TEX(alive) supports the exploration of temporality in textile interfaces, opening up a design space for unforeseen future application scenarios and alive-like expressions in material-driven design. Finally, we suggest coupling TEX(alive) with a computational simulation tool to allow designers to predict spatial shape change when the textile interface increases in size or complexity.

Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape. Our method consists of two major steps: the first optimizes concurrently the shape (including its topology) and the distribution of orthotropic lattice materials inside the shape to maximize stiffness under application-specific external loads; the second takes the optimized configuration (i.e., locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. Our approach is robust and works for both 2D planar and 3D volumetric domains. Numerical results and physical verifications demonstrate remarkable structural properties of conforming lattice structures generated by our method.

3D printing techniques such as Fused Deposition Modeling (FDM) have enabled the fabrication of complex geometry quickly and cheaply. Objects are produced by filling (a portion of) the 2D polygons of consecutive layers with contour-parallel extrusion toolpaths. Uniform width toolpaths consisting of inward offsets from the outline polygons produce over- and underfill regions in the center of the shape, which are especially detrimental to the mechanical performance of thin parts. In order to fill shapes with arbitrary diameter densely the toolpaths require adaptive width. Existing approaches for generating toolpaths with adaptive width result in a large variation in widths, which for some hardware systems is difficult to realize accurately. In this paper we present a framework which supports multiple schemes to generate toolpaths with adaptive width, by employing a function to decide the number of beads and their widths. Furthermore, we propose a novel scheme which reduces extreme bead widths, while limiting the number of altered toolpaths. We statistically validate the effectiveness of our framework and this novel scheme on a data set of representative 3D models, and physically validate it by developing a technique, called back pressure compensation, for off-the-shelf FDM systems to effectively realize adaptive width.

Abstract We present a visualization technique for 2D stress tensor fields based on the construction of a globally conforming lattice. Conformity ensures that the lattice edges follow the principal stress directions and the aspect ratio of lattice elements represents the stress anisotropy. Since such a lattice structure cannot be space‐filling in general, it is constructed from multiple intersecting lattice beams. Conformity at beam intersections is ensured via a constrained optimization problem, by computing the aspect ratio of elements at intersections so that their edges meet when continued along the principal stress lines. In combination with a coloring scheme that encodes relative stress magnitudes, a global visualization is achieved. By introducing additional constraints on the positional variation of the beam intersections, coherent visualizations are achieved when external loads or material parameters are changed. In a number of experiments using non‐trivial scenarios, we demonstrate the capability of the proposed visualization technique to show the global and local structure of a given stress field.

This paper introduces a novel approach for sensing the bending deformation on soft robots by leveraging multicolor 3D printing. The measurement of deformation enables to complete the feedback loop of deformation control on soft actuators. The working principle of our approach is based on using compact color sensors to detect deformation that is visualized by the change of color ratios. Two novel designs are presented to generate color signals on 3D printed objects, which we call an external signal generator and an internal signal generator. Signal processing and calibration methods are developed to transform the raw RGB-data into a meaningful deformation metric. Our experimental tests taken on soft pneumatic actuators verify that color signals can be stably generated and captured to indicate the bending deformation. The results also demonstrate the usability of this sensing approach in deformation control.

Offsetting-based hollowing is a solid modeling operation widely used in 3D printing, which can change the model's physical properties and reduce the weight by generating voids inside a model. However, a hollowing operation can lead to additional supporting structures for fabrication in interior voids, which cannot be removed. As a consequence, the result of a hollowing operation is affected by these additional supporting structures when applying the operation to optimize physical properties of different models. This paper proposes a support-free hollowing framework to overcome the difficulty of fabricating voids inside a solid. The challenge of computing a support-free hollowing is decomposed into a sequence of shape optimization steps, which are repeatedly applied to interior mesh surfaces. The optimization of physical properties in different applications can be easily integrated into our framework. Comparing to prior approaches that can generate support-free inner structures, our hollowing operation can reduce more volume of material and thus provide a larger solution space for physical optimization. Experimental tests are taken on a number of 3D models to demonstrate the effectiveness of this framework.

Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p-norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.

This paper introduces a novel method for designing personalized orthopedic casts which are aware of thermal-comfort while satisfying mechanical requirements. Our pipeline starts from thermal images taken by an infrared camera, by which the distribution of thermal-comfort sensitivity is generated on the surface of a 3D scanned model. We formulate a hollowed Voronoi tessellation pattern to represent the covered region for a web-like cast design. The pattern is further optimized according to the thermal-comfort sensitivity calculated from thermal images. Working together with a thickness variation method, we generate a solid model for a personalized cast maximizing both thermal comfort and mechanical stiffness. To demonstrate the effectiveness of our approach, 3D printed models of personalized casts are tested on body parts of different individuals.

A key requirement in 3D fabrication is to generate objects with individual exterior shapes and their interior being optimized to application-specific force constraints and low material consumption. Accomplishing this task is challenging on desktop computers, due to the extreme model resolutions that are required to accurately predict the physical shape properties, requiring memory and computational capacities going beyond what is currently available. Moreover, fabrication-specific constraints need to be considered to enable printability. To address these challenges, we present a scalable system for generating 3D objects using topology optimization, which allows to efficiently evolve the topology of high-resolution solids towards printable and light-weight-high-resistance structures. To achieve this, the system is equipped with a high-performance GPU solver which can efficiently handle models comprising several millions of elements. A minimum thickness constraint is built into the optimization process to automatically enforce printability of the resulting shapes. We further shed light on the question how to incorporate geometric shape constraints, such as symmetry and pattern repetition, in the optimization process. We analyze the performance of the system and demonstrate its potential by a variety of different shapes such as interior structures within closed surfaces, exposed support structures, and surface models.

Abstract Virtual cutting of deformable bodies has been an important and active research topic in physically based modelling and simulation for more than a decade. A particular challenge in virtual cutting is the robust and efficient incorporation of cuts into an accurate computational model that is used for the simulation of the deformable body. This report presents a coherent summary of the state of the art in virtual cutting of deformable bodies, focusing on the distinct geometrical and topological representations of the deformable body, as well as the specific numerical discretizations of the governing equations of motion. In particular, we discuss virtual cutting based on tetrahedral, hexahedral and polyhedral meshes, in combination with standard, polyhedral, composite and extended finite element discretizations. A separate section is devoted to meshfree methods. Furthermore, we discuss cutting‐related research problems such as collision detection and haptic rendering in the context of interactive cutting scenarios. The report is complemented with an application study to assess the performance of virtual cutting simulators.

Several techniques exist to automatically synthesize a 2D image resembling an input exemplar texture. Most of the approaches optimize a new image so that the color neighborhoods in the output closely match those in the input, across all scales. In this paper we revisit by-example texture synthesis in the context of additive manufacturing. Our goal is to generate not only colors, but also structure along output surfaces: given an exemplar indicating 'solid' and 'empty' pixels, we generate a similar pattern along the output surface. The core challenge is to guarantee that the pattern is not only fully connected, but also structurally sound. To achieve this goal we propose a novel formulation for on-surface by-example texture synthesis that directly works in a voxel shell around the surface. It enables efficient local updates to the pattern, letting our structural optimizer perform changes that improve the overall rigidity of the pattern. We use this technique in an iterative scheme that jointly optimizes for appearance and structural soundness. We consider fabricability constraints and a user-provided description of a force profile that the object has to resist. Our results fully exploit the capabilities of additive manufacturing by letting users design intricate structures along surfaces. The structures are complex, yet they resemble input exemplars, resulting in a modeling tool accessible to casual users.

Abstract Piecewise linear polygonal model has onlyG0continuity, thus users can easily feel the edges when using haptic device to touch a solid represented by coarse polygonal meshes. To produce an appealing haptic sensation for smooth solids, a large number of polygons are needed in conventional approaches. This, however, slows down computation and consumes much more memory. In this paper, we present a method to generate smooth feedback force in haptic interaction with coarse polygonal meshes. Our method calculates the interaction force based on Gregory patches, which are locally constructed fromn‐sided polygons and ensureG1continuity across boundaries of patches. During the real time haptic interaction, the contact point is continuously tracked on the locally constructed Gregory patches and thus generates smooth haptic forces to be rendered. Our method is validated on various models with comparison to conventional force rendering techniques. Copyright © 2010 John Wiley & Sons, Ltd.