Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parameterised models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented

From 3D Models to 3D Prints: an Overview of the Processing Pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens of methods that prepare the 3D model for fabrication, while analysing and optimizing geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and Innovation action; Grant agreement N. 68044

Topology optimization of 2.5D parts using the SIMP method with a variable thickness approach

In this study, the Solid Isotropic Material with Penalization (SIMP) topology optimization method is employed on the artifacts via keeping the penalization factor as unity. When the penalization is not carried out, the finite elements of the artifact have intermediate material densities. These density values are then used as the thicknesses of the corresponding finite elements and conformal surfaces are formed utilizing these heights in the proposed method. We evaluated the performance of the method with the conventional SIMP method, having penalization factors larger than one, in terms of numerical analysis and experiments. The results revealed that the proposed approach outperforms the classical SIMP method. (C) 2018 The Authors. Published by Elsevier B.V

Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures

A novel surface interrogation technique is proposed to compute the intersection of curves with spline surfaces in isogeometric analysis. The intersection points are determined in one-shot without resorting to a Newton-Raphson iteration or successive refinement. Surface-curve intersection is required in a wide range of applications, including contact, immersed boundary methods and lattice-skin structures, and requires usually the solution of a system of nonlinear equations. It is assumed that the surface is given in form of a spline, such as a NURBS, T-spline or Catmull-Clark subdivision surface, and is convertible into a collection of B\'ezier patches. First, a hierarchical bounding volume tree is used to efficiently identify the B\'ezier patches with a convex-hull intersecting the convex-hull of a given curve segment. For ease of implementation convex-hulls are approximated with k-dops (discrete orientation polytopes). Subsequently, the intersections of the identified B\'ezier patches with the curve segment are determined with a matrix-based implicit representation leading to the computation of a sequence of small singular value decompositions (SVDs). As an application of the developed interrogation technique the isogeometric design and analysis of lattice-skin structures is investigated. The skin is a spline surface that is usually created in a computer-aided design (CAD) system and the periodic lattice to be fitted consists of unit cells, each containing a small number of struts. The lattice-skin structure is generated by projecting selected lattice nodes onto the surface after determining the intersection of unit cell edges with the surface. For mechanical analysis, the skin is modelled as a Kirchhoff-Love thin-shell and the lattice as a pin-jointed truss. The two types of structures are coupled with a standard Lagrange multiplier approach

Foundry: Hierarchical Material Design for Multi-Material Fabrication

We demonstrate a new approach for designing functional material definitions for multi-material fabrication using our system called Foundry. Foundry provides an interactive and visual process for hierarchically designing spatially-varying material properties (e.g., appearance, mechanical, optical). The resulting meta-materials exhibit structure at the micro and macro level and can surpass the qualities of traditional composites. The material definitions are created by composing a set of operators into an operator graph. Each operator performs a volume decomposition operation, remaps space, or constructs and assigns a material composition. The operators are implemented using a domain-specific language for multi-material fabrication; users can easily extend the library by writing their own operators. Foundry can be used to build operator graphs that describe complex, parameterized, resolution-independent, and reusable material definitions. We also describe how to stage the evaluation of the final material definition which in conjunction with progressive refinement, allows for interactive material evaluation even for complex designs. We show sophisticated and functional parts designed with our system.National Science Foundation (U.S.) (1138967)National Science Foundation (U.S.) (1409310)National Science Foundation (U.S.) (1547088)National Science Foundation (U.S.). Graduate Research Fellowship ProgramMassachusetts Institute of Technology. Undergraduate Research Opportunities Progra

Procedural function-based spatial microstructures

We propose a new approach to modelling heterogeneous objects containing internal spatial geometric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides a compact, precise, and arbitrarily parameterized model allowing for modelling coherent microstructures, which can undergo blending, offsetting, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations. In particular, modelling of regular lattices and porous media is discussed and illustrated. Examples of microstructure models rendering and fabrication using a variety of digital fabrication machines and materials are presented

Implicit Functionally Graded Conforming Microstructures

The tensor product parametric representations are the most commonly used representation in geometric modeling. Yet, other representations have advantages in certain aspects, and in this work, we focus on employing implicit representations in the construction of microstructures. An implicit function, either functionally precise, or spline trivariate-based, is used to populate a macro-shape trivariate parametric form, and construct a conforming microstructure. Either the implicit tile or the macro-shape can be functionally graded or be heterogeneous, carrying graded properties such as material, translucency, or color alongside the geometry. Further, the implicit tiles can be parametrized and hence their geometry can vary across the macro-shape. The representation is locally precise and we demonstrate that in a slicing process that employs no (piecewise-linear) approximation. Finally, we demonstrate this framework on several 3D printed heterogeneous models

Biomimetic scaffolds using triply periodic minimal surface-based porous structures for biomedical applications

The design of biomimetic porous scaffolds has been gaining attention in the biomedical sector lately. Shells, marine sponges, shark teeth, cancellous bone, sea urchin spine, and the armadillo armor structure are examples of biological systems that have already been studied to drive the design of innovative, porous, and multifunc-tional structures. Among these, triply periodic minimal surfaces (TPMSs) have attracted the attention of scientists for the fabrication of biomimetic porous scaffolds. The interest stems from their outstanding properties, which include mathematical controllable geometry features, highly interconnected porous architectures, high surface area to volume ratio, less stress concentration, tunable mechanical properties, and increased permeability. All these distinguishing features enable better cell adhesion, optimal integration to the surrounding tissue avoiding stress shieldings, a good permeability of fluid media and oxygen, and the possibility of vascularization. How-ever, the sophisticated geometry of these TPMS-based structures has proven challenging to fabricate by con-ventional methods. The emergence of additive manufacturing (AM) and the enhanced manufacturing freedoms and flexibility it guarantees could solve some of the bottlenecks, thus leading to a surge of interest in designing and fabricating such structures in this field. Also, the feasibility of using AM technologies allows for obtaining size programmable TPMS printable in various materials, from polymers to metal alloys. Here, a comprehensive overview of 3D-printed TPMS porous structures is provided from a design for additive manufacturing (DfAM) and application perspective. First, design strategies, geometry design algorithms, and related topological opti-mization are introduced according to diverse requirements. Based on that, the performance control of TPMS and the pros and cons of the different AM processes for fabricating TPMS scaffolds are summarized. Lastly, practical applications of 3D-printed biomimetic TPMS porous structures for the biomedical field are presented to clarify the advantages and potential of such structures