Orthotropic k-nearest foams for additive manufacturing

International audienceAdditive manufacturing enables the fabrication of objects embedding metamaterials. By creating fine-scale structures, the object's physical properties can be graded (e.g. elasticity, porosity), even though a single base material is used for fabrication. Designing the fine and detailed geometry of a metamaterial while attempting to achieve specific properties is difficult. In addition, the structures are intended to fill comparatively large volumes, which quickly leads to large data structures and intractable simulation costs. Thus, most metamaterials are defined as periodic structures repeated in regular lattices. The periodicity simplifies modeling, simulation, and reduces memory costs -- however it limits the possibility to smoothly grade properties along free directions.In this work, we propose a novel metamaterial with controllable, freely orientable, orthotropic elastic behavior -- orthotropy means that elasticity is controlled independently along three orthogonal axes, which leads to materials that better adapt to uneven, directional load scenarios, and offer a more versatile material design primitive. The fine-scale structures are generated procedurally by a stochastic process, and resemble a foam. The absence of global organization and periodicity allows the free gradation of density, orientation, and stretch, leading to the controllable orthotropic behavior. The procedural nature of the synthesis process allows it to scale to arbitrarily large volumes at low memory costs.We detail the foam structure synthesis, analyze and discuss its properties through numerical and experimental verifications, and finally demonstrate the use of orthotropic materials for the design of 3D printed objects

Numerical Modeling and Experimental Investigation of Effective Elastic Properties of the 3D Printed Gyroid Infill

A numerical homogenization approach is presented for the effective elastic moduli of 3D printed cellular infills. A representative volume element of the infill geometry is discretized using either shell or solid elements and analyzed using the finite element method. The elastic moduli of the bulk cellular material are obtained through longitudinal and shear deformations of a representative volume element under periodic boundary conditions. The method is used to analyze the elastic behavior of gyroid infills for varying infill densities. The approach is validated by comparing the Young’s modulus and Poisson’s ratio with those obtained from compression experiments. Results indicate that although the gyroid infill exhibits cubic symmetry, it is nearly isotropic with a low anisotropy index. The numerical predictions are used to develop semi-empirical equations of the effective elastic moduli of gyroid infills as a function of infill density in order to inform design and topology optimization workflows

Polyhedral Voronoi diagrams for additive manufacturing

International audienceA critical advantage of additive manufacturing is its ability to fabricate complex small-scale structures. These microstructures can be understood as a metamaterial: they exist at a much smaller scale than the volume they fill, and are collectively responsible for an average elastic behavior different from that of the base printing material making the fabricated object lighter and/or flexible along specific directions. In addition, the average behavior can be graded spatially by progressively modifying the microstructure geometry.The definition of a microstructure is a careful trade-off between the geometric requirements of manufacturing and the properties one seeks to obtain within a shape: in our case a wide range of elastic behaviors. Most existing microstructures are designed for stereolithography (SLA) and laser sintering (SLS) processes. The requirements are however different than those of continuous deposition systems such as fused filament fabrication (FFF), for which there is currently a lack of microstructures enabling graded elastic behaviors.In this work we introduce a novel type of microstructures that strictly enforce all the requirements of FFF-like processes: continuity, self-support and overhang angles. They offer a range of orthotropic elastic responses that can be graded spatially. This allows to fabricate parts usually reserved to the most advanced technologies on widely available inexpensive printers that also benefit from a continuously expanding range of materials

Explicit Topology Optimization of Conforming Voronoi Foams

Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent cells, and achieving high simulation accuracy. To resolve the issues, borrowing the concept from Voronoi tessellation, we propose to use the site (or seed) positions and radii of the beams as the DOFs for open-cell foam design. Such DOFs cover extensive design space and have clear geometrical meaning, which makes it easy to provide explicit controls (e.g. granularity). During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of the shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The mechanical property of our foam is computed from its highly heterogeneous density field counterpart discretized on a background mesh, with a much improved accuracy via a new material-aware numerical coarsening method. We also explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a local finite difference method to estimate the derivatives efficiently. We do not only show the improved foam performance of our Voronoi foam in comparison with classical topology optimization approaches, but also demonstrate its advantages in various settings, especially when the target volume fraction is extremely low