Related papers: Printing non-Euclidean solids
Accurately digitizing physical objects is central to many applications, including virtual/augmented reality, industrial design, and e-commerce. Prior research has demonstrated efficient and faithful reconstruction of objects' geometric…
Conforming materials to rigid substrates with Gaussian curvature --- positive for spheres and negative for saddles --- has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters, and liquid…
Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is…
We study the geometrical frustration scenario of glass formation for simple hard sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing…
The common layer-by-layer deposition of regular, 3-axis 3D printing simplifies both the fabrication process and the 3D printer's mechanical design. However, the resulting 3D printed objects have some unfavourable characteristics including…
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…
The main goal of this work is to clarify and quantify, by means of mathematical analysis, the role of structural viscoelasticity in the biomechanical response of deformable porous media with incompressible constituents to sudden changes in…
Mechanical metamaterials are periodic lattice structures with complex unit cell architectures that can achieve extraordinary mechanical properties beyond the capability of bulk materials. A new class of metamaterials is proposed, whose…
Additive manufacturing strives to combine any combination of materials into three dimensional functional structures and devices, ultimately opening up the possibility of 3D printed machines. It remains difficult to actuate such devices,…
The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for…
Strength, ductility, and failure properties of metals are tailored by plastic deformation routes. Predicting these properties requires modeling of the structural dynamics and stress evolution taking place on several length scales. Progress…
Biological living materials, such as animal bones and plant stems, are able to self-heal, regenerate, adapt and make decisions under environmental pressures. Despite recent successful efforts to imbue synthetic materials with some of these…
In order to enhance the modeling of metallic materials behavior in non proportional loadings, a modification of the classical elastic-plastic models including distortion of the yield surface is proposed. The new yield criterion uses the…
We show that geometric frustration in a broad class of deformable and naturally curved, shell-like colloidal particles gives rise to self-limiting assembly of finite-sized stacks that far exceed particle dimensions. When inter-particle…
Helical structures are ubiquitous in nature and engineering, ranging from DNA molecules to plant tendrils, from sea snail shells to nanoribbons. While the helical shapes in natural and engineered systems often exhibit nearly uniform radius…
Growth-elasticity is a powerful model framework for understanding complex shape development in soft biological tissues. At each instant, by mapping how continuum building blocks have grown geometrically and how they respond elastically to…
In topology optimization, the treatment of stress constraints for very large scale problems has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the…
The self-assembly of particles into organized structures is a key feature of living organisms and a major engineering challenge. While it may proceed through the binding of perfectly matched, puzzle-pieces-like particles, many other…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
When subjected to specific prestresses, continuum elastic shells can exhibit geometric zero modes: complex motions that require vanishing elastic energy to excite, enabling them to be driven by weak and generic energy inputs. Despite recent…