6,394 research outputs found
The mechanical response of cellular materials with spinodal topologies
The mechanical response of cellular materials with spinodal topologies is
numerically and experimentally investigated. Spinodal microstructures are
generated by the numerical solution of the Cahn-Hilliard equation. Two
different topologies are investigated: "solid models," where one of the two
phases is modeled as a solid material and the remaining volume is void space;
and "shell models," where the interface between the two phases is assumed to be
a solid shell, with the rest of the volume modeled as void space. In both
cases, a wide range of relative densities and spinodal characteristic feature
sizes are investigated. The topology and morphology of all the numerically
generated models are carefully characterized to extract key geometrical
features and ensure that the distribution of curvatures and the aging law are
consistent with the physics of spinodal decomposition. Finite element meshes
are generated for each model, and the uniaxial compressive stiffness and
strength are extracted. We show that while solid spinodal models in the density
range of 30-70% are relatively inefficient (i.e., their strength and stiffness
exhibit a high-power scaling with relative density), shell spinodal models in
the density range of 0.01-1% are exceptionally stiff and strong. Spinodal shell
materials are also shown to be remarkably imperfection insensitive. These
findings are verified experimentally by in-situ uniaxial compression of
polymeric samples printed at the microscale by Direct Laser Writing (DLW). At
low relative densities, the strength and stiffness of shell spinodal models
outperform those of most lattice materials and approach theoretical bounds for
isotropic cellular materials. Most importantly, these materials can be produced
by self-assembly techniques over a range of length scales, providing unique
scalability
Finding Hexahedrizations for Small Quadrangulations of the Sphere
This paper tackles the challenging problem of constrained hexahedral meshing.
An algorithm is introduced to build combinatorial hexahedral meshes whose
boundary facets exactly match a given quadrangulation of the topological
sphere. This algorithm is the first practical solution to the problem. It is
able to compute small hexahedral meshes of quadrangulations for which the
previously known best solutions could only be built by hand or contained
thousands of hexahedra. These challenging quadrangulations include the
boundaries of transition templates that are critical for the success of general
hexahedral meshing algorithms.
The algorithm proposed in this paper is dedicated to building combinatorial
hexahedral meshes of small quadrangulations and ignores the geometrical
problem. The key idea of the method is to exploit the equivalence between quad
flips in the boundary and the insertion of hexahedra glued to this boundary.
The tree of all sequences of flipping operations is explored, searching for a
path that transforms the input quadrangulation Q into a new quadrangulation for
which a hexahedral mesh is known. When a small hexahedral mesh exists, a
sequence transforming Q into the boundary of a cube is found; otherwise, a set
of pre-computed hexahedral meshes is used.
A novel approach to deal with the large number of problem symmetries is
proposed. Combined with an efficient backtracking search, it allows small
shellable hexahedral meshes to be found for all even quadrangulations with up
to 20 quadrangles. All 54,943 such quadrangulations were meshed using no more
than 72 hexahedra. This algorithm is also used to find a construction to fill
arbitrary domains, thereby proving that any ball-shaped domain bounded by n
quadrangles can be meshed with no more than 78 n hexahedra. This very
significantly lowers the previous upper bound of 5396 n.Comment: Accepted for SIGGRAPH 201
Wire mesh design
We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods
Subdivision Shell Elements with Anisotropic Growth
A thin shell finite element approach based on Loop's subdivision surfaces is
proposed, capable of dealing with large deformations and anisotropic growth. To
this end, the Kirchhoff-Love theory of thin shells is derived and extended to
allow for arbitrary in-plane growth. The simplicity and computational
efficiency of the subdivision thin shell elements is outstanding, which is
demonstrated on a few standard loading benchmarks. With this powerful tool at
hand, we demonstrate the broad range of possible applications by numerical
solution of several growth scenarios, ranging from the uniform growth of a
sphere, to boundary instabilities induced by large anisotropic growth. Finally,
it is shown that the problem of a slowly and uniformly growing sheet confined
in a fixed hollow sphere is equivalent to the inverse process where a sheet of
fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless,
quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl
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