Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Geometric Deformations Of Sodalite Frameworks, Ciprian Borcea, Ileana Streinu
Geometric Deformations Of Sodalite Frameworks, Ciprian Borcea, Ileana Streinu
Computer Science: Faculty Publications
In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for frameworks modeled on sodalite.
Geometric Auxetics, Ciprian Borcea, Ileana Streinu
Geometric Auxetics, Ciprian Borcea, Ileana Streinu
Computer Science: Faculty Publications
We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures.
Liftings And Stresses For Planar Periodic Frameworks, Ciprian Borcea, Ileana Streinu
Liftings And Stresses For Planar Periodic Frameworks, Ciprian Borcea, Ileana Streinu
Computer Science: Faculty Publications
We formulate and prove a periodic analog of Maxwell’s theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks.