Related papers: Periodic auxetics: Structure and design
Poisson structures of divisor-type are those whose degeneracy can be captured by a divisor ideal, which is a locally principal ideal sheaf with nowhere-dense quotient support. This is a large class of Poisson structures which includes all…
It is widely assumed that disordered auxetic structures (i.e. structures with a negative Poisson's ratio) must contain re-entrant polygons in $2$D and re-entrant polyhedra in $3$D. Here we show how to design disordered networks in $2$D with…
In this work, a novel hierarchical mechanical metamaterial is proposed that is composed of re-entrant truss-lattice elements. It is shown that this system can deform very differently and can exhibit a versatile extent of the auxetic…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is…
We consider 2- and 3-dimensional cubic monocrystalline and polycrystalline materials. Expressions for Young's and shear moduli and Poisson's ratio are expressed in terms of eigenvalues of the stiffness tensor. Such a form is well suited for…
We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…
Bilayers, soft substrates coated with stiff films, are commonly found in nature with examples including skin tissue, vesicles, and organ membranes. They exhibit different types of instabilities when subjected to compression, depending on…
Mechanical metamaterials designed around a zero-energy pathway of deformation, known as a mechanism, have repeatedly challenged the conventional picture of elasticity. However, the complex spatial deformations these structures are able to…
The problem of obtaining anisotropic auxetic composite laminates, i.e. having a negative Poisson's ratio for at least some directions, is examined in this paper. In particular, the possibility of obtaining auxeticity stacking…
We investigate a lattice of coupled logistic maps where, in addition to the usual diffusive coupling, an advection term parameterized by an asymmetry in the coupling is introduced. The advection term induces periodic behavior on a…
We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manifolds are privileged by the fact that their deformation…
Auxetic metamaterials are commonly thought to exhibit favorable mechanical properties, notably high energy absorption. Here we investigate disordered metamaterials obtained from random beam networks by optimizing simultaneously auxeticity…
Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
Dilational materials are stable three-dimensional isotropic auxetics with an ultimate Poisson's ratio of -1. We design, evaluate, fabricate, and characterize crystalline metamaterials approaching this ideal. To reveal all modes, we…
Acoustic fields scattered by poroelastic materials contain key information about the materials' pore structure and elastic properties. Therefore, such materials are often characterised with inverse methods that use acoustic measurements.…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…
Understanding the mechanical response and failure of solids is of obvious importance in their use as structural materials. The nature of plastic deformation leading to yielding of amorphous solids has been vigorously pursued in recent…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…