Related papers: Periodic auxetics: Structure and design
The flowing, jamming and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: a granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular…
The architecture of mechanical metamaterialsis designed to harness geometry, non-linearity and topology to obtain advanced functionalities such as shape morphing, programmability and one-way propagation. While a purely geometric framework…
The last decade has seen major progresses in studies of elementary mechanisms of deformation in amorphous materials. Here, we start with a review of physically-based theories of plasticity, going back to the identification of…
The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…
The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Though the nonlinear regime holds promise for new functionality, the design in this…
The structural complexity of metamaterials is limitless, although in practice, most designs comprise periodic architectures which lead to materials with spatially homogeneous features. More advanced tasks, arising in e.g. soft robotics,…
We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…
Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…
In this paper we study the asymptotic behavior of a structure made of curved rods of thickness 2\delta when \delta rightarrow 0. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on…
There are a variety of industrial products that possess periodic textures or surfaces, such as carbon fiber textiles and display panels. Traditional image-based quality inspection methods for these products require identifying the periodic…
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
Heterogeneous materials exhibit anisotropy which is influenced by factors such as individual phase properties and microstructural configuration that form crucial descriptors of heterogeneity. A review of anisotropy indices proposed in the…
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which…
Soft electronics have recently gathered considerable interest thanks to their bio-mechanical compatibility. An important feature of such deformable conductors is their electrical response to strain. While development of stretchable…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
A new model for elucidating the mathematical foundation of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts in addition to elementary hypotheses based on well-established…
Negative Poisson's ratio as the anomalous characteristic generally exists in artificial architectures, such as re-entrant and honeycomb structures. The structures with negative Poisson's ratio have attracted intensive attention due to their…
Although recent developments in 3D printing technology have made it possible to fabricate metamaterials with characteristic mechanical properties, it is not easy to fabricate complex shapes containing cavities. In this study, a composite…
Models of smectic-C liquid crystal elastomers predict that it can display soft elasticity, in which the shape of the elastomer changes at no energy cost. The amplitude of the soft mode and the accompanying shears are dependent on the…