Related papers: Geometric approach to mechanical design principles…
In this paper we focus on the mechanical properties of oligomeric glasses (waxes), employing a microscopic model that provides, via numerical simulations, information about the shear modulus of such materials, the failure mechanism via…
High speed machining has been improved thanks to considerable advancement on the tools (optimum geometry, harder materials), on machined materials (increased workability and machining capacity for harder workpieces) and finally on the…
We report a method for describing plasticity in a broad class of amorphous materials. The method is based on nonlinear (geometric) deformation theory allowing the separation of the plastic deformation from the general deformation tensor.…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to…
Mechanical extremal materials, a class of metamaterials that exist at the bounds of elastic theory, possess the extraordinary capability to engineer any desired elastic behavior by harnessing mechanical zero modes -- deformation modes that…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into non-trivial shapes with…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
We review the recent literature on the simulation of the structure and deformation of amorphous glasses, including oxide and metallic glasses. We consider simulations at different length and time scales. At the nanometer scale, we review…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…
The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…
We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
Mechanical cloaks are materials engineered to manipulate the elastic response around objects to make them indistinguishable from their homogeneous surroundings. Typically, methods based on material-parameter transformations are used to…
In this letter, we investigate the geometrically tailorable elasticity in the twisting behavior of biomimetic scale-covered slender soft substrate. Motivated by our qualitative experiments showing a significant torsional rigidity increase,…