Related papers: Simple deformation measures for Discrete elastic r…
Elastic ribbons, slender structures whose length ($L$), width ($W$), and thickness ($b$) satisfy $L \gg W \gg b$, exhibit mechanical behaviors intermediate between one-dimensional rods ($L \gg W, b$) and two-dimensional plates ($L, W \gg…
This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…
This paper addresses the task of modeling Deformable Linear Objects (DLOs), such as ropes and cables, during dynamic motion over long time horizons. This task presents significant challenges due to the complex dynamics of DLOs. To address…
Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of…
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and discussing topological effects of periodic rods, we prove…
In this paper, we consider rods whose thickness vary linearly between $\eps$ and $\eps^2$. Our aim is to study the asymptotic behavior of these rods in the framework of the linear elasticity. We use a decomposition method of the…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
The variational discrete element method developed in [28] for dynamic elasto-plastic computations is adapted to compute the deformation of elastic Cosserat materials. In addition to cellwise displacement degrees of freedom (dofs), cellwise…
We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
Particle based methods such as the Discrete Element Method and the Lattice Spring Method may be used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction…
We study three-dimensional deformations of thin inextensible elastic rods with non-vanishing spontaneous curvature and torsion. In addition to the usual description in terms of curvature and torsion which considers only the configuration of…
Compression experiments are widely used to study the mechanical properties of materials at micro- and nanoscale. However, the conventional engineering stress measurement method used in these experiments neglects to account for the…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
A novel approach was derived to compute the elastic displacement field from a measured elastic deformation field (i.e., deformation gradient or strain). The method is based on integrating the deformation field using Finite Element…
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…
Experimental analysis of the mechanics of a deformable object, and particularly its stability, requires repetitive testing and, depending on the complexity of the object's shape, a testing setup that can manipulate many degrees of freedom…
The elastic energy functional of a system of discrete dislocation lines is well known from dislocation theory. In this paper we demonstrate how the discrete functional can be used to systematically derive approximations which express the…
We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also…
Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This…