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Register a new userVIPER: Volume Invariant Position-based Elastic Rods
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Added by
Baptiste Angles
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We extend the formulation of position-based rods to include elastic volumetric deformations. We achieve this by introducing an additional degree of freedom per vertex -- isotropic scale (and its velocity). Including scale enriches the space of possible deformations, allowing the simulation of volumetric effects, such as a reduction in cross-sectional area when a rod is stretched. We rigorously derive the continuous formulation of its elastic energy potentials, and hence its associated position-based dynamics (PBD) updates to realize this model, enabling the simulation of up to 26000 DOFs at 140 Hz in our GPU implementation. We further show how rods can provide a compact alternative to tetrahedral meshes for the representation of complex muscle deformations, as well as providing a convenient representation for collision detection. This is achieved by modeling a muscle as a bundle of rods, for which we also introduce a technique to automatically convert a muscle surface mesh into a rods-bundle. Finally, we show how rods and/or bundles can be skinned to a surface mesh to drive its deformation, resulting in an alternative to cages for real-time volumetric deformation.
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This paper presents a new curved layer volume decomposition method for multi-axis support-free printing of freeform solid parts. Given a solid model to be printed that is represented as a tetrahedral mesh, we first establish a geodesic distance field embedded on the mesh, whose value at any vertex is the geodesic distance to the base of the model. Next, the model is naturally decomposed into curved layers by interpolating a number of iso-geodesic distance surfaces (IGDSs). These IGDSs morph from bottom-up in an intrinsic and smooth way owing to the nature of geodesics, which will be used as the curved printing layers that are friendly to multi-axis printing. In addition, to cater to the collision-free requirement and to improve the printing efficiency, we also propose a printing sequence optimization algorithm for determining the printing order of the IGDSs, which helps reduce the air-move path length. Ample experiments in both computer simulation and physical printing are performed, and the experimental results confirm the advantages of our method.
We study the elastic response of composites of rods embedded in elastic media. We calculate the micro-mechanical response functions, and bulk elastic constants as functions of rod density. We find two fixed points for Poissons ratio with respect to the addition of rods in 3D composites: there is an unstable fixed point for Poissons ratio=1/2 (an incompressible system) and a stable fixed point for Poissons ratio=1/4 (a compressible system). We also derive an approximate expression for the elastic constants for arbitrary rod density that yields exact results for both low and high density. These results may help to explain recent experiments [Physical Review Letters 102, 188303 (2009)] that reported compressibility for composites of microtubules in F-actin networks.
The automatic shape control of deformable objects is a challenging (and currently hot) manipulation problem due to their high-dimensional geometric features and complex physical properties. In this study, a new methodology to manipulate elastic rods automatically into 2D desired shapes is presented. An efficient vision-based controller that uses a deep autoencoder network is designed to compute a compact representation of the objects infinite-dimensional shape. An online algorithm that approximates the sensorimotor mapping between the robots configuration and the objects shape features is used to deal with the latters (typically unknown) mechanical properties. The proposed approach computes the rods centerline from raw visual data in real-time by introducing an adaptive algorithm on the basis of a self-organizing network. Its effectiveness is thoroughly validated with simulations and experiments.
A recent development, called isogeometric analysis, provides a unified approach for design, analysis and optimization of functional products in industry. Traditional volume rendering methods for inspecting the results from the numerical simulations cannot be applied directly to isogeometric models. We present a novel approach for interactive visualization of isogeometric analysis results, ensuring correct, i.e., pixel-accurate geometry of the volume including its bounding surfaces. The entire OpenGL pipeline is used in a multi-stage algorithm leveraging techniques from surface rendering, order-independent transparency, as well as theory and numerical methods for ordinary differential equations. We showcase the efficiency of our approach on different models relevant to industry, ranging from quality inspection of the parametrization of the geometry, to stress analysis in linear elasticity, to visualization of computational fluid dynamics results.
We report detailed theoretical investigations of the micro-mechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments published in Physical Review Letters [102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rod-like inclusions. We show that the Poissons ratio $ u$ of such a composite evolves with increasing rod density towards a particular value, or {em fixed point}, independent of the material properties of the matrix, so long as it has a finite initial compressibility. This fixed point is $ u=1/4$ in three dimensions and $ u=1/3$ in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites, which have been shown to have highly tunable mechanics.
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