Discrete viscous sheets

Abstract

Figure 1: A thin sheet of molten chocolate enrobes a spherical truffle. As viscous sheets deform they exhibit behaviors that combine both the fluidity of liquids, and the buckling and wrinkling instabilities of thin materials, as evidenced here in the beautiful spindly legs. AbstractWe present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the Stokes-Rayleigh analogy to derive a simple yet consistent model for viscous forces. We incorporate nonlinear surface tension forces with a formulation based on minimizing discrete surface area, and preserve the quality of triangular mesh elements through local remeshing operations. Simultaneously, we track and evolve the thickness of each triangle to exactly conserve liquid volume. This approach enables the simulation of extremely thin sheets of viscous liquids, which are difficult to animate with existing volumetric approaches. We demonstrate our method with examples of several characteristic viscous sheet behaviors, including stretching, buckling, sagging, and wrinkling.

Data-driven synthesis of smoke flows with CNN-based feature descriptors

“…Several works have also investigated viscosity for uid animations, e.g., by proposing stable and accurate methods for discretization [Batty and Bridson 2008], e cient representations of viscous sheets [Batty et al 2012], or illustrating the importance of viscosity for resolving shear ows near obstacles in the ow [Zhang et al 2016]. While these are highly interesting extensions, most practical uid solvers for computer animation omit solving for viscosity in order to reduce the computational work.…”

“…In the following, we choose neural networks (NNs) to represent f , for which a thorough overview can be found, e.g., in the book by C. Bishop [Bishop 2007].…”

“…This makes them considerably more di cult to train, while convolutional networks lead to very reasonable network sizes and training times, making them very attractive in practice. Smaller networks also have greatly reduced requirements for the amounts of input data, and can be bene cial for regularization [Bishop 2007].…”

Crustal failure on icy Moons from a strong tidal encounter

“…with LS the length of an edge and DF equal to the flexural rigidity or bending stiffness of the plate (e.g., Batty et al 2012). This is approximate as simulated static load tests have not been carried out with the membrane/hinge model (though simulated static beam tests have been done for the lattice and random spring models, see Kot et al 2015).…”

Texture Mapping Real‐World Objects with Hydrographics

“…Water transfer printing involves a solid object interacting with a viscous polymer film floating on water. In that sense, our work is related to studies of thin viscous materials (e.g., [BUAG12]), solid-fluid interaction (e.g., [BBB07]) and water (e.g., [EB14]). These works consider these three elements in isolation or in pairs, and it is unclear how they could be combined to model the water transfer process in its entirety.…”