Heating and melting deformable models

Abstract

We develop physically‐based graphics models of non‐rigid objects capable of heat conduction, thermoelasticity, melting and fluid‐like behaviour in the molten state. These deformable models feature non‐rigid dynamics governed by Lagrangian equations of motion and conductive heat transfer governed by the heat equation for non‐homogeneous, non‐isotropic media. In its solid state, the discretized model is an assembly of hexahedral finite elements in which thermoelastic units interconnect particles situated in a lattice. The stiffness of a thermoelastic unit decreases as its temperature increases, and the unit fuses when its temperature exceeds the melting point. The molten state of the model involves a molecular dynamics simulation in which ‘fluid’ particles that have broken free from the lattice interact through long‐range attraction forces and short‐range repulsion forces. We present a physically‐based animation of a thermoelastic model in a simulated physical world populated by hot constraint surfaces.

Practical Animation of Liquids

“…Terzopoulos, Platt and Fleischer [27] simulated melting deformable solids using a molecular dynamics approach to simulate the particles in the liquid phase.…”

Particle-based simulation and visualization of fluid flows through porous media

“…Miller and Pearce (1989) utilize pairwise particle interactions to model viscous fluids. Terzopoulos et al (1991) model melting objects with interacting particles connected by springs whose constants are modified as the object changes its phase. Tonnesen (1991) incorporates a discrete form of heat transfer equation into inter-particle force equations to simulate change in particle positions due to thermal energy.…”

Animation and rendering of complex water surfaces

“…A viscous spring particle representation of a liquid has been proposed by [Miller and Pearce 1989]. An alternative molecular dynamics approach to the simulation of particles in the liquid phase has been developed by [Terzopoulos et al 1989]. Particle methods, while quite versatile, can pose difficulties when trying to reconstruct a smooth water surface from the locations of the particles alone.…”