@techreport{TR-IC-97-12,
number = {IC-97-12},
author = {Liesenfeld, RogĂ©rio L. W. and Stolfi, Jorge},
title = {Realistic Simulation of Viscoelastic Bodies},
month = {September},
year = {1997},
institution = {Institute of Computing, University of Campinas},
note = {In English, 22 pages.
\par\selectlanguage{english}\textbf{Abstract}
We describe an animation system that simulates the dynamics of
viscoelastic bodies subject to equality and inequality constraints.
We show how Lagrange's method can be used to derive the equations of
motion of such bodies from general formulas for the elastic and
kinetic energy, the viscous power loss, and mechanical constraints, in
terms of generalized coordinates.
\par
We also describe a convenient two-parameter non-linear model for the
elastic forces, that agrees with Hooke's law for small deformations,
but does not allow the material to be compressed to zero or negative
volume. In particular, we derive the equations of motion for elastic
bodies modeled by tetrahedral finite elements with affine deformations.
Finally, we show
how collisions between such bodies can be efficiently and accurately
detected by combining Hermite interpolation of the non-penetration
constraints with Lin and Manocha's bounding box tests.
}
}