Jernej Barbic

Real-time large-deformation solid mechanics using model reduction

Abstract:
I will talk about my PhD thesis work (at Carnegie Mellon University)
on model reduction for solid mechanics. In computer graphics, we often
want to simulate deformations of geometrically complex meshes at
real-time rates, such as, for example, to model human tissue in a
surgery simulator, or a deformable bridge in a computer game.

In our work, we apply model reduction on large-deformation Finite
Element Method deformable models of solid mechanics (geometrically
nonlinear models (quadratic Green strain) with a linear stress-strain
relationship). Each mesh vertex of a general 3D deformable object has
three degrees of freedom. Non-interactive computation times result
when simulating large-deformation dynamics of such \emph{unreduced}
systems (assuming non-trivial geometry). \emph{Reduced} deformable
objects are obtained by substituting these general degrees of freedom
for a much smaller appropriately defined set of reduced degrees of
freedom. This dimensionality reduction  enables much faster simulation
times, with some loss of simulation accuracy.

The reduced deformable degrees of freedom need to be defined carefully
so that they support ``typical'' large deformations. We present two
useful approaches for generating low-dimensional simulation subspaces:
modal derivatives and an interactive sketching technique. Mass-scaled
principal component analysis (mass-PCA) is suggested for
dimensionality reduction.

Model reduction of geometrically nonlinear deformable objects results
in reduced internal forces with an exact analytical formula: these
forces are simply cubic polynomials in reduced coordinates.
Coefficients of these polynomials can be precomputed, for efficient
runtime evaluation. This allows real-time simulation of nonlinear
dynamics with integration costs independent of geometric complexity.
Joint work with Prof Doug L. James (now at Cornell Univ).