  We present a new method for real-time physics-based simulation supporting
many different types of hyperelastic materials. Previous methods such as
Position Based or Projective Dynamics are fast, but support only limited
selection of materials; even classical materials such as the Neo-Hookean
elasticity are not supported. Recently, Xu et al. [2015] introduced new
"spline-based materials" which can be easily controlled by artists to achieve
desired animation effects. Simulation of these types of materials currently
relies on Newton's method, which is slow, even with only one iteration per
timestep. In this paper, we show that Projective Dynamics can be interpreted as
a quasi-Newton method. This insight enables very efficient simulation of a
large class of hyperelastic materials, including the Neo-Hookean, spline-based
materials, and others. The quasi-Newton interpretation also allows us to
leverage ideas from numerical optimization. In particular, we show that our
solver can be further accelerated using L-BFGS updates (Limited-memory
Broyden-Fletcher-Goldfarb-Shanno algorithm). Our final method is typically more
than 10 times faster than one iteration of Newton's method without compromising
quality. In fact, our result is often more accurate than the result obtained
with one iteration of Newton's method. Our method is also easier to implement,
implying reduced software development costs.
