We introduce a new framework for simulating the dynamics of musculoskeletal systems, with volumetric muscles in close contact and a novel data-driven muscle activation model. Muscles are simulated using an Eulerian-on-Lagrangian discretization that handles volume preservation, large deformation, and close contact between adjacent tissues. Volume preservation is crucial for accurately capturing the dynamics of muscles and other biological tissues. We show how to couple the dynamics of soft tissues with Lagrangian multi-body dynamics simulators, which are widely available. Our physiologically based muscle activation model utilizes knowledge of the active shapes of muscles, which can be easily obtained from medical imaging data or designed to meet artistic needs. We demonstrate results with models derived from MRI data and models designed for artistic effect.

We describe an Eulerian-on-Lagrangian solid simulator that reduces or eliminates many of the problems experienced by fully Eulerian methods but retains their advantages. Our method does not require the construction of an explicit object discretization and the fixed nature of the simulation mesh avoids tangling during large deformations. By introducing Lagrangian modes to the simulation we enable unbounded simulation domains and reduce the time-step restrictions which can plague Eulerian simulations. Our method features a new solver that can resolve contact between multiple objects while simultaneously distributing motion between the Lagrangian and Eulerian modes in a least-squares fashion. Our method successfully bridges the gap between Lagrangian and Eulerian simulation methodologies without having to abandon either one.

Simulating viscoelastic solids undergoing large, nonlinear deformations in close contact is challenging. In addition to inter-object contact, methods relying on Lagrangian discretizations must handle degenerate cases by explicitly remeshing or resampling the object. Eulerian methods, which discretize space itself, provide an interesting alternative due to the fixed nature of the discretization. In this paper we present a new Eulerian method for viscoelastic materials that features a collision detection and resolution scheme which does not require explicit surface tracking to achieve accurate collision response. Time-stepping with contact is performed by the efficient solution of large sparse quadratic programs; this avoids constraint sticking and other difficulties. Simulation and collision processing can share the same uniform grid, making the algorithm easy to parallelize. We demonstrate an implementation of all the steps of the algorithm on the GPU. The method is effective for simulation of complicated contact scenarios involving multiple highly deformable objects, and can directly simulate volumetric models obtained from medical imaging techniques such as CT and MRI.