VeeDynamics is a soft body simulation addon for Blender that integrates a custom solver. It can simulate thin meshes and fine details that are impossible to achieve with default Blender physics tools.
The simulation produced by this addon are extremely stable and they run at near interactive speeds.
The physics solver is non-deterministic, meaning each run of the simulation may produce slightly different results even if the starting parameters are the same.
Like most external simulators, there are some gotchas. In the case of VeeDynamics, the soft bodies cannot be animated directly. However, they can be controlled by assigning parts of the mesh to a vertex group called "V dynamics anim" and using vertex hooks to link them to external objects like empties or bones. For more detailed instructions, please watch the video below.