1. This paper presents a semi-implicit cloth simulation technique that is very stable yet also responsive.

2. Challenges and solutions
2.1 Cloth is characterized by strong resistance to stretch and weak resistance to bending, which leads to a stiff set of equations and thus prohibits the use of large time steps. 

Solution: Implicit methods can solve this problem well.

2.2 It is crucial for the fabrics in motion to have buckling behavior. The buckling of a thin material involves a very unstable state, regardless of whether it is rigid or flexible. The instability of the post-buckling response arises from a structural instability, not from the stiff equations. The damping forces help to stabilize the physical system, but they can significantly degrade the realism of the simulated cloth movement.

Solution 1: Although artificial damping is expected to be partially responsible for the degradation of the quality of the out-of-plane movement of the cloth, the degradation in the quality arises mainly from fictitious damping. The system proposed in this paper includes artificial damping and material intrinsic damping, but does not include fictitious damping. The need for fictitious damping is avoided through the use of the predicted static post-buckling response as an effective way to handle the instabilities associated with post-buckling situations. Because fictitious damping is not used, this method gives significantly more realistic cloth motion.

Solution 2: Instead of physically simulating the unstable post-buckling dynamic response, the instability problem is solved by calculating the deformation energy of the shape at the predicted static equilibrium of the post-buckling state. The numerical instability caused by stiff equations is solved by using implicit time stepping. Using the physical model outlined above and implicit time stepping, we could stably integrate the equation of motion with a large fixed time step and without the need for fictitious damping forces.