Fast But Accurate: A Real-Time Hyperelastic Simulator with Robust Frictional Contact

TL;DR

This work tackles real-time implicit simulation of hyperelastic materials under frictional contact by integrating nonlinear complementarity conditions into a local-global solver. It introduces a sparse inverse approach that precomputes a representation of the system inverse as ${f A}^{-1} = {f S}^T {f S}$ to enable highly parallel global steps and two SpMV operations per iteration. A splitting strategy for non-smooth indicators reduces Schur-complement computations, while a non-smooth Newton method and a carefully designed complementarity preconditioner (based on the delasus operator ${f W}$) ensure accurate frictional behavior within the L-G framework. The resulting GPU-friendly pipeline demonstrates robust performance across large-scale, highly deformable, and contact-rich scenarios, including large stiffness and codimensional contacts, with real-time frame rates on commodity hardware. Overall, the method offers a simple core reliant on standard sparse matrix operations while delivering high accuracy and scalability for problems in computer graphics, robotics, and related fields.

Abstract

We present a GPU-friendly framework for real-time implicit simulation of elastic material in the presence of frictional contacts. The integration of hyperelasticity, non-interpenetration contact, and friction in real-time simulations presents formidable nonlinear and non-smooth problems, which are highly challenging to solve. By incorporating nonlinear complementarity conditions within the local-global framework, we achieve rapid convergence in addressing these challenges. While the structure of local-global methods is not fully GPU-friendly, our proposal of a simple yet efficient solver with sparse presentation of the system inverse enables highly parallel computing while maintaining a fast convergence rate. Moreover, our novel splitting strategy for non-smooth indicators not only amplifies overall performance but also refines the complementarity preconditioner, enhancing the accuracy of frictional behavior modeling. Through extensive experimentation, the robustness of our framework in managing real-time contact scenarios, ranging from large-scale systems and extreme deformations to non-smooth contacts and precise friction interactions, has been validated. Compatible with a wide range of hyperelastic models, our approach maintains efficiency across both low and high stiffness materials. Despite its remarkable efficiency, robustness, and generality, our method is elegantly simple, with its core contributions grounded solely on standard matrix operations.

Figures (10)

• Figure 1: Grabbing Raptor: stable catching of an elastic raptor with a soft gripper actuated by cables. Lifting, rotating, and moving the raptor by the fingers are complex operations where friction constraints are necessary.
• Figure 2: Pulling Wooper: a moving positional constraint is applied on the tail of the wooper, pulling it through the thin gap between two cylinders.
• Figure 3: Sparse solution: after reducing the matrix pattern fill-in through nested dissection, the Cholesky factor ${\mathbf{L}}$ is reordered and partitioned into sub-blocks. For a given column $k$ in the identity matrix ${\mathbf{I}}$, the requisite structure to be processed in ${\mathbf{L}}$ consists of $k$ and its ancestors (red nodes) in the elimination tree.
• Figure 4: Squeezing Ball: the rolling cylinders strongly squeeze the soft ball, thereby generating large frictional forces (with $\mu = 0.5$) that drive the ball through the gaps.
• Figure 5: Sharp Corner: stable simulation of cloth mesh on sharp corner obstacle, with rich and non-smooth contacts.

Theorems & Definitions (1)

• Theorem 1