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<p>The explicit integration scheme in the Moving Least Squares Material Point Method (MLS-MPM) is often constrained by small time steps, as larger steps approaching the CFL condition can lead to instability. As a result, traditional explicit MLS-MPM struggles to achieve interactive performance in large-scale simulations. Inspired by recent advancements in position-based MPM (Lewin, A position based material point method. In: ACM SIGGRAPH 2024 Talks, SIGGRAPH ’24. <a href="https://doi.org/10.1145/7663641233.3664323">https://doi.org/10.1145/7663641233.3664323</a>, 2024), we address this limitation by introducing the Affine Projection Stabilizer (APS), a novel technique that enhances the stability of explicit MLS-MPM while preserving visually plausible results. This enhancement is achieved through an XPBD-style affine projection at the particle level, applied across multiple grid-to-particle-to-grid (G2P2G) stages. By leveraging the computational power of modern GPUs, APS-MPM demonstrates a speedup of 2.9 to 3.3 times over GPU-optimized traditional explicit MLS-MPM across a range of large-scale scenarios. This enables interactive simulations of hyperelastic materials with approximately one million material points , paving the way for real-time simulation and interaction in practical applications.</p>

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Enhanced material point method with affine projection stabilizer for efficient hyperelastic simulations

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Cheng Fang,
  • Siyan Zhu,
  • Junjun Pan

摘要

The explicit integration scheme in the Moving Least Squares Material Point Method (MLS-MPM) is often constrained by small time steps, as larger steps approaching the CFL condition can lead to instability. As a result, traditional explicit MLS-MPM struggles to achieve interactive performance in large-scale simulations. Inspired by recent advancements in position-based MPM (Lewin, A position based material point method. In: ACM SIGGRAPH 2024 Talks, SIGGRAPH ’24. https://doi.org/10.1145/7663641233.3664323, 2024), we address this limitation by introducing the Affine Projection Stabilizer (APS), a novel technique that enhances the stability of explicit MLS-MPM while preserving visually plausible results. This enhancement is achieved through an XPBD-style affine projection at the particle level, applied across multiple grid-to-particle-to-grid (G2P2G) stages. By leveraging the computational power of modern GPUs, APS-MPM demonstrates a speedup of 2.9 to 3.3 times over GPU-optimized traditional explicit MLS-MPM across a range of large-scale scenarios. This enables interactive simulations of hyperelastic materials with approximately one million material points , paving the way for real-time simulation and interaction in practical applications.