implement material point method

This work proposes a novel topology optimization framework that integrates the implicit Material Point Method (MPM) to address numerical instabilities arising from mesh distortion and large rotations in large-deformation problems. For the first time, MPM is incorporated into topology optimization within an end-to-end differentiable pipeline, leveraging automatic differentiation and hyperelastic constitutive models to enable stable and efficient quasi-static optimization of structures undergoing finite deformations. The approach naturally supports both single- and multi-material designs and demonstrates robust performance on complex geometries, including soft robotic grippers. By circumventing the limitations of traditional finite element–based methods, the proposed framework significantly enhances the robustness and applicability of topology optimization in highly nonlinear deformation regimes.

This work addresses the challenge of efficient weak coupling between the Material Point Method (MPM) and rigid-body dynamics under frictional contact. We propose the first asynchronous time-splitting convex optimization framework: contact mechanics is convexified to enable asynchronous integration of MPM and rigid-body subsystems; a globally convergent parallel quasi-Newton solver is designed and GPU-accelerated (500× faster than CPU execution); and we release the first open-source, interactive MPM–rigid-body coupled simulator integrated into Drake. Our method achieves stable real-time performance (>30 FPS) in robotic manipulation scenarios—such as granular and fabric handling—while delivering significantly higher accuracy and robustness compared to state-of-the-art MPM simulators. This establishes a scalable, high-fidelity paradigm for real-time simulation of deformable objects.

This work addresses the limited accuracy and robustness in modeling frictional contact within the Material Point Method (MPM) by proposing a unified solver framework for implicit MPM. The approach precisely locates contact points using particle-centered geometric primitives and formulates frictional contact—including impenetrability, Coulomb friction, and the principle of maximum dissipation—as a nonlinear complementarity problem (NCP) in terms of contact impulses. An ADMM-based algorithm is employed for efficient solution. Notably, this is the first method to cast frictional contact uniformly as an NCP and embed it within implicit MPM while reusing its linearized structure. The framework demonstrates high-precision contact localization, reliable friction handling, and broad applicability across seven diverse scenarios involving elastic and elastoplastic materials, complex geometries, and varied contact conditions.

This work addresses the computational inefficiency of the material point method (MPM) in problems involving strong local deformation, contact, and large geometric nonlinearities by proposing a spacetime adaptive refinement framework based on the overlapping Schwarz method. The computational domain is partitioned into overlapping coarse and fine subdomains with heterogeneous spacetime discretizations, and subdomain coupling is achieved through mass-weighted spatial prolongation and temporal subcycling interpolation—without modifying basis functions or imposing interfacial constraints, thereby preserving the modularity of standard MPM. Crucially, the coupling complexity is shifted to non-matching interface operators within the Schwarz iterations. Numerical experiments demonstrate that the proposed approach reproduces high-fidelity reference solutions in both two- and three-dimensional cases, achieving up to a 9.15× reduction in computational cost while maintaining error levels comparable to or better than those of fully refined meshes.

Reconstructing high-quality, manifold, and feature-preserving triangular meshes from unstructured point clouds remains challenging. Method: This paper proposes an isotropic reconstruction method based on unit-sphere covering. It systematically models local point cloud geometry using spherical covering theory, rigorously derives parameter bounds to theoretically guarantee manifold output, and jointly optimizes geometric uniformity (edge-length and angle distributions) and topological correctness. The approach integrates geometric approximation analysis, adaptive neighborhood graph construction, and Delaunay-type triangulation optimization, supporting feature detection and multi-patch remeshing. Results: Experiments show that our method reduces edge-length and angle standard deviations by ~35% compared to Poisson surface reconstruction and Ball-Pivoting, while decreasing average runtime by 45% (1.8× speedup). Under reasonable sampling conditions, the resulting mesh is provably manifold.

This work proposes an implicit compact-kernel material point method (CK-MPM) that integrates implicit time integration with compactly supported kernel functions to simultaneously achieve smoothness, locality, low numerical dissipation, and high contact accuracy in large-deformation solid mechanics. Traditional material point methods struggle to balance these competing requirements, and the suitability of compact kernels within implicit frameworks has remained unclear. The proposed CK-MPM preserves locality while fulfilling the smoothness necessary for robust large-deformation simulations. This study presents the first validation of compact kernels in an implicit setting, demonstrating significantly reduced stress noise and numerical dissipation. Compared to quadratic B-spline MPM, CK-MPM enhances contact locality, eliminates artificial gaps and premature contact artifacts, and maintains comparable accuracy and computational efficiency.

This work addresses the inefficiency of the standard Material Point Method (MPM) in large-scale simulations where material occupies only a small fraction of the computational domain, due to its reliance on dense background grids. The authors propose a unified sparse background grid framework that formulates sparsity as a general active-node indexing problem and introduces tailored, high-performance implementations for both CPU and GPU architectures—based on scan and hash-based strategies, respectively. This approach maintains simulation accuracy while dramatically improving computational and memory efficiency in sparse scenarios. Under strong sparsity conditions, it reduces both runtime and memory consumption by one to two orders of magnitude compared to conventional dense MPM, with excellent consistency in results.

This work addresses the compatibility and stability challenges that arise when coupling the approximate full mass matrix method (FMPM(k)) with lumped-mass-dependent Material Point Method (MPM) features—such as velocity boundary conditions and multi-material contact. To resolve these issues, the authors propose a reformulated FMPM(k) implementation that streamlines the FMPM loop to execute only once per time step and adapts the algorithm to seamlessly integrate with standard MPM functionalities. This study presents the first successful integration of FMPM(k) with lumped-mass-dependent MPM capabilities, while systematically analyzing the influence of the polynomial order \(k\) on time-step stability and computational efficiency. The proposed approach significantly enhances the applicability and performance of high-order FMPM(k) in complex multiphysics simulations.

This study addresses the computational inefficiency of simulating large-deformation flexible multibody systems at high resolution by proposing an efficient GPU-accelerated framework within a total Lagrangian finite element setting. The approach integrates implicit backward Euler time integration with the augmented Lagrangian method to enforce constraints. Key contributions include a two-stage GPU parallelization strategy for accelerating internal force and tangent stiffness computations, an asynchronous collision detection algorithm that avoids bounding volume hierarchies, and a fixed sparsity pattern strategy to enhance Newton solver efficiency. The system incorporates T10 tetrahedral elements, ANCF beam and shell formulations, hyperelastic constitutive models, and Kelvin–Voigt viscoelasticity, leveraging cuDSS for sparse Hessian assembly and factorization. Experiments demonstrate nearly an order-of-magnitude real-time speedup over CPU baselines at the highest tested resolution, while frictional contact scenarios confirm model accuracy.

本文提出一种基于简化算法的变形控制点计算方法，通过迭代代数简化优化控制点以匹配输入变形，实现高效实时弹性动力学模拟。