The numerical performance of the material point method (MPM) is strongly governed by the particle-grid kernel, which controls the trade-off among smoothness, locality, numerical diffusion, contact accuracy, and computational cost. Although wide-support smooth kernels can effectively suppress cell-crossing instability, they often introduce increased numerical diffusion, artificial contact gaps, and higher transfer cost. In contrast, the suitability of compact-kernel designs for implicit computational solid mechanics remains unclear. In this work, we develop an implicit formulation of the Compact-Kernel Material Point Method (CK-MPM) and assess its performance through benchmark problems in linear and nonlinear solid mechanics, including cantilever bending, Hertzian contact, narrow-clearance free fall, and colliding hyperelastic rings. The results show that implicit CK-MPM retains the advantages of compact support while preserving the smoothness required for robust large-deformation simulation. Compared with linear MPM, it reduces cell-crossing-induced stress noise and excessive numerical dissipation; compared with quadratic B-spline MPM, it improves contact locality and reduces artificial contact gaps and early-contact artifacts while maintaining comparable overall smoothness and accuracy. These results indicate that CK-MPM provides a viable implicit MPM framework for computational mechanics.

翻译：物质点法的数值性能在很大程度上受粒子-网格核函数的影响，该核函数控制着光滑性、局部性、数值耗散、接触精度与计算成本之间的权衡。尽管大支撑光滑核能有效抑制跨单元不稳定性，但往往引入增大的数值耗散、人工接触间隙及更高的传递成本。相比之下，紧致核设计在隐式计算固体力学中的适用性仍不明确。本研究构建了紧致核物质点法的隐式格式，并通过线性和非线性固体力学中的基准问题评估其性能，包括悬臂梁弯曲、赫兹接触、窄间隙自由落体及碰撞超弹性环。结果表明，隐式紧致核物质点法在保持紧致支撑优势的同时，保留了鲁棒大变形模拟所需的光滑性。与线性物质点法相比，它降低了跨单元引起的应力噪声和过度的数值耗散；与二次B样条物质点法相比，它在保持相当的整体光滑性和精度的同时，改善了接触局部性，减少了人工接触间隙和早期接触伪影。这些结果表明，紧致核物质点法为计算力学提供了一种可行的隐式物质点法框架。