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A mortar segment-to-segment frictional contact approach in material point method
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2024-08-20 , DOI: 10.1016/j.cma.2024.117294
Weijian Liang , Huangcheng Fang , Zhen-Yu Yin , Jidong Zhao
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2024-08-20 , DOI: 10.1016/j.cma.2024.117294
Weijian Liang , Huangcheng Fang , Zhen-Yu Yin , Jidong Zhao
Handling contact problems in the Material Point Method (MPM) has long been a challenge. Traditional grid-based contact approaches often face issues with mesh dependency, while material point-based methods can be computationally intensive. To address these challenges, this study develops a novel mortar segment-to-segment frictional contact approach for MPM. We first introduce boundary vertices and propose an innovative kinematic update scheme for precise representation of the boundaries of the continuum media and their continuously evolving contact normals throughout the contact process. Then, we construct a weak form of contact constraints based on the mortar method to facilitate a stable segment-to-segment contact detection. To rigorously ensure the non-penetration condition, the energetic barrier method is further adopted and implemented in MPM for enforcing the contact constraints. The proposed kinematic update scheme for boundary vertices is first verified through a cantilever beam benchmark test. The verified framework is further examined through a wide range of contact scenarios, including rolling, sliding, collision of two rings, and multi-body contacts, in both small and finite deformations. The simulation results are thoroughly discussed, highlighting the significant improvements in accuracy and versatility. Potential limitations of the proposed method are also examined.
中文翻译:
质点法中砂浆段与段之间的摩擦接触方法
处理质点法 (MPM) 中的接触问题长期以来一直是一个挑战。传统的基于网格的接触方法通常面临网格依赖性问题,而基于材料点的方法可能需要大量计算。为了应对这些挑战,本研究开发了一种新型的 MPM 砂浆段到段摩擦接触方法。我们首先引入边界顶点,并提出一种创新的运动学更新方案,用于精确表示连续介质的边界及其在整个接触过程中不断变化的接触法线。然后,我们基于迫击炮方法构造了一种弱形式的接触约束,以促进稳定的段与段接触检测。为了严格保证非穿透条件,MPM 中进一步采用和实施能量势垒方法来强制接触约束。所提出的边界顶点运动学更新方案首先通过悬臂梁基准测试进行验证。经过验证的框架通过各种接触场景进行了进一步检查,包括滚动、滑动、两个环的碰撞以及小变形和有限变形下的多体接触。对模拟结果进行了深入讨论,强调了准确性和多功能性方面的显着改进。还检查了所提出方法的潜在局限性。
更新日期:2024-08-20
中文翻译:
质点法中砂浆段与段之间的摩擦接触方法
处理质点法 (MPM) 中的接触问题长期以来一直是一个挑战。传统的基于网格的接触方法通常面临网格依赖性问题,而基于材料点的方法可能需要大量计算。为了应对这些挑战,本研究开发了一种新型的 MPM 砂浆段到段摩擦接触方法。我们首先引入边界顶点,并提出一种创新的运动学更新方案,用于精确表示连续介质的边界及其在整个接触过程中不断变化的接触法线。然后,我们基于迫击炮方法构造了一种弱形式的接触约束,以促进稳定的段与段接触检测。为了严格保证非穿透条件,MPM 中进一步采用和实施能量势垒方法来强制接触约束。所提出的边界顶点运动学更新方案首先通过悬臂梁基准测试进行验证。经过验证的框架通过各种接触场景进行了进一步检查,包括滚动、滑动、两个环的碰撞以及小变形和有限变形下的多体接触。对模拟结果进行了深入讨论,强调了准确性和多功能性方面的显着改进。还检查了所提出方法的潜在局限性。