标题： 一种用于大变形分析的动态隐式三维材料点与刚体接触方法 显示英文标题

标题： A dynamic implicit 3D material point-to-rigid body contact approach for large deformation analysis

摘要： 准确且稳健的大变形三维接触相互作用建模是工程领域的一个重要方面，但从计算力学的角度来看，它也具有挑战性。 当存在显著的穿透和接触表面演变时，例如相对刚性体与高度可变形体之间的相互作用情况，这种情况尤为明显。 数值挑战来自几个非线性来源：大变形力学、历史依赖材料行为以及滑动/粘着摩擦接触。 在本文中，采用物质点法（MPM）来表示可变形材料，并结合离散化的刚体，以提供接触表面的精确表示。 通过使用与每个物质点相关的域来检测物体之间的三维相互作用。 这提供了一种通用且一致的可变形体范围表示方法，而无需在物质点法中引入边界表示。 动态控制方程允许刚体的轨迹根据与可变形体的相互作用进行演化，并在高效的隐式框架内求解控制方程。 该方法在多个具有解析解的基准问题上进行了验证。 该方法还应用于土-结构相互作用的特定情况，使用地质技术离心机实验数据，证实了所提出方法的正确性。 显示英文摘要

摘要： Accurate and robust modelling of large deformation three dimensional contact interaction is an important area of engineering, but it is also challenging from a computational mechanics perspective. This is particularly the case when there is significant interpenetration and evolution of the contact surfaces, such as the case of a relatively rigid body interacting with a highly deformable body. The numerical challenges come from several non-linear sources: large deformation mechanics, history dependent material behaviour and slip/stick frictional contact. In this paper the Material Point Method (MPM) is adopted to represent the deformable material, combined with a discretised rigid body which provides an accurate representation of the contact surface. The three dimensional interaction between the bodies is detected though the use of domains associated with each material point. This provides a general and consistent representation of the extent of the deformable body without introducing boundary representation in the material point method. The dynamic governing equations allows the trajectory of the rigid body to evolve based on the interaction with the deformable body and the governing equations are solved within an efficient implicit framework. The performance of the method is demonstrated on a number of benchmark problems with analytical solutions. The method is also applied to the specific case of soil-structure interaction, using geotechnical centrifuge experimental data that confirms the veracity of the proposed approach.