标题： 基于中平面的三维单向无偏段到段接触相互作用的惩罚法 显示英文标题

标题： Midplane based 3D single pass unbiased segment-to-segment contact interaction using penalty method

摘要： 本文提出了一种接触相互作用方法，用于无偏处理接触表面，而无需指定主从表面。在单次迭代中，通过中平面评估相互作用离散段之间的接触力，从而内在地维持力的平衡。这些接触力基于相反表面之间真实穿透的惩罚，并且本文描述了离散接触段的积分程序。为了发展对相互作用三维段的不同几何配置的直观理解并提高接触力评估的准确性，详细分析了这些可能的几何配置。所提出的方法的准确性和鲁棒性通过接触补丁测试、两梁弯曲、赫兹接触和刚性压头测试的解析解得到验证，从而证明了其再现平面表面、曲面以及接触尖角之间接触的能力。该方法在接触压力均匀传递的情况下通过了接触补丁测试，并且其精度达到了有限元的水平。随着网格细化和适当高的惩罚因子，该方法收敛于解析解。所提出的算法的有效性还扩展到了自接触问题，并且已经针对具有非弹性的平坦和曲面之间的自接触进行了测试。此外，还展示了杆弹性碰撞和非弹性碰撞以及圆柱体斜碰撞的动力学问题。该算法能够以高精度解决非共形网格中平面与曲面之间的接触，表明其在通用接触问题中的多功能性。 显示英文摘要

摘要： This work introduces a contact interaction methodology for an unbiased treatment of contacting surfaces without assigning surfaces as master and slave. The contact tractions between interacting discrete segments are evaluated with respect to a midplane in a single pass, inherently maintaining the equilibrium of tractions. These tractions are based on the penalisation of true interpenetration between opposite surfaces, and the procedure of their integral for discrete contacting segments is described in this paper. A meticulous examination of the different possible geometric configurations of interacting 3D segments is presented to develop visual understanding and better traction evaluation accuracy. The accuracy and robustness of the proposed method are validated against the analytical solutions of the contact patch test, two-beam bending, Hertzian contact, and flat punch test, thus proving the capability to reproduce contact between flat surfaces, curved surfaces, and sharp corners in contact, respectively. The method passes the contact patch test with the uniform transmission of contact pressure matching the accuracy levels of finite elements. It converges towards the analytical solution with mesh refinement and a suitably high penalty factor. The effectiveness of the proposed algorithm also extends to self-contact problems and has been tested for self-contact between flat and curved surfaces with inelastic material. Dynamic problems of elastic and inelastic collisions between bars, as well as oblique collisions of cylinders, are also presented. The ability of the algorithm to resolve contacts between flat and curved surfaces for nonconformal meshes with high accuracy demonstrates its versatility in general contact problems.