Zimmerman Brandon K, Ateshian Gerard A
Department of Mechanical Engineering, Columbia University, New York, NY 10027.
J Biomech Eng. 2018 Aug 1;140(8):0810131-08101315. doi: 10.1115/1.4040497.
This study formulates a finite element algorithm for frictional contact of solid materials, accommodating finite deformation and sliding. The algorithm uses a penalty method regularized with an augmented Lagrangian scheme to enforce contact constraints in a nonmortar surface-to-surface approach. Use of a novel kinematical approach to contact detection and enforcement of frictional constraints allows solution of complex problems previously requiring mortar methods or contact smoothing algorithms. Patch tests are satisfied to a high degree of accuracy with a single-pass penalty method, ensuring formulation errors do not affect the solution. The accuracy of the implementation is verified with Hertzian contact, and illustrations demonstrating the ability to handle large deformations and sliding are presented and validated against prior literature. A biomechanically relevant example addressing finger friction during grasping demonstrates the utility of the proposed algorithm. The algorithm is implemented in the open source software febio, and the source code is made available to the general public.
本研究针对固体材料的摩擦接触制定了一种有限元算法，该算法可适应有限变形和滑动。该算法采用惩罚方法，并通过增广拉格朗日格式进行正则化，以在非 mortar 面到面的方法中强制实施接触约束。使用一种新颖的运动学方法进行接触检测和摩擦约束的实施，使得以前需要 mortar 方法或接触平滑算法才能解决的复杂问题得以解决。单步惩罚方法能高度精确地满足分片检验，确保公式化误差不会影响解。通过赫兹接触验证了该实现的准确性，并给出了说明处理大变形和滑动能力的示例，并与先前文献进行了对比验证。一个与生物力学相关的解决抓握过程中手指摩擦问题的示例展示了所提算法的实用性。该算法在开源软件 FEBio 中实现，并且向公众提供了源代码。
