This work presents a numerical method for the solution of variational inequalities arising in nonsmooth flexible multibody problems that involve set-valued forces. For the special case of hard frictional contacts, the method solves a second order cone complementarity problem. We ground our algorithm on the Alternating Direction Method of Multipliers (ADMM), an efficient and robust optimization method that draws on few computational primitives. In order to improve computational performance, we reformulated the original ADMM scheme in order to exploit the sparsity of constraint jacobians and we added optimizations such as warm starting and adaptive step scaling. The proposed method can be used in scenarios that pose major difficulties to other methods available in literature for complementarity in contact dynamics, namely when using very stiff finite elements and when simulating articulated mechanisms with odd mass ratios. The method can have applications in the fields of robotics, vehicle dynamics, virtual reality, and multiphysics simulation in general.

中文翻译：

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用乘法器交替方向法求解非光滑动力学中的变分不等式和锥互补问题

这项工作提出了一种数值方法，用于求解涉及定值力的非光滑柔性多体问题中出现的变分不等式。对于硬摩擦接触的特殊情况，该方法解决了二阶锥互补问题。我们的算法基于乘法器交替方向法 (ADMM)，这是一种利用少量计算原语的高效且稳健的优化方法。为了提高计算性能，我们重新制定了原始的 ADMM 方案以利用约束雅可比的稀疏性，并添加了优化，例如热启动和自适应步进缩放。所提出的方法可用于对文献中可用的其他方法构成重大困难的场景，以实现接触动力学的互补性，即当使用非常僵硬的有限元和模拟具有奇数质量比的铰接机构时。该方法可广泛应用于机器人、车辆动力学、虚拟现实和多物理场仿真等领域。