Projective dynamics with dry frictional contact
Projective dynamics with dry frictional contact
复制标题
干摩擦接触的射影动力学
DOI：
10.1145/3386569.3392396
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Florence Bertails
中科院分区：
文献类型：
--
作者：
Mickaël Ly;J. Jouve;Laurence Boissieux;Florence Bertails
投影动力学在几年前被引入，作为一种快速的方法来产生一个近似的但稳定的解，节点系统的动力学刚性内力。以前尝试将接触力包括在该框架中考虑向全局系统添加二次罚能，然而这打破了全局线性方程的简单常数矩阵结构，同时未能以隐式方式处理接触。在本文中，我们提出了一个简单而有效的方法来整合在一个统一的和半隐式的方式接触以及干摩擦力到嵌套结构的投影动力学。假设接触仅适用于节点，关键是将全局矩阵分裂为对角矩阵和正矩阵，并在局部步骤中使用这种分裂，以便在下一次迭代时对摩擦接触力进行良好的预测。每个摩擦接触力在局部步骤中被独立地细化，而全局步骤的原始有效结构保持不变。我们将我们的算法应用于布料模拟，并表明，接触和干摩擦可以在一个合理的精度内捕获几次迭代，因此一个数量级的速度比全球隐式接触求解器的文献。
Projective dynamics was introduced a few years ago as a fast method to yield an approximate yet stable solution to the dynamics of nodal systems subject to stiff internal forces. Previous attempts to include contact forces in that framework considered adding a quadratic penalty energy to the global system, which however broke the simple - constant matrix - structure of the global linear equation, while failing to treat contact in an implicit manner. In this paper we propose a simple yet effective method to integrate in a unified and semi-implicit way contact as well as dry frictional forces into the nested architecture of Projective dynamics. Assuming that contacts apply to nodes only, the key is to split the global matrix into a diagonal and a positive matrix, and use this splitting in the local step so as to make a good prediction of frictional contact forces at next iteration. Each frictional contact force is refined independently in the local step, while the original efficient structure of the global step is left unchanged. We apply our algorithm to cloth simulation and show that contact and dry friction can be captured at a reasonable precision within a few iterations only, hence one order of magnitude faster compared to global implicit contact solvers of the literature.