This paper presents a new contact boundary condition for finite volume simulations of frictional contact problems involving geometrical and material non-linearities. Deformation of bodies in contact is described by the updated Lagrangian form of the momentum equation which is discretised in space using the cell-centred finite volume method. The proposed contact boundary condition is based on the finite volume implementation of the penalty based segment-to-segment contact force calculation method in which normal contact pressure, governed by a penalty law, is integrated across the discretised contact surface, enforcing contact constraints in an integral manner. Such an approach, as opposed to the pointwise contact force calculation algorithm, allows for more accurate and more robust treatment of the contact area edge, simultaneous calculation of contact forces on both contact surfaces as well as smoother contact force during large sliding. The proposed numerical method is tested on challenging mechanical contact problems showing very good agreement with the available benchmark results.

本文提出了一种新的接触边界条件，用于对涉及几何和材料非线性的摩擦接触问题进行有限体积模拟。接触物体的变形由动量方程的更新拉格朗日形式描述，该方程使用以单元为中心的有限体积方法在空间中离散。建议的接触边界条件基于基于惩罚的段到段接触力计算方法的有限体积实现，在该方法中，法向接触压力由惩罚定律控制，在离散接触表面上进行积分，在离散接触面上强制执行接触约束。积分方式。与逐点接触力计算算法相反，这种方法允许对接触区域边缘进行更准确和更稳健的处理，同时计算两个接触面上的接触力，以及在大滑动过程中更平滑的接触力。所提出的数值方法在具有挑战性的机械接触问题上进行了测试，表明与可用的基准结果非常吻合。