Coulomb friction model with unilateral contact is a basic, but reliable, model to represent the resistance to sliding between solid bodies. It is nowadays well-known that this model can be formulated as a second–order cone complementarity problem, or equivalently, as a variational inequality. In this article, the Coulomb friction model is enriched to take into account the resistance to rolling, also known as rolling friction. Introducing the rolling friction cone, an extended Coulomb's cone, and its dual, a formulation of the Coulomb friction with rolling resistance as a cone complementarity problem is shown to be equivalent to the standard formulation of the Coulomb friction with rolling resistance. Based on this complementarity formulation, the maximum dissipation principle and the bi-potential function are derived. Several iterative numerical methods based on projected fixed point iterations for variational inequalities and block-splitting techniques are given. The efficiency of these methods strongly relies on the computation of the projection onto the rolling friction cone. In this article, an original closed-form formula for the projection on the rolling friction cone is derived. The abilities of the model and the numerical methods are illustrated on the examples of a single sphere sliding and rolling on a plane, and of the evolution of spheres piles under gravity.

具有单边接触的库仑摩擦模型是基本但可靠的模型，用于表示实体之间的滑动阻力。如今众所周知，该模型可以表述为二阶锥互补问题，或者等效地表示为变分不等式。在本文中，丰富了库仑摩擦模型，以考虑到滚动阻力，也称为滚动摩擦。引入滚动摩擦圆锥，扩展的库仑圆锥及其对偶关系，将具有滚动阻力的库仑摩擦公式作为圆锥互补问题介绍出来，等效于具有滚动阻力的库仑摩擦的标准公式。基于这种互补性公式，推导了最大耗散原理和双势函数。给出了基于投影定点迭代的变分不等式和块分解技术的几种迭代数值方法。这些方法的效率在很大程度上取决于在滚动摩擦圆锥上的投影的计算。在本文中，得出了滚动摩擦圆锥上投影的原始封闭形式公式。通过在平面上滑动和滚动单个球体以及在重力作用下球体桩的演化示例，说明了模型和数值方法的功能。推导了滚动摩擦圆锥上投影的原始封闭形式公式。通过在平面上滑动和滚动单个球体以及在重力作用下球体桩的演化示例，说明了模型和数值方法的功能。推导了滚动摩擦圆锥上投影的原始封闭形式公式。通过在平面上滑动和滚动单个球体以及在重力作用下球体桩的演化示例，说明了模型和数值方法的功能。