AI 中文总结
本文提出一种基于真实接触面积的关联库仑摩擦模型，通过引入微凸体塑性变形驱动的内部变量，在保持类库仑行为的同时符合广义标准材料框架，并验证了与经典库仑预测的一致性。
AI 中文摘要
库仑摩擦是一种非关联定律：它包含一个依赖于接触压力的阈值，即一个与任何内部变量都不共轭的应力，因此它在广义标准材料（GSM）意义上不具有耗散势，且增量摩擦接触问题不是最小化问题。在本文中，我们提出了一种替代摩擦模型，该模型在保持类库仑行为的同时是关联的且完全符合GSM。我们公式的关键是引入一个新的内部变量，该变量由粗糙表面的微观接触状态驱动，其演化由微凸体的塑性变形驱动。在非递增接触压力且低于阈值压力的情况下，该模型可恢复库仑摩擦，直至微凸体尺度的穿透深度。该深度具有物理意义，可通过校准来重现已知的摩擦学结果。在接触压力递减的情况下，由于微凸体的不可逆塑性变形，模型表现出记忆效应，而在压力阈值以上，模型则产生摩擦牵引力的饱和。我们提出了该模型的罚函数和拉格朗日乘子两种公式。罚方法的二维有限元实现证实了在两个基准测试中与经典库仑预测的极好一致性。
英文摘要
Coulomb friction is a non-associated law: it contains a threshold that depends on the contact pressure, i.e. a stress that is not conjugate to any internal variable, hence it admits no dissipation potential in the sense of generalized standard materials (GSM), and the incremental frictional contact problem is not a minimization problem. In this paper, we propose an alternative friction model that retains Coulomb-like behavior while being associated and fully GSM-compatible. Key to our formulation is the introduction of a new internal variable motivated by the microscopic contact state of rough surfaces, whose evolution is driven by the plastic deformation of the asperities. Under a non-decreasing contact pressure and below a threshold pressure, the model recovers Coulomb friction up to an asperity-scale penetration depth. This depth is physically meaningful and can be calibrated to reproduce known tribology results. Under decreasing contact pressures, the model exhibits a memory effect due to irreversible plastic deformation of the asperities, whereas above the pressure threshold it yields a saturation of the frictional traction. We present both penalty and Lagrange multiplier formulations of the model. A 2D finite element implementation of the penalty approach confirms excellent agreement with the classical Coulomb predictions across two benchmark tests.
