增量接触定律与永久压痕下的重复二元直接共线碰撞：一种混合系统表述
Repeated Binary Direct Collinear Impacts Under Incremental Contact Laws With Permanent Indentation: A Hybrid Systems Formulation
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中文总结 AI 辅助
本文针对带永久压痕的增量接触定律，提出一种混合系统表述，将接触界面建模为无质量元件，实现重复二元直接共线碰撞的建模，并验证了无源性等性质。
中文摘要 AI 辅助
增量接触定律通过携带内部状态的微分方程来规定法向接触力，该微分方程由压痕及其速率驱动。在某些定律中，力在非零压痕处消失，无论是由于塑性变形还是弹性后效，因此在分离时仍存在残余变形。此类定律在不容许变形的刚体动力学中显得格格不入。当压痕相对于物体较小时，这种张力是可以容忍的，因为此时压痕可以在本构层面而非几何层面被承载。即便如此，仅接触定律本身并不能决定物体的相互作用。由于力和压痕不再同时消失，接触开始和终止的条件必须单独提供。变形和内部状态在分离时的归宿也必须单独规定，而这两者都不包含在运动方程中。本文将在外力作用下的两个凸体的重复直接共线碰撞表述为一个混合动力系统。接触界面被建模为一个无质量元件，承载接触定律及其状态，通过相对速度和由接触状态决定的相互作用力与物体耦合。因此，所有切换和重置都局限于界面模型，而物体的几何形状和固有运动方程保持不变。本文确立了所得表述的主要解析性质，其中包括无源性、完备性和解的非唯一性。该框架通过包含基于Bouc-Wen迟滞模型的两种接触定律的完整两体系统模拟得到了验证。
英文摘要
Incremental contact laws specify the normal contact force through a differential equation carrying an internal state, driven by the indentation and its rate. In some, the force is extinguished at a nonzero indentation, whether by plastic deformation or by an elastic aftereffect, so that a residual deformation remains at the separation. Such laws sit uneasily within rigid body dynamics, which admits no deformation. The tension is tolerable when the indentation is small relative to the bodies, so that it may be carried constitutively rather than geometrically. Even then, the contact law alone does not determine the interaction of the bodies. Because force and indentation no longer vanish together, conditions for the commencement and termination of contact must be supplied separately. So must the fate of the deformation and internal state at separation, neither of which the equations of motion contain. This article formulates the repeated direct collinear impact of two convex bodies under external forces as a hybrid dynamical system. The contact interface is modeled as a massless element carrying the contact law and its state, coupled to the bodies through relative velocity and an interaction force dictated by the contact state. Consequently, all switching and resets are confined to the interface, leaving the geometry and the equations of motion of the bodies unaltered. The principal analytical properties of the resulting formulations are established, among them passivity and completeness; the branching of solutions at the onset and termination of contact is also examined. The framework is demonstrated through numerical simulations.
发表机构
- Auburn University（奥本大学）
机构由 AI 辅助整理，请以论文原文为准。
