考虑磨损扩散的摩擦接触问题
A frictional contact problem with wear diffusion
摘要：
本文建立了粘弹性体与移动基础之间的动摩擦接触模型，并进行了分析。接触涉及接触表面的磨损和磨屑的扩散。接触边界上的应力和位移之间的关系由正常的柔度定律和干摩擦的库仑定律的一个版本来模拟。接触表面的磨损率由Archard定律的微分形式描述。考虑了不能离开接触表面的磨损颗粒在表面上扩散的影响。这项工作的新颖之处在于，接触表面是一个歧管，因此，碎片的扩散发生在弯曲的表面上。该模型的兴趣与机械关节和骨科生物力学的磨损有关，其中磨损碎屑被捕获，它们扩散并经常导致关节假体和各种植入物的性能退化。该模型对机械接触采用微分包含的形式，对磨粒在接触面上的扩散采用微分方程的形式。利用截断变元和Kakutani-Ky Fan-Glicksberg不动点定理证明了弱解的存在性。
英文摘要：
This paper constructs and analyzes a model for the dynamic frictional contact between a viscoelastic body and a moving foundation. The contact involves wear of the contacting surface and the diffusion of the wear debris. The relationships between the stresses and displacements on the contact boundary are modeled by the normal compliance law and a version of the Coulomb law of dry friction. The rate of wear of the contact surface is described by the differential form of the Archard law. The effects of the diffusion of the wear particles that cannot leave the contact surface on the surface are taken into account. The novelty of this work is that the contact surface is a manifold and, consequently, the diffusion of the debris takes place on a curved surface. The interest in the model is related to the wear of mechanical joints and orthopedic biomechanics where the wear debris are trapped, they diffuse and often cause the degradation of the properties of joint prosthesis and various implants. The model is in the form of a differential inclusion for the mechanical contact and the diffusion equation for the wear debris on the contacting surface. The existence of a weak solution is proved by using a truncation argument and the Kakutani--Ky Fan--Glicksberg fixed point theorem.
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