冰面摩擦软化的非线性模型
Nonlinear model of ice surface softening during friction
摘要：
摩擦过程中冰面软化是由于外部超临界加热引起的剪切应变的自发出现。粘弹性介质的Kelvin-Voigt方程、Landau-Khalatnikov型松弛方程和热传导方程描述了这种变换。研究表明，上述方程形式上符合协同Lorenz系统，其中序参量约化为剪应变，应力作为共轭场，温度作为控制参量.使用绝热近似，这些量的稳态值导出。松弛剪切模量对应变的依赖性的检查解释了冰面软化根据一级转变机制。临界加热速率与冰剪切模量的松弛值成正比，与其典型值成反比。
英文摘要：
The ice surface softening during friction is shown as a result of spontaneous appearance of shear strain caused by external supercritical heating. This transformation is described by the Kelvin-Voigt equation for viscoelastic medium, by the relaxation equations of Landau-Khalatnikov-type and for heat conductivity. The study reveals that the above-named equations formally coincide with the synergetic Lorenz system, where the order parameter is reduced to shear strain, stress acts as the conjugate field, and temperature plays the role of a control parameter. Using the adiabatic approximation, the stationary values of these quantities are derived. The examination of dependence of the relaxed shear modulus on strain explains the ice surface softening according to the first-order transition mechanism. The critical heating rate is proportional to the relaxed value of the ice shear modulus and inversely proportional to its typical value.
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