论文标题
在热力学环境中的Stefan问题，裂缝和流体流动
The Stefan problem in a thermomechanical context with fracture and fluid flow
论文作者
论文摘要
在这里，经典的Stefan问题，即仅在固液相变期间仅进行热转移的问题，在这里对机械效应有所增强。大量位移的欧拉描述与对流和Zaremba-Jaumann旋转时间衍生物一起使用，通过在（客观）速率中使用添加剂绿色-naghdi的分解来线性化。特别是，液相是一种粘弹性流体，而在jeffreys粘弹性流变学中考虑了利用相位场模型的蠕变和固相破裂，并且是略微（所谓的“半”可压缩材料）的概念。 $ l^1 $ - 通过在固体液相变过期间允许动力学过热/超冷的效果，用于放松的Stefan问题，采用了$ l^1 $ - 理论。使用弱解决方案存在的严格证明是用于使用时间限制的不完全熔化的。
The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann corotational time derivatives, linearized by using the additive Green-Naghdi's decomposition in (objective) rates. In particular, the liquid phase is a viscoelastic fluid while creep and rupture of the solid phase is considered in the Jeffreys viscoelastic rheology exploiting the phase-field model and a concept of slightly (so-called "semi") compressible materials. The $L^1$-theory for the heat equation is adopted for the Stefan problem relaxed by allowing for kinetic superheating/supercooling effects during the solid-liquid phase transition. A rigorous proof of existence of weak solutions is provided for an incomplete melting, employinga time-discretisation approximation.
