AI 中文总结
研究有限应变固体完全熔化为粘弹性流体的斯蒂芬问题，在欧拉框架大应变下建模，采用杰弗里斯流变学，通过纳入动力学过热和过冷扩展经典问题，利用多极非简单连续统概念及时间离散分析求解。
AI 中文摘要
在欧拉框架内大应变条件下，建立了具有热机械相变的可压缩流固相互作用模型。对于偏量部分，采用了具有附加粘性的杰弗里斯（也称为反齐纳）流变学。机械固液转变的核心原理是粘性（或粘塑性）响应取决于温度，解冻时可能完全退化为粘弹性流体，剪切变形时无弹性响应。这使得流体能够自由流动，随后冻结成新构型，并可能再次融化成流体，循环可无限重复。经典斯蒂芬问题通过纳入动力学过热和过冷进行了扩展。利用多极非简单连续统概念，对原始公式的高阶梯度修正进行了适当截断的时间离散分析。
英文摘要
The compressible fluid-solid interaction (FSI) with a thermomechanical phase transition is formulated at large strains within the Eulerian frame. For the deviatoric part, the Jeffreys (also called anti-Zener) rheology with an additional viscosity is adopted. The core philosophy governing the mechanical solid-liquid transition is that the viscous (or viscoplastic) response is temperature-dependent and may fully degenerate to a viscoelastic fluid during thawing, so that there is no elastic response on the shear distortion. This behavior enables the free flow of the fluid, its subsequent freezing into a new configuration, and potential re-melting back into a fluid, allowing such cycles to repeat indefinitely. The classical Stefan problem, associated with the latent heat of the first-order (thawing-freezing) phase transition, is augmented by incorporating kinetic overheating and undercooling. The analysis by a time discretization with an appropriate truncation is applied to a higher-gradient modification of the original formulation, utilizing the concept of multipolar nonsimple continua.
