In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the thermal problem (the classical Stefan’s problem) from the elasticity problem, and often limit themselves to linear elasticity with small strains. Treating solidification as an accretion problem, with the growth velocity correlated with the jump in the heat flux across the boundary, it presents an initial boundary-value problem (IBVP) over a domain whose boundary location is a priori unknown. This IBVP is solved numerically for the specific example of radially inward solidification in a spherical container. Several parametric studies are conducted to compare the numerical results with the rigid cases in the literature and gain insights into the role of elastic deformations in solidification.

中文翻译：

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相变诱导吸积的非线性力学


在本文中，我们在有限应变耦合热弹性力学的背景下制定了凝固的连续体理论。我们的目标是填补现有文献中的空白，因为现有的凝固研究通常会将热问题（经典的 Stefan 问题）与弹性问题解耦，并且通常将自身局限于具有小应变的线弹性。将凝固视为吸积问题，其生长速度与跨边界的热通量跳跃相关，它提出了一个边界位置先验未知的域的初始边界值问题 （IBVP）。该 IBVP 针对球形容器中径向向内凝固的具体示例进行数值求解。进行了几项参数研究，将数值结果与文献中的刚性情况进行比较，并深入了解弹性变形在凝固中的作用。