标题： 无条件稳定的，用于由机械化学旋节分解驱动的固态相变的二阶精度格式 显示英文标题

标题： Unconditionally stable, second-order accurate schemes for solid state phase transformations driven by mechano-chemical spinodal decomposition

摘要： 我们考虑由应变-成分空间中具有非凸性的自由能密度引起的固态相变；我们将这些非凸区域称为机械化学自旋线。 相对于成分和应变的非凸性导致不同晶体结构的相分离。 我们基于一个现有的模型，该模型将经典的Cahn-Hilliard模型与Toupin的有限应变梯度弹性理论相结合。 这两个系统均由四阶、非线性、偏微分方程表示。 本工作的目标是开发无条件稳定的二阶精度时间积分方案，这是为了进行三维动态演变微观结构的大规模计算的需要。 我们还引入了从这些提出方案中自然导出的简化公式，以实现更快的计算，同时保持二阶精度。 尽管我们的方法在此针对特定类型的机械化学问题进行开发和分析，但可以很容易地将相同的方法应用于任何自由能密度函数为解组分和组分梯度的多变量多项式的问题，以开发无条件稳定的二阶精度方案。 除了方法的分析和构建外，我们还提供了一套数值结果，以展示这些方案的实际应用。 显示英文摘要

摘要： We consider solid state phase transformations that are caused by free energy densities with domains of non-convexity in strain-composition space; we refer to the non-convex domains as mechano-chemical spinodals. The non-convexity with respect to composition and strain causes segregation into phases with different crystal structures. We work on an existing model that couples the classical Cahn-Hilliard model with Toupin's theory of gradient elasticity at finite strains. Both systems are represented by fourth-order, nonlinear, partial differential equations. The goal of this work is to develop unconditionally stable, second-order accurate time-integration schemes, motivated by the need to carry out large scale computations of dynamically evolving microstructures in three dimensions. We also introduce reduced formulations naturally derived from these proposed schemes for faster computations that are still second-order accurate. Although our method is developed and analyzed here for a specific class of mechano-chemical problems, one can readily apply the same method to develop unconditionally stable, second-order accurate schemes for any problems for which free energy density functions are multivariate polynomials of solution components and component gradients. Apart from an analysis and construction of methods, we present a suite of numerical results that demonstrate the schemes in action.