This paper considers numerical modeling of intensive heating induced thermo-mechanical failure processes in granitic rock. For this end, a numerical method based on polygonal finite elements and a damage-plasticity model is developed. A staggered scheme is employed to solve the global thermo-mechanical problem. The rock failure is described by a Rankine-Mohr-Coulomb plasticity model with separate scalar damage variables for tension and compression. Consistent tangent operator is derived for this model. Special attention is given to the temperature dependence of the thermo-mechanical material properties of heterogeneous rock. In the numerical examples, the method is first verified with an analytical solution of thermal stresses in a hollow cylinder, and then qualitatively validated with the problems of thermal cracking of concentric cylinders and uniaxial compressive test on rock under elevated temperatures. Finally, the method is applied in novel simulations inspired by the degradation of sauna stones under slow heating-rapid cooling and the comminution by rapid heating-cooling cycles.

中文翻译：

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用多边形有限元模拟花岗岩热机械破坏过程

本文考虑了花岗岩中强加热引起的热机械破坏过程的数值模拟。为此，开发了一种基于多边形有限元和损伤塑性模型的数值方法。采用交错方案来解决全局热机械问题。岩石破坏由 Rankine-Mohr-Coulomb 塑性模型描述，该模型具有单独的拉伸和压缩标量损伤变量。为该模型导出了一致切线算子。特别注意非均质岩石的热机械材料特性的温度依赖性。在数值例子中，首先用空心圆柱体中热应力的解析解来验证该方法，然后对同心圆柱体的热裂问题和高温岩石单轴压缩试验问题进行定性验证。最后，该方法被应用于新的模拟，其灵感来自桑拿石在缓慢加热-快速冷却下的降解和快速加热-冷却循环的粉碎。