Asymptotic and numerical modelling of faults and thermal striping in materials with a micro-structure (linked proposal with I.S. Jones, LJMU)

该项目结合了两种类型的数学模型，用于描述结构化介质中的动态宏观裂纹。有限尺寸的表面断裂裂纹将受到由温度的时间调和振荡产生的动态载荷的影响。这与热剥离现象有关，例如，在核反应堆的冷却轮廓内或管道系统内的混合区中，由于出现表面破裂裂纹而出现热剥离现象。这种裂纹的深度在很大程度上取决于外部热振荡的频率。第一种类型的结构将涉及桁架状网架，其中弯曲变形可以忽略不计。第二类是指框架状弹性结构中的宏观裂纹，包括宏观裂纹周围弹性杆件的弯曲。将特别注意宏观裂纹和微观缺陷之间的相互作用的影响，这些缺陷被建模为晶格中不完美的弹簧状结。

The project incorporates two types of mathematical models for dynamic macro-cracks in structured media. Surface breaking cracks of finite size and subjected to a dynamic loading generated by a time-harmonic oscillation of temperature will be considered. This is related to the phenomenon of thermal striping which occurs, for example, within the cooling contours of nuclear reactors or in the mixing zones within piping systems due to the appearance of surface breaking cracks. The depth of such cracks is greatly dependent on the frequency of the external thermal oscillations. The first type of structures will involve truss-like lattices where flexural deformation can be neglected. The second type refers to macro-cracks in frame-like elastic structures incorporating bending of elastic links around the macro-crack. Particular attention will be paid to the effect of interaction between the macro-crack and micro defects modelled as imperfect spring-like junctions within the lattice.