Celllular automata applications in the field of mechanical engineering and aerospace material science

元胞自动机（CA）是一种完全离散的、空间分布的动力系统，它是对物理系统进行数学描述的一种替代框架。拟开展的研究项目旨在延续申请人目前在CA方面的研究活动，并将其扩展到材料科学、机械工程、断裂力学和无损方法等领域。具体地说，CA模型将用于评估非均质材料的力学测试（疲劳和驻留疲劳）和非破坏性方法（超声波检查）的行为。用于模拟的材料是近α钛合金，众所周知，当在低环境温度（冷停留）下施加最大载荷时，这种材料会遭受严重的疲劳寿命损失，这极大地限制了它们在喷气发动机关键部件设计中的应用。由于申请人先前的发现拨款而开发的CA将进一步发展，以赶上与微观结构的局部弹塑性行为相关的微观力学的更多细节。将介绍更复杂的蠕变行为规律和加载阶段的一些塑性。特别地，一些晶体织构性质将被介绍。另一方面，目前可用的CA弹性模型将适用于研究和理解这些非均质材料的超声响应。这些弹性模型将帮助申请人的研究团队更好地理解一些已经在生产部件上获得的、尚未完全理解的具体结果。这些结果也有望使目前正在设计的非破坏性方法得到改进（与NRC - IMI Boucherville合作）。预期的结果对于学术数学发展世界和许多工业应用程序（具体应用程序和模式）都是有价值的。

Cellular automata (CA) are fully discrete, spatially distributed dynamical systems which serve as an alternative framework for mathematical descriptions of physical systems to finite element. The proposed resarch program aims to pursue the applicant's present research activities on CA and to extend them to material science, mechanical engineering, fracture mechanics, and non destructive methods. Concretely, the CA models will be usedto evaluate the behavior of heterogeneous materials for both, mechanical tests (fatigue and dwell fatigue) and non destructive methods (ultrasonic inspections). The materials to be used for simulation are near alpha titanium alloys which are known to suffer from significant fatigue life debit when a dwell is applied at the maximum load at low ambiant temperature (cold dwell debit), which considerably limits their application for the design of critical components of jet engines. The CA which has been developed thanks to the applicant's previous discovery grant will be further developed in order to catch up more details of the micromechanics related to the local elasto-plastic behavior of microstructures. More complex creep behavior laws and some plasticity during the loading stages will be introduced. In particular, some crystallographic texture properties will be introduced. On the other hand, the elastic models for CA that are now available will be adapted to investigate and understand the ultrasonic response of these heterogeneous materials. These elastic models will help a the applicant's research team to better understand some specific results that have been obtained on production parts and that are not yet fully understood. These results are also expected to allow the refinement of non destructive methods that are presently being patterned (in collaboration with the NRC - IMI Boucherville). The expected results should be valuable for both the academic mathematical development world and numerous industrial applications (concrete applications and patterns).