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，可作为从物理系统到有限元的数学描述的另一种框架。拟议的研究计划旨在继续申请人目前在CA方面的研究活动，并将其扩展到材料科学、机械工程、断裂力学和非破坏性方法。具体地说，CA模型将用于评估非均质材料的力学试验(疲劳和停留疲劳)和无损方法(超声波检测)的行为。用于模拟的材料是近α钛合金，当在低温下施加最大载荷时，已知存在显著的疲劳寿命下降(冷下降)，这在很大程度上限制了它们在喷气发动机关键部件设计中的应用。由于申请者之前的发现拨款而开发的CA将进一步发展，以便了解与微结构的局部弹塑性行为有关的微观力学的更多细节。将引入更复杂的蠕变行为规律和加载阶段的一些塑性。特别是，将介绍一些晶体织构特性。另一方面，现有的CA弹性模型将被用来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。这些结果还有望改进目前正在设计的非破坏性方法(与NRC-IMI Boucherville合作)。预期的结果应该对学术数学开发世界和许多工业应用(具体应用和模式)都有价值。

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).