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

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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).