This research proposal intends the development of nonlinear formulations based on the Boundary Element Method (BEM) for random fracture and fatigue crack growth modelling. The BEM is a numerical method accurate for solving fracture problems. Because of the non-requirement of the domain mesh, the stresses concentration at the crack tip are accurately described. Moreover, the mesh dimension reduction provided by the BEM makes simpler the remeshing procedures during the crack propagation. In the context of cracked materials, the mechanical behaviour at the fracture process zone is represented properly by the cohesive approach. Then, cohesive forces represent the residual material strength along such zone. This fracture approach is coupled to the standard BEM and to the enriched BEM approaches, in which the latter origins the XBEM formulation. The crack propagation in nonhomogeneous structural systems caused by either fatigue or fracture is handled, in which emphasis is dedicated to the multiple crack propagation and coalescence modelling. The material failure is subjected to the large influence of randomness. Then, the nonlinear BEM models are coupled to the reliability algorithms. Therefore, mechanical-probabilistic formulations are developed, which enable the assessment of the most probable failure configurations and the limit loads values accounting for uncertainties scenarios. The probability of failure information is utilized into the formulation of optimisation problems. The Reliability Based Design Optimisation, Risk Optimisation and Robust Optimisation approaches for cohesive crack growth with BEM/XBEM are developed. Finally, this proposal intends to contribute with the application field of BEM. Particularly in domains in which the BEM is efficient than other numerical approaches.
News published in Agência FAPESP Newsletter about the scholarship: