Computational methods for multi-scale fracture

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In this project, we aim at a novel computational framework on multiscale fracture mechanism. Therefore, we plan to extent the recently proposed IGA^2 framework, a generalization of the conceptual similar well-known FE^2 method towards higher-order continua. Within this two-scale framework, we aim at a phase-field fracture formulation on both scales. First, a brittle fracture formulation is proposed, using independent, but thermodynamically consistent fracture fields on the different scales. Second, a ductile fracture formulation combining gradient plasticity and gradient damage models will be introduced on the micro-scale. Third, suitable investigations on the asymptotic behavior of the proposed computational multi-scale method will accomplish the investigation and ensure a correct convergence. To obtain an efficient numerical framework, a two-scale multi-grid formulation is proposed, combined with a pseudo mixed approach for enhanced convergens and thus, reduced computational cost throughout the Newton-Raphson iteration. This framework, including sophisticated technical enhancements, will be published on GitHub to provide additional information for the research community.