Nonlocal continuum damage models for quasi-brittle fracture: algorithms and applications

Quasi-brittle fracture – characteristic for mineral-based materials typical in construction – concerns a large number of structural failures which, due to the abrupt nature of the phenomenon, may cause loss of lives and damage to infrastructure. Therefore, it is crucial to develop numerical methods, besides certain theoretical and experimental approaches, to predict the whole process of mechanical failure from the elastic phase, the damage initiation, the stable and unstable propagation of failure until the final rupture. This dissertation studies a continuum damage approach, by focusing on the development of a nonlocal model with enhanced performance and accuracy in the modeling of localized quasi-brittle damage. The damage model is formulated to cope with a wide range of mineral-based materials, including plain and spatially random heterogenous concrete in which the variability of material properties substantially influences the global response of the structures. For the class of microarchitectural materials, the damage model is enriched in light of a simplified form of Mindlin's strain gradient elasticity theory. The gradient-enriched model is proved to be capable of capturing the size effects induced by microarchitectures in both the elastic and the softening regimes, especially in finer scales where the characteristic size of the internal structure is of the same order as the exterior dimensions of the specimen itself. For thin-walled structures, the damage model is integrated into a plate model of third-order shear deformation theory to remedy the computational burden of the corresponding simulations with nonlinear three-dimensional models. The plate formulations cover various functionally graded material configurations with material properties set to smoothly vary in the direction of the plate thickness. For the numerical implementations of the dissertation, either the finite element or isogeometric Galerkin methods are employed in the form of an in-house software package. The former, as a de facto industrially accepted methodology for computational mechanics, boasts an excellent capability in meshing complex geometries, whereas the latter is exploited in the present dissertation for the non-standard gradient-enhanced problem settings that require higher-order continuity over element boundaries. Through a series of benchmark problems, the implementations of the numerical methods are verified and the damage models are validated, and the roles of their key features are demonstrated.