Multiscale Discrete Damage Theory For Failure Modeling of Composite Materials
The dissertation develops a new reduced order homogenization model named “multiscale discrete damage theory” (MDDT) for failure analysis of composite materials. MDDT adopts discrete representation of fracture process within the microstructure and consistently bridges them to continuum representation of damage at the coarse scale. The issue of mesh-size sensitivity due to continuum description of localized damage is alleviated by adjusting the microstructure domain size in an effective manner, in which a scaling relationship is established between the reduced-order model and size of macroscopic element. A series of investigations are conducted by leveraging and extending extend MDDT to model failure mechanisms in 3 scenarios: (1). Tensile failure (2) fatigue (3) crack reorientation. The numerical experiments in the context of three-dimensional open-hole composite laminates subjected to tensile loads indicate the capabilities of MDDT to reproduce multiscale failure mechanisms including fiber fracture, splitting crack and transverse matrix cracking with mesh-size objectivity. The non-additive scheme of cyclic-sensitive damage evolution law is incorporated into MDDT for composite fatigue analysis. The evaluation of fatigue response is accelerated by leveraging a temporal multiscale model, which integrates the unit cycle response to extrapolate long-term fatigue degradation. The numerical experiments of open-hole composite laminates subjected to fatigue loading are used to verify the capabilities of MDDT to model complex fatigue failure mechanisms with particular emphasis on mesh-size objectivity. Another extension of MDDT points to rotational adaptation of microstructure with a prescribed failure path to account for arbitrary direction of crack propagation. This extension leverages rotational invariance in certain planes in the material microstructure. A dynamic crack nucleation and orientation criteria are also defined. The proposed extension is validated in the context of delamination migration test. The dissertation also explored introducing viscoplasticity to the matrix material for describing shear non-linearity effects. The potentials of multiple partitions and coefficient tensor regularization are investigated for alleviating the over-stiff response prediction of non-linear response in composite material when transformation field analysis based reduced-order approaches are used. The dissertation also proposes an optimization framework for inverse characterization of in-situ composite material elastic properties. The constituent properties are considered to have spatial variance and characterized by the coefficients of a spatial distribution function. The optimization solution is demonstrated with statistical consistency under the effect of measurement noise. The efficacy of the proposed approach is verified based on synthetic measurements of fiber centroid displacements, and the outcomes indicate a significant noise mitigation with increasing number of fiber samplings (i.e. larger size of specimen and more loading times) and larger size of matrix pocket.