CONSTITUTIVE MODELING AND NUMERICAL IMPLEMENTATION OF BRITTLE AND DUCTILE MATERIAL BEHAVIOR WITH THE AID OF INELASTIC XFEM AND DAMAGE-PLASTICITY MODELS

Constitutive equations establish the relationship between kinetic with kinematic quantities to characterize the specific properties of the material. Mechanical constitutive relations are formulated to describe nonlinear and inelastic response behavior as well as brittle or ductile failure of metallic and cementitious materials in form of plastic and damage material formulations.

This dissertation addresses three topics: The first topic is focused on the peak response behavior of brittle and ductile materials by coupling plasticity with extended finite element method in order to model and follow discrete crack initiation and fracture propagation. This is accomplished by exploiting appropriate crack initiation criteria and performing analytical and numerical localization analysis to determine the critical orientation of the emerging failure surface. A series of experiments are performed on perforated metallic flat bars and the observations are used to validate the computational failure predictions.

The second topic is the finite element approximation of the field data obtained by photogrammetric non-contact digital image correlation analysis. This study includes experimental observations on various perforated metallic flat bars to evaluate displacements and strains by using digital image correlation analysis. The displacement images are used in order to determine the best approximation of finite element nodal displacement values based on least square approximation of the optical measurement data. Moreover, infinitesimal and finite strains are calculated and contrasted with the results processed by the commercial Aramis imaging software.

The last topic is focused on the localization of triaxial concrete behavior by a damage-plasticity model. In this constitutive formulation a three-invariant yield function is introduced to model plastic deformations and a damage function is used to determine the nonlinear and inelastic behavior of concrete. Coupling of the inelastic damage and plasticity processes is introduced by a damage variable that enters the plastic yield function in terms of the effective stress. Localization properties of the combined damage-plasticity model are studied and the differences of the damage vs. plasticity constituents are explored and compared. A series of experimental tests are performed on concrete cylinders in cyclic compression and digital images are recorded to provide complementary field data of surface deformations and cracks.