Study Of Plastic-Damage Models For Concrete

In recent years, plastic-damage constitutive models for concrete have been increasingly popular in the nonlinear analysis of structures, serving as important fundamental theories and practical analysis tools for the investigation of the mechanical behavior, in particular the aseismic behavior, of concrete structures. In current research on plastic-damage models, the damage part is relatively active, while the plasticity part somewhat lags behind; the widely used plastic-damage models still face some limitations in their description of yielding, hardening and flow of concrete. In this dissertation, theoretical research is carried out on the yield criteria and relevant hardening laws for plastic-damage models for concrete. The major contents and findings include the following:1) Reclassification of strength theories of concrete. From a viewpoint of the geometrical meanings of the various stress invariants in the stress space, the numerous strength theories of concrete are classified into the Cartesian coordinates form, cylindrical coordinates form, cylindrical-Cartesian coordinates mixed form, and other forms in accordance with their representation. The analysis shows that most modern strength theories of concrete are represented in the pure cylindrical coordinates form and almost all of these strength criteria can be expressed by homogeneous functions with respect to the stress tensor and uniaxial compressive strength.2) Examination of the defect of the Lubliner yield criterion. By the analysis of the dependence of the meridians and deviatoric traces on the relevant parameter, it is demonstrated that the deviatoric shape and opening angles of the Lubliner irregular cones in the triaxial compression region cannot be controlled at the same time. A calibration strategy for the relevant parameter in the Lubliner criterion in accordance with the angle of internal friction is proposed for uniformly confined concrete.3) Extension of the types of yield functions applicable in plastic-damage models for concrete. The mapping and evolution of the yield criteria in a class of plastic-damage models and the homogeneous functions in the yield criteria are analyzed. It is proposed to lift the too tight restriction on the yield functions and relax the requirement to homogeneity with respect to the stress tensor and cohesions. 4) Construction of a new class of homogeneous yield functions for plastic-damage models for concrete. By developing the strengths in various stress states, which are used to calibrate parameters in modern strength theories, into the corresponding cohesions in various simple loading paths, a class of homogeneous yield functions with respect to the stress tensor and cohesions are constructed. It is demonstrated that this new class of yield functions can substantially improve the accuracy of plastic-damage models and extend their scope of application.5) Summarization of the definitions of hardening-damage parameters in plastic-damage models for concrete. A qualitative hypothesis is put forward in regard to how the plastic deformation of concrete advances the progress of the various basic hardening-damage modes. Two kinds of definitions for multiple hardening-damage parameters are summarized——allocation of the equivalent plastic strain rate and combination of the principal components of the plastic strain rate tensor.6) Construction of new hardening functions and damage functions for the calibration of plastic-damage models for concrete. A modification to the existing hardening function is proposed to reduce the mesh sensitivity of the plastic strain at peak stress. Further, a piecewise function is constructed, one piece for hardening and the other for softening, which achieves uniform and concentrated energy dissipations respectively and helps to formulate an explicit stress-strain relation whose ascending branch is mesh-insensitive.7) Derivation of plastic-damage consistent tangent stiffness. A fictitious effective stress tensor, which is orthogonally similar to the (real) effective stress tensor, is introduced to facilitate the transformation between stress components in the initial and principal coordinate systems. A consistent tangent stiffness that can be used in spectral return-mapping algorithms is derived for plastic-damage models based on scalar damage variables.