Canonical elastoplastic - damage modelling of reinforced concrete

Abstract

Reinforced concrete is per se neither elastic nor plastic material. It exhibits damage attributable to irreversible changes; i.e. slip and microcracking. Three phases of bahavior exist and interact: elesticity, plasticity and damage. An extensive literature review is carried out to figure out the phenomenological aspects of damage along with the existing constitutive models. New concepts in the framework of continues damage mechanics are established. The notions of metaphorical generalized damage variables, generalized material degradation paths and generalized effective stress are defined. Free energy terms are derived based on the concepts of thermodynamics of irreversible changes. Incorporation with the classical theory of plasticity and micromechanics are made. A canonical elastoplastic damage model is proposed for concrete. The model is initially formulated through a rudimentary scrutiny of the uniaxial behavior. The derivation stems form recoverable energy equivalence based on the formal split of the total strain to its components; elastic damage and plastic-damage strain. On the basis of the proposed theory of dichotomy, the model is extended to handle biaxial orthotropic damage associated with cyclic bahavior. Verification is carried out againts a wide set of experimental data. The model is shown to properly predict strain softening, stiffness degradation, volumetric dilatancy under compression, strength increase under biaxial compressive states. Furthermore, a damage model is then proposed for the uniaxial behavior of steel. Numerical implementation of the proposed damage model in terms of a computational framework is carried out by development of two nonlinear finite element programs; DMGTRUSS and DMGPLSTS. The first package deals with multi-dimensional trusses while the other handles two-dimensional plane stress states. Practical applications to plain and reinforced concrete structural members are shown to be in good agreement with well documented results.