In this paper a new rheological-dynamical continuum damage model for concrete under compression is used to research the behaviour of reinforced concrete beams subjected to bending. Within the framework of this approach the stress-strain curve of a concrete under compression in the pre-peak regime can be computed if the compressive strength, elastic modulus, concrete density and Poisson’s ratio are experimentally evaluated. The ultimate strain is determined in the post-peak regime only, using the secant stress-strain relation from damage mechanics. Experimental stress-strain data in the pre-peak regime for five concrete compositions were obtained during the examination presented herein. The numerical predictions regarding moment-curvature and ductility of a reinforced concrete beam are presented for five concrete compositions, demonstrating capabilities of a new analytical model.

Purpose: The purpose of this paper is to contribute to the solution of the fatigue damage problem of reinforced concrete frames in bending.Design/methodology/approach: The problem of fatigue damage is formulated based on the rheological–dynamical analogy, including a scalar damage variable to address the reduction of stiffness in strain softening. The modal analysis is used by the finite element method for the determination of modal parameters and resonance stability of the selected frame cross-section. The objectivity of the presented method is verified by numerical examples, predicting the ductility in bending of the frame whose basic mechanical properties were obtained by non-destructive testing systems.Findings: The modal analysis in the frame of the finite element method is suitable for the determination of modal parameters and resonance stability of the selected frame cross-section. It is recommended that the modulus of elasticity be determined by non-destructive methods, e.g. from the acoustic response.Originality/value: The paper presents a novel method of solving the ductility in bending taking into account both the creep coefficient and the aging coefficient. The rheological-dynamical analogy (RDA) method uses the resonant method to find material properties. The characterization of the structural damping via the damping ratio is original and effective.

A theoretical model for porous viscoelastoplastic (VEP) materials in the dry state is investigated in this research study. The model is based on the principles of conservation of mass and energy using the rheological dynamic theory (RDT). The model provides expressions for the creep coefficient, Poisson’s ratio, modulus of elasticity, damage variable, and strength as a function of porosity and/or void volume fraction (VVF). The reliability of the proposed model was analyzed by comparing numerical results with experimental ones on hardened concrete. A numerical model was created and analyzed in the commercial software Abaqus and validated by comparison with experimental data obtained by geodetic measurements on a composite wood–lightweight concrete girder. The deflections and stresses of the beam resulting from the influence of concrete creep and porosity were analyzed at the initial moment of time and after 6 years. The results showed that the RDT provided a reliable model for estimating parameters after exposure to long-term loads.

It is assumed that the porous material is based on the principle of conservation of mass and the principle of conservation of energy. The validity of both principles relies on experimental observations. Experimental results of different metals were used to compare the Poisson ratio as a function of porosity. A comparison is made between the theory of percolation and the model proposed in this paper based on the rheological-dynamic analogy (RDA). The results show that there is an excellent agreement between percolation theory and the RDA model. Finally, a new relationship between the creep coefficient and porosity was proved for all analyzed metals by defining their damage variable in the range of measurable porosities.