analytical stress-strain model and damage index for confined and unconfined concretes to simulate rc structures under cyclic loading

an analytical nonlinear stress-strain model and a microscopic damage index for confined and unconfined concretes together with a macroscopic damage index for reinforced concrete (rc) structures under cyclic loading are proposed. in order to eliminate the problem of scale effect, an adjustable finite element computer program was generated to simulate rc structures subjected to cyclic loading. by comparing the simulated and experimental results of tests on the full-scale structural members and concrete cylindrical samples, the proposed stress-strain model for confined and unconfined concretes under cyclic loading was accordingly modified and then validated. the proposed model has a strong mathematical structure and can readily be adapted to achieve a higher degree of precision by modifying the relevant coefficients based on more precise tests. to apply the proposed damage indices at the microscopic and macroscopic levels, respectively, stress-strain data of finite elements (confined and unconfined concrete elements) and moment-curvature data of critical section are employed. the proposed microscopic damage index can easily be calculated by using the proposed simple analytic nonlinear stress-strain model for confined and unconfined concretes. the proposed macroscopic damage index is based on the evaluation of nonlinear local degradation of materials and taking into account the pseudo-plastic hinge produced in the critical section of the structural element. one of the advantages of the macroscopic damage index is that the moment-curvature data of the critical section is sufficient in itself and there is no need to obtain the force-displacement data of the structural member.