An elastoplastic damage model of concrete under cyclic loading and its numerical implementation

Abstract

A novel elastoplastic damage model describing the complex mechanical behaviors such as stiffness degradation and irreversible deformation of concrete under cyclic loading is constructed and the complete procedure for numerical implementation is presented. To solve the key problems including multi-axial stress states, asymmetry in tension and compression and conversion between tension and compression under cyclic loading, a series of approaches are put forward. A scalar equivalent strain based on the Hsieh-Ting-Chen strength criterion in the framework of strain space is used to convert the complex multiaxial stress state to the simple uniaxial one. Correspondingly, the equivalent strain obtained by the characteristic strength curve addresses the asymmetry in tension and compression, so that the stress–strain relationship in both uniaxial tension and uniaxial compression can be represented by the same curve, and a single damage scalar is available to characterize both tensile damage and compressive damage. To overcome the difficulty of conversion between tension and compression owing to the non-negative equivalent strain, a net equivalent strain is defined to keep the curve proceeding in the first quadrant under reverse loading. Meanwhile, a nominal damage variable is proposed to ensure that the reloading curve can return to the original stress–strain envelope. A new framework of the model with a concise mathematical form has been numerically implemented and is independent of the selection of fundamental governing equations. Typical experimental tests involving three-point bending test, mixed-mode bending test, cyclic uniaxial test, and reciprocating loading test are used for verification. The results calculated by the proposed model are all in good agreement with the tests. As a result, the correctness and reliability of the novel model are demonstrated.