Theory of Dichotomy for Concrete Modelling under Cyclic Biaxial Loading

An orthotropic model which accounts for the inelastic behavior of concrete elements loaded biaxially is developed using the theory of dichotomy. The proposed theory replaces the continuum by a system of orthogonal springs. The behavior of concrete is idealized as elastoplastic damage through splitting the strain tensor into two main components. Consequently, three possible forms of constitutive relation are presented which associate the stress tensor to the total strain, the elastic-damage strain and the plastic-damage strain, respectively. These relations are adopted in diagonal tensorial form in the principal space using proper damage variables. The interdependence between the stress components are taken into account using the biaxiality ratio for all possible combinations of the principal stresses, i.e., compression-compression, compression-tension and tension-tension. Thermodynamical considerations in view of the proposed theory are discussed. The model is shown to be simple and in close agreement with a wide set of the well documented existing experimental data where the salient features of concrete behavior-such as strain softening, stiffness degradation, volumetric dilatation-are captured.