Elastic Plastic and Damage Model for Concrete Materials : Part I - Theoretical Formulation
thermodynamically consistent macroscopic constitutive model for concrete that incorporates concrete effective stress space plasticity and fracture energy based - continuum damage mechanics is presented. A plasticity yield criterion, with multiple hardening functions and a non-associative plastic flow rule, is used simultaneously with two (tensile and compressive) isotropic damage criteria. The spectral decomposition of the stress tensor into tensile and compressive components is utilized in all criteria in order to simulate different responses of the material under various loading patterns. The damage criteria are based on the hydrostaticdeviatoric sensitive damage energy release rates in tension and compression derived from the Helmholtz free energy function. Three dissipation mechanisms are defined, one for plasticity and two for damage, to control the dissipation process in the material model. The consistent elastic-plastic-damage tangent operator is also derived, which concludes the theoretical formulation of the proposed model. Verification examples are provided in order to evaluate the ability of the proposed model to capture the behavior of concrete under different states of loading. The detailed scheme of numerical integration of the constitutive equations and the application of the proposed model to study concrete and reinforced concrete members are important issues discussed in part II of this work.