Analysis of Concrete Pressure Vessels in the Framework of Continuum Damage Mechanics

Abstract

In this article, a constitutive model in the framework of continuum damage mechanics is proposed to simulate the elastic behavior of concrete in tension and compression states. We assume two parts for Gibbs potential energy function: elastic and damage parts. In order to obtain the elastic-damage constitutive relation with the internal variables, two damage thermodynamic release rates in tension and compression derived from the elastic part of Gibbs potential energy are introduced. Also, two anisotropic damage tensors (tension and compression) are defined which characterize the tensile and compressive behaviors of concrete. Furthermore, two different linear hardening rules for tension and compression states are adopted for characterizing the damage evolution. The spectral decomposition technique is used to resolve the stress tensor into tensile and compressive components. The accuracy and performance of the proposed model are validated by comparing the predicted results with different experimental data, such as monotonic uniaxial tension and compression tests, and monotonic biaxial compression test. As an application, an analytic closed-form solution for a concrete thick-walled cylinder is obtained. It is shown that two damages: tensile damage $D_{\theta }^{+}$ and shear damage $D_r^{-}$ propagate in the cylinder. These two damages introduce anisotropy in the elastic behavior of the concrete structure. The influence of these two damages is investigated on the stress field in the cylinder. It is found that effect of shear damage $D_r^{-}$ on radial and tangential stresses as well as the effect of tensile damage $D_{\theta }^{+}$ on radial stress are negligible, while the effect of tensile damage $D_{\theta }^{+}$ on the tangential stress in a concrete thick-walled cylinder is significant.