The Analytical Solutions Of Concrete Thick-walled Cylinder With A Gradient Dependent Damage Model

The thick-walled cylinder is one of typical engineering components. Kinds of cement channel, tunnel, coal mine's alley, plane's body, boiler, pressure vessel etc, and they all can simplified as thick-walled cylinder to calculate. Because of the broad application of thick-walled cylinder in national defense and civil industry of shipping and ocean engineering, architecture, petroleum, electricity, chemical engineering and mechanical engineering etc, so the study in thick-walled cylinder has important sense in engineering.This paper sums up the basic concept and theory of damage mechanics. Using the concept of damage to describe the rupture process of concrete, give the development of damage of concrete stress-strain curve in every stage, and reveal the substance of rupture mechanism of concrete. Introduce several kinds of damage model of concrete. Introduce the non-local theory of concrete and several kinds of non-local damage gradient model of concrete.In the context of classical plasticity, the internally pressurized thick-walled cylinder problem has been well studied. Solutions of internally pressurized thick-walled cylinder with different materials (elastic perfectly plastic, elastic strain-hardening plastic etc) in different state (plane strain state and plane stress state) have been driven which based on different constitutive models by scholars, but the studies for material of concrete were less, especially for the size effect of quasibrittle material, the classical plasticity wasn't fit well. To solve these problems, use damage gradient constitutive model to analyze the internally pressurized thick-walled cylinder, and expect to get better solution.An analytical solution for the stress in an internally pressurized thick-walled cylinder in the plane strain state is presented. For the internally thick-walled cylinder, use the Mohr-Coulomb yield criterion which is put damage and damage gradient in it to judge the internally pressurized thick-walled cylinder's yield, divide the yielded one into elastic region and damage region. Use isotropic damage which makes damage gradient a numeric value not a tensor, and adopt the Mazars damage model. A damage gradient theory is used to describe the constitutive behavior of the material response undergoing damage, whereas the generalized Hooke's law is invoked to represent the material response in the elastic region. For this derived solution of this paper, the application is the numerical results of damage region of internally pressurized thick-walled cylinder.