Studies On The Damage Constitutive Equation Of The Structural Steel With A Large Deformation

So-called constitutive equation is the equation which describes the relation between the stress and the strain or the relation between the rate of the stress change and the rate of the strain change. It is the physics equation for deformation of the plasmodium, and it is an equation to describe the character of the materials. It is a really important combination between mechanics and construction work. And it is a start when the damage is considered. That using a correct material constitutive equation is the foundation to set up a mechanics model. Damage is that under the function which refers to loading outside and environment, the degradation course of the material or structure caused by the defect within the plasmodium (such as little crackle , little hole in a utensil ) of the detailed view structure. Look from macroscopic, the damage is a kind irreversible course which consumes energy. While to describe the constitutive equation of material objectively, it is can't neglect the degradate influence which the damage coursed.The structure steel is a kind of isotropic material with better toughness. For the small deformation, the development of the constitutive theory is more and more mature. It is the model as follows that is applied to do the plasticity analyses : elastic-plastic model in ideal and strengthening models ,etc. With the big deformation, some author usually adopt a kind of simple means to get the big deformation constitutive equation. That is to say, the change rate of the elastic deformation is replaced with the elastic part of the deformation rate, and the change rate of the stress is replaced with the Jaumann differential coefficient of the Cauchy stress .So the small deformation constitutive equation is popularized. When damage is considered, first get the rate of the damage energy consume with the energy equivalent principle under the condition of small deformation, and then get the damage constitutive equations with the thermodynamics second methods. This is a kind of simple method , which obey the objectivity theory. The shortcoming is lacking of the basis in theory.Under normal or higher temperature , the plastic deformation of the steel structure often bring the plastic damage . At present, the constitutive equation which is get by using the forenamed method , is often applied to do the elastic-plastic analyses. Some people had gained the small deformation constitutive equation with second law of thermodynamics. And in the condition of the big deformation, he adopt the Jaumann stress increment of the Cauchy stress, then with the conversion principle between the Kirchhoff stress increment and the Cauchy stress increment , he get the big deformation elastic-plastic anisotropic damage constitutive equation with the parameter of the Lagrange.Based on the Rice-Hill big deformation elastic-plastic constitutive equation, the thesis tries to get the big deformation damage elastic-plastic constitutive equation, in conformity with stress field , strain field and damage field coupling . The thesis change the second type P-K stress tensor and Green strain tensor , which is described with the Lagrange parameter, into the tensor of Cauchy stress and tensor of Almansi strain described with the Euler parameter in instant type separately. Then, get the big deformation elesto-plastic constitutive equations in the instant type. The thesis couple the plasticity and damage to consider the influence of the damage. That is to say, the thesis get the dissipate tendency concluded the plasticity dissipation tendency and the damage dissipation tendency, and couple the two linearly. Among them, this thesis adapt the mixing strengthening yield condition in the elementary type. Then turn it into instant type. The thesis adapt the damage tensor, get the energy releasing rate of anisotropism damage of the rate material, then get the damage dissipation tendency according to the semi-rational formula of half a experience.