Theory Of Non-linear Dynamic Damage Mechanics And Numerical Modeling

Damage mechanics is a developing new branch of mechanics. It has mainly been developed since the late 1970's. At present, the study of damage mechanics still mainly concentrates on problems of damaged material and structrure under the static load. These are seldom researches on nonlinear dynamic damage of the material under the dynamic load. Nonlinear dynamic damage theory of concrete, joint rock mass has just been studied. So, the study of nonlinear dynamic damage is frontal subject of structural dynamics theory and damage mechanics theory. Aseismic design and protection of important structures or great dam are important engineering problem relating with national welfare and people's livelihood. It is very important to study nonlinear dynamic response and nonlinear dynamic damage process of important building or great dam structure system the under the action of dynamic loading, special earthquake loading. This study may supply some useful information and knowledge necessary for the aseismic design of many important structures. Therefore, the study of non-linear dynamic damage in important structures or great dam structures has a great important meaning not only in the academic but also in the practical engineering.First, the principle of minimum dissipative energy has been applied on brittle damage problem of linear elastic material. Based on "hypothesis of strain equivalence" and "hypothesis of complementary energy equivalence", two brittle damage models A and B of isotropy material have been established. Brittle damage evolution equation, constitutive equation and strain energy release rate model against two damage models A and B respectively have been given in this paper. The concept of the net effective stress which involves the affects of damage, pore pressure and porosity evolution in cracked rock mass have been introduced into the Mohr-Coulomb failure model. The nonlinear brittle dynamic damage failure model for damaged rock structures which can take consideration of the process of medium damage, rock mass fracture, pore press variation and porosity evolution has been developed. This model can describe the influence of material damage deterioration to cohesive strength and internal friction angle of damaged rock mass. The concepts of effective cohesive strength and effective internal friction angle have been put forward. It is pointed that the relative error of two damage models is 0.25. So, it is suggested that it is betterto choose model A for isotropic high strength and hardly cracked materials (for example most of metals) and to choose model B for isotropic weak strength materials, cracked materials and for anisotropic damage problems (for example geological materials). The brittle dynamic damage model has been compared with experiment result in literature. It is shown that numerical results get well with experiment results.Two damage models based on "hypothesis of strain equivalence" and "hypothesis of complementary energy equivalence" have been introduced into visco-elastic plastic constitutive equation respectively. And the principle of minimum dissipative energy has been connected with damage theory of damaged rock like medium. Based on some experiments, the visco-elastic plastic damage evolution equation of rock like medium has been given, and which including velocity of visco-plastic strain, visco-plastic damage development and accumulation strain hardening or softening. A visco-elastic plastic dynamic damage model of rock like medium has been established. And based on some numerical results, the nonlinear evolution character of visco-elastic plastic damage model has been discussed. This dynamic damage model has also been compared with experiment result in literature. It is shown that numerical results get well with experiment results.Finite element discretization methods of damaged structure has been given in this paper, which includes the calculation of dynamic equilibrium equation, damaged stiffness matrix, strain-displacement matrix and damaged damping matrix. The cases of geometric large displ...