Strong Discontinuity Analysis For Brittle Material

Strong discontinuity approach studies displacement discontinuity problems and has been attracted more attentions. The essential features of the method are to study displacement discontinuity problems in continuous displacement field and to simulate discontinuity by introducing enhanced assumed strain.Firstly displacement discontinuity has been introduced in the thesis and it is traced to the development of displacement discontinuity. And research findings of main stages are introduced, where strong (weak) discontinuity approach is highlighted. Secondly fundamental principle of strong discontinuity is stated and the constitutive equations of damage model and plasticity model in the strong discontinuity line are obtained according to brittle material and plastic material. By comparing many different algorithms, the paper applies the variational principle of total potential energy to the theory of strong discontinuity, and the balance on the discontinuity line is satisfied in weak form, so a symmetrical element stiffness matrix is obtained. One-dimensional and two-dimensional numerical results illustrate good performance of the present method in eliminating the stress locking phenomena in the symmetrical element stiffness matrix. In contrast with the traditional Petrov-Galerkin finite element method, this algorithm shows outstanding advantage on the computational efficiency aspect. Finally the strong discontinuity approach is applied to a structure with reinforced concrete columns and by introducing embedded discontinuities elements, crack in the structure is gotten.Strong discontinuity approach has many applications in engineering problems and is applied to many materials including brittle material and plastic material. Strong discontinuity approach links continuum and discrete approaches to the strain localization phenomena and provides a new approach to solve displacement discontinuity problems. Therefore the approach sets up a bridge between continuum mechanics and discontinuity mechanics.