A MODEL FOR DISCONTINUOUS DEFORMATION OF MULTI-BODY SYSTEM AND ITS APPLICATION

The theoretical importance and practical significance of discontinuous deformation analysis have been well recognized in geotechnical engineering. A number of attempts have been made in past studies. Nevertheless, at present there seem no methods available which can well deal with both continuous and discontinuous phenomena in the same mechanics framework. In this paper, a computational model for discontinuous deformation analysis of multi-body system is presented. In the model, various generalized finite elements with general interpolation modes which can include both rigid displacements and rotation and strain components are employed. Such generalized forms can be reduced to rigid finite elements, the displacement mode in discontinuous deformation analysis, and conventional finite elements. A contact-force element is developed for simulating the interface behavior. A certain distribution of interaction forces along the interface is pre-assumed and the behavior of the interfaces is controlled by both Mohr-Coulombs yield criterion for statics of the system and corresponding flow rule for kinematics of the system. The multi-body system comprising of rigid or/and deformable, continuous or discontinuous blocks is discretized by the generalized finite elements and the contact-force elements. On the basis of principle of virtual work, the so-called parametric variational principle for the discrete system is established in conjunction with the assumption that the contact stresses or forces at contact joints on the interfaces are taken as parametric variables which will be subjected to the constrain conditions given by both Mohr-Coulombs criterion and flow rule. According to the variational stationary conditions of the functional, the basic governing equations of the system which will be coupled with the constraint conditions of the parametric variables are formulated. The resulting issue of the problem is reduced to a linear complementary statement containing free variables and equality constraining conditions. A numerical algorithm is developed for a general multi-body system. Numerical examples for four typical problems are performed to illustrate the present method. It is shown that the proposed method can simulate complicated nonlinear behavior of interaction or contact problems of multi-body systems.