A coupled discontinuous deformation analysis and boundary element method for two-dimensional elastostatic problems

The use of numerical modeling techniques for dealing with continuum and discontinuum domains individually, has increased rapidly and proved valuable in the analysis of many engineering problems. Geotechnical engineering, by its very nature, often involves problems that are composed of both a continuum and discontinuum domains, and a coupling of two classes of numerical methods is desirable. This study aims at developing a methodology that couples two distinct modeling techniques, namely, the Discontinuous Deformation Analysis (DDA) and the Boundary Element Method (BEM) in solving two-dimensional elastostatics problems.; DDA and BEM are used to model different portions of a problem domain under consideration. Specifically, the DDA is used to simulate the problem in the near field, whereas the BEM is used to model the far field. The two methods are to be coupled through the mechanical interaction along the interface.; The DDA analyzes a region that is bounded by pre-existing discontinuities into individual blocks that obey certain kinematics constraints. The study adopts the updated Lagrangian formulation using the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor. The DDA model uses the coefficients of polynomial basis functions as the independent variables. Numerical examples together with simple physical experiments have been conducted to verify this DDA model.; The BEM domain is assumed to be linearly elastic and homogeneous, and may be extended to the infinite or semi-infinite domain. The direct BEM approach is used in which the displacements and tractions for a given problem are solved directly in terms of each other.; The formulation of the coupled work is implicit in nature; therefore, boundary element matrices are transformed into a stiffness matrix in order to be combined with the DDA. The contact constraints are implemented using the penalty method. The coupling formulation uses Coulomb's law to model the DDA-DDA and DDA-BEM interface behavior.; The developed hybrid model has been numerically verified. Potential applications examples of the present model are also introduced. Through these examples, the efficiency and capability of the developed hybrid model have been clearly demonstrated.