NUMERICAL SIMULATION OF CONTACT PROBLEMS USING XFEM/EFGM

Abstract

There are many problems in solid mechanics in which contact exists between two bodies. Some of the practical problems in which contact can be observed include metal forming operations, crack propagation, drilling pile etc. Contact problems are highly nonlinear and complex because the contact tractions as well as the area of contact are unknown. When two bodies come in contact with each other, the normal and the tangential stresses are generated in the contact zone and it is very important to consider these additional stresses created in the contact zone. The contact constraints are in the form of unilateral inequalities and need to be satisfied during the modeling of contact problems. The numerical modeling of frictional contact problems is one of the most challenging tasks in computational solid mechanics. The extended finite element method (XFEM) is an efficient and elegant technique to model diflerent types of discontinuities in solid mechanics problems. This method does not require conformal meshing or mesh adaption while modeling the discontinuities. The element free Galerkin method (EFGM) discretizes the whole domain into a set of nodes and the approximation function is entirely constructed from the knowledge of these nodes only. This method forms a strong and efficient tool to model different types of discontinuities present in the domain. In this work, the numerical simulation of frictional contact problems has been carried out using XFEM and EFGM. The nonlinear equations of equilibrium have been solved by the Newton-Raphson method. Several problems have been solved in order to demonstrate the efficiency, applicability and accuracy of these methods in solving contact problems. First of all, simple elastic contact problems were solved in which the two bodies are in contact with each other but there is no relative motion at the interface. 'l'hree elastic contact problems have been solved in chapter 4. Then, the work was extended to large deformation fTictional contact problems, in which both the geometric as well as the contact types of non-linearities were modeled. in such problems, the geometric non-linearity arises because of large deformation and the contact type of non-linearity arises because of frictional contact at the interface. Three large deformation frictional contact problems have been solved in chapter 5. Finally, the contact problems including large sliding at the interface were modeled and simulated. 'l'hree problems are solved in chapter 6 to demonstrate the applicability of node-to-segment approach in modeling and simulating large sliding contact problems.