Finite Element Modeling of Contact Problems

Contact is the principal way load is transferred to a body. The study of stresses and deformations arising due to contact interaction of solid bodies is thus of paramount importance in many engineering applications. In this work, problems involving contact interactions are investigated using finite element modeling. In the first part, a new augmented Lagrangian multiplier method is implemented for the finite element solution of contact problems. In this method, a stabilizing term is added to avoid the instability associated with overconstraining the nonpenetration condition. Numerical examples are presented to show the influence of stabilization term. Furthermore, dependence of error on different parameters is investigated. In the second part, a disc brake is investigated by modeling the disc in an Eulerian framework which requires significantly lower computational time than the more common Lagrangian framework. Thermal stresses in the brake disc are simulated for a single braking operation as well as for repeated braking. The results predict the presence of residual tensile stresses in the circumferential direction which may cause initiation of radial cracks on the disc surface after a few braking cycles. It is also shown that convex bending of the pad is the major cause of the contact pressure concentration in middle of the pad which results in the appearance of a hot band on the disc surface. A multi-objective optimization study is also performed, where the mass of the back plate, the brake energy and the maximum temperature generated on the disc surface during hard braking are optimized. The results indicate that a brake pad with lowest possible stiffness will result in an optimized solution with regards to all three objectives. Finally, an overview of disc brakes and related phenomena is presented in a literature review. In the third part, a lower limb donned in a prosthetic socket is investigated. The contact problem is solved between the socket and the limb while taking friction into consideration to determine the contact pressure and resultant internal stress-strain in the soft tissues. Internal mechanical conditions and interface stresses for three different socket designs are compared. Skin, fat, fascia, muscles, large blood vessels and bones are represented separately, which is novel in this work.