On Application of the Third Medium Contact Method in Analysis of Geotechnical Problems

In computational contact mechanics, the contact constraints are usually applied using the Lagrange multiplier method, the penalty method, or alternative variants. Traditional contact approaches discretise the contact constraints in a weak sense, providing a stable interpolation scheme. However, they demand complicated search algorithms for contact detection at the interface between the intersecting bodies, and they usually lead to formulations that yield highly nonlinear tangent matrices, particularly for cases with realistic soil models and frictional contact. Recently, a new contact method based on the concept of a third medium has been developed, which overcomes the drawbacks of the conventional contact mechanics techniques. This new scheme is based on a space filling mesh in which the contacting bodies can move and interact. Contact constraints are enforced by changing the mechanical properties of medium with respect to the movements of the bodies. This new method has been developed for contact bodies undergoing large deformations using a hyper-elastic material law. In this study, the method is further extended to solve geomechanics problems in which the material behaviour is elastoplastic and the soil is subjected to large deformations. Potential merits of the third medium contact concept for analysing the geotechnical problems by the finite element method will also be addressed.