Penalty method for 1d problem of two rods with basic concepts of contact mechanics of frictionless contact

Problems involving contact are of great importance in industry related to mechanical and civil engineering, but also in biomechanics and other applications. The contact interaction between surfaces in a bolted splice connection joint or area through which tire interacts with the road is not known a priori, leading to a nonlinear boundary value problem. Due to the rapid improvement of modern computer technology, today one can apply the tools of computational mechanics to analyze contact problems with limited accuracy, depending on design requirements. However, even now most of the standard finite element software is not fully capable of solving contact problems, including friction, using robust algorithms. The aim of this paper is to present some basic concepts of Contact Mechanics. To illustrate the difficulties arising in computational contact mechanics, Newton-Raphson scheme was used to solve simple 1D contact problem using penalty method