Rula Ismael Hamad

Abstract :

This paper explores the role of variational inequalities and complementarity problems in solving complex contact mechanics phenomena, including non-penetration constraints, friction, and multibody interactions. Traditional methods in contact mechanics often fall short in modeling nonlinearities and discontinuities encountered in practical engineering scenarios such as tire-road interactions, gear contacts, and biomechanical joint modeling. Using mathematical frameworks such as variational inequalities and complementarity problems, this research provides a comprehensive theoretical and numerical basis for solving such problems. Case studies, including gear contact analysis and wear simulation of a total knee replacement, illustrate the use and effectiveness of these methods in structural design and analysis. The goal of the findings is to improve predictive models, increase safety and efficiency in the mechanical and biomedical field.