A Comparative Study on Modeling and Simulation of Contact Problems Using Enriched Techniques

This study presents a comprehensive comparison of three enriched numerical techniques – Extended Finite Element Method (XFEM), Element Free Galerkin Method (EFGM), and Coupled Finite Element- Element Free Galerkin Method (Coupled FE-EFGM) for solving frictional contact problems. Contact constraints are imposed using two distinct and widely adopted approaches – the penalty method and the Lagrange multiplier method within a numerical framework. These techniques illustrate diverse modeling paradigms, covering enriched finite element methods, meshless approximation, and hybrid formulations. The study examines the relative performance of these enriched techniques in handling contact problems, focusing on their mathematical formulation, computational efficiency in handling contact interactions with varying boundary conditions, material properties, and practical implementation challenges. The research examines the fundamental differences among these enriched numerical techniques in terms of discretization, basis functions, and treatment of contact conditions. The effectiveness of XFEM, EFGM and Coupled FE-EFGM is evaluated against benchmark problems from the literature considering aspects such as solution robustness, enforcement accuracy, numerical convergence, and computational cost. The comparative analysis highlights the unique features of each enriched technique in handling contact constraints, including XFEM’s ability to model discontinuities independent of mesh, EFGM’s meshless nature, and the hybrid competencies of Coupled FE-EFGM in combining the strengths of finite element and meshless techniques. The study provides a comprehensive comparison, offering practical guidelines for selecting the most appropriate enriched numerical technique (XFEM, EFGM, or Coupled FE-EFGM) based on factors such as computational cost, accuracy requirements, and complexity of the contact geometry for frictional contact problems in engineering applications.