A body-force formulation for analyzing adhesive interactions with special considerations for handling symmetry

Adhesive interactions between particles are important in situations ranging from technological applications like atomic force microscopy to the initial stages of planet formation. In this work, we present a body force formulation with first-order convergence rate for the finite element analysis of adhesive interactions due to van der Waals force, which overcomes the restrictions of the commonly used surface force formulation. Though the classical Newton-Raphson method offers second-order convergence, substantial reduction in the computational cost per iteration justifies the use of present method in this case. First we discuss the general formulation, which is later modified for special cases like handling symmetry. We present a convenient implementation for reflective symmetry formulation, which can be easily extended to problems with any number of planes of symmetry. The axisymmetric formulation developed in this work provides significant computational benefits compared to a full three-dimensional formulation. The comparison of the results of our analyses with analytical solutions is provided for a number of benchmark problems. We also provide a comparison among general, reflective-symmetry and axisymmetric formulations in terms of accuracy and computational speed.