Multiple nonlinearities in the process of embedding and pulling out of nails: A numerical approach

Abstract

This paper presents a numerical approach to analyze the embedding and withdrawal process of nails. Multiple nonlinearities are considered: law of orthotropic large strain elasto-plastic materials and contact with friction. The Uzawa algorithm based on the bi-potential method is used to describe the nonlinearity of boundary conditions. A return mapping algorithm is applied to deal with the elasto-plastic constitutive laws. On the basis of the Updated Lagrangian formulation, we adopt a Rotationally Neutralized Objective hypothesis to describe the geometrically nonlinear behavior. The Newton–Raphson iterative method is employed to solve the nonlinear equation. The simulation results show the deformation and the stress distribution of wood in the process of the nail embedding and withdrawal. The effectiveness and accuracy of the numerical scheme are proved by comparing with the existing engineering experiments. The influence of friction coefficients on the nail embedding and withdrawal strength is also explored.