Solution bound and nearly exact solution to nonlinear solid mechanics problems based on the smoothed FEM concept

Node-based and edge-based smoothed FEM (NS-FEM and ES-FEM), and α-FEM are extended to solve nonlinear problems. The nonlinear strain field is smoothed using the gradient smoothing. The continuous scalar scaling factor α enables the α-FEM continuously transforming from overestimated model to underestimated model. Numerical examples reveal that ES-FEM is a robust and stable method with high accuracy and computational efficiency for nonlinear problems. The exact solution in strain energy of force driven problems can be bounded by NS-FEM and FEM. The α-FEM can also be “tuned” to find nearly exact solution to nonlinear mechanics problems of solids of complicated geometry.