Numerical simulation of superimposed finite strains using spectral element method

A novel approach to the numerical modeling of superimposed finite strains is proposed in the article. The spectral element method is used for analysis. This method is an effective modification of the finite element method that provides exponential decrease of computational error as the order of element. The discretization of static problems of nonlinear elasticity under superimposed finite strains is carried out for spectral elements using the Galerkin method. The developed approach is further used for solution of some model problems of superimposed finite strains. The presented examples include the insertion of hyperelastic cylinder into the prestressed cylinder, the formation of a hole in a preloaded nonlinear-elastic sample, and the nonlinear bending of the layered beam with a prestressed layer. The examples demonstrate the robustness of the proposed algorithms. The results obtained are in good agreement with the analytical solutions.