The effect of the mesh refinement on a multiscale domain decomposition method for the non-linear simulation of composite structures

Abstract

This article is focused on the study of a micro-macro LaTIn based Domain Decomposition Method (LaTIn-DDM) for the prediction of the nonlinear behavior of slender composite structures subjected to bending, buckling and delamination. Previous studies have shown that an adequate selection of the iterative parameters (search directions and macroscopic space) allow to improve the convergence rate and ensure scalability (i.e. number of iterations is independent of the number of subdomains) of the iterative schema. To obtain precise solutions, only the size reduction of the subdomains' discretization has been addressed (h-refinement), disregarding the option of increasing the polynomial degree of the finite elements (p-refinement) and ignoring their underlying effects on the information's transmission through the interfaces between subdomains. In this work and using linear and quadratic finite elements, h and p refinements on the subdomains and local h-refinement only along the edges of the subdomains were investigated. It is conclude that the prefinement in the whole subdomain not only enables to reach more exact solutions than using global or local h-refinement, but also the convergence rate is improved. These enhancements allow more complex simulations but using less degrees of freedom and less calculation time, even up to 97% faster.