LAUSR

Abstract This paper presents a novel methodology for the solution of nonlinear problems using the Stable Generalized/eXtended Finite Element Method (SGFEM) in two-scale approach. The nonlinear analysis is performed in a coarse mesh and the solution of a local problem, represented by a fine mesh, is used to enrich the partition of unity of the coarse mesh in the so-called global–local strategy. The SGFEM is adopted to deal with the problem of ill-conditioning of the stiffness matrix triggered by the enrichment strategy. Here, this problem is investigated for the first time for global–local analysis of physically nonlinear problem. In addition to the use of SGFEM, it is noteworthy that the relationship between the incremental-iterative process and changes in the constitutive variables are simultaneously updated on both scales. Differently from original GFEM global–local strategies, the evolution of the state variables is conduced only in the global scale. The local problem heritages the material degradation of the global scale, by using a mapping technique, and provides the numerically obtained functions that enriches the global approximation. Different constitutive models and material laws are adopted to incorporate the material degradation. Numerical examples are presented for validating this approach and to show its generality and efficiency.