A global–local strategy with the generalized finite element framework for continuum damage models

This paper presents a global–local strategy with the generalized finite element framework to simulate structural failure through nonlinear continuum damage models. The global problem is the scale of the structure which is discretized with relative coarse meshes while the local problem is a subdomain of interest of the global problem where refined meshes can be used to simulate localized crack growth. The proposed method uses the converged nonlinear local problem solution as enrichment functions for the global problem which is considered linear with no need for an iterative procedure to solve it. The strategy is validated and compared with reference solutions and experimental results with crack propagation in mode I and mixed-mode conditions in monotonic tests of quasi-brittle materials. The results show that the method has the capability to transfer the kinematic effects and the damage state variable that occurs in the local problem to accurately predict the global structural behavior under the damage process. The proposed strategy demonstrated the capability to accurately predict the experimental crack paths and load–displacement curves with a reduced number of iterations and degrees of freedom in relation to the conventional finite element and generalized finite element methods. •Nonlinear iterative procedure only at the local problem while global remains linear.•Kinematics of the local domain is transferred through enrichment functions.•Damage state is only updated in local problem and transferred to the global domain.•Accurate predictions for mode I and mixed mode quasi-brittle crack propagation.•It requires fewer iterations and processes much fewer DOFs than conventional FEM.