Multiscale analysis of composite materials and structures

The manuscript presents a nonlinear multiscale computational procedure based on the philosophy of multilevel methods and which exploits the similarity between the classical engineering global–local design practice and multilevel methods. Both approaches separate the system response into the global and local effects. While classical substructuring-based schemes separate the global and local effects on the basis of domain decomposition principles often resorting to intuition and understanding the physics of the problem, multilevel approaches, carry out de facto a spectral decomposition automatically as part of the solution process. Seven multiscale problems were considered to validate the present formulation.