Evaluation of stresses at the macro level based on computational micromechanics under finite strains

• An RVE-based multiscale methodology is developed to evaluate macro-stresses.
• The formulation is based on Hill–Mandel Principle, thus allowing treatment of finite strain problems and plasticity.
• Homogenization is performed by using control nodes without having to integrate in the RVE domain.

A post-processing methodology to evaluate stresses at the macro level is presented. The methodology involves homogenization of a Representative Volume Element (RVE) or Unit Cell at the micro level by means of control nodes, with the consequence that numerical integration in the domain is not needed. This can be employed in cases of infinitesimal or finite strains; elastic, hyper-elastic or elastic-plastic materials under quasi-static processes. The paper shows that evaluation of stresses or material properties can be done in a RVE of simple shape, such as a prism, or in a RVE of complex shape, such as a truncated octahedron, using the proposed methodology. Use of the methodology is illustrated for cases under various conditions, for which comparison with independent results shows excellent agreement.