A simple procedure to evaluate Cauchy stress tensor at the macro level based on computational micromechanics under general finite strain states

Abstract

This paper presents a new methodology to evaluate the Cauchy stress tensor at the macro level in computational micromechanics models. The use of control nodes to specify boundary conditions of a Representative Volume Element (RVE) allows deriving equations for the Cauchy stress components, with the consequence that numerical integration in the RVE is not performed. The proposed method allows use of computational micromechanics in commercial Finite Element software for a RVE subjected to general infinitesimal or finite strains. Because this methodology is obtained from the equivalence of power in the microscopic and macroscopic scales (Hill–Mandel principle) in a quasi-static problem, it is capable of dealing with micro-constituents under several constitutive laws. Numerical examples presented include simulations of elastic, hyper-elastic, and elasto-plastic fiber composite materials and a honeycomb microstructure. The present methodology can be used in multi-scale models to analyze non-linear structures made of heterogeneous materials.