Elastic-plastic multi scale approach for localization problems—the embedded unit cell

This paper presents theoretical research of multi scale analysis of wide variety of composite materials, such as aluminum alloy or cement matrix with fibers or cement mass containing aggregates. We propose analysis approach, called Embedded Unit Cell (EUC), based on milestones of homogenization theory. The developed mathematical formulation was implemented using the Finite Elements Software package Simulia Abaqus. The aim of the EUC approach is to evaluate the response of composites using the solution sequence of homogenization theory, but to enhance the applicability of classical homogenization to structure zones that can’t be analyzed using classical homogenization due to method restrictions, such as the essential periodicity assumption. The verification studies include several selected cases, such as Local Global problem or boundary zones of homogeneous structure. The mathematical formulation as well as the numerical and thus software implementation are compatible with physical cases containing pure elastic and combined elastic plastic types of response. For the approach validation purposes, the selected examples can be mostly solved using classical homogenization, since they are based on heterogeneous material with periodic structure. Nevertheless, the benefit of the presented approach is in accurate evaluation of mechanical response in zones, where both or any of geometrical and material periodicity can’t be assumed.