A computational homogenization approach for uniaxial stress state analyses of wavy fibrous materials

Abstract

Most of the classical computational homogenization techniques at finite strains comprise strain-driven homogenization approaches, in the sense that all the components of the macroscopic deformation gradient F are known as the input data to the homogenization procedure, being the macroscopic stress tensor computed afterwards. On the other hand, a macroscopic uniaxial stress state renders to a multiscale boundary condition driven by the knowledge of both macroscopic conditions, i.e., stress and strain. In this regard, this manuscript presents a computational homogenization approach for the analyses of such mechanical conditions. Aiming further numerical investigations of soft tissues and tissue engineering scaffolds, materials whose microstructures are composed of wavy arrangements of fibers, are investigated. The proposed numerical approach is grounded within a variational framework based on representative volume elements (RVEs) and formulated at finite strains. Tensile tests performed on numerical specimens larger than the RVEs are proposed as reference solutions. The numerical results point out that the present homogenization approach is able to predict not only the macroscopic (homogenized) quantities but also the microscopic kinematic fields investigated. One of the major contributions of the present work is the possibility to investigate how the changes of the macroscopic volume depend on the strain distribution at the microscale under macroscopic uniaxial stress states, since this behavior is intrinsically related to the microstructural material response.

A note on the multiscale volume changes of auxetic metamaterials assessed via digital image correlation

“…This work should be understood as a first approach to investigate, experimentally, the volume changes of auxetic metamaterials and their relations with the multiscale fields. Moreover, the results retrieved from such approach intend to provide important data to further investigations based on computations homogenization techniques [14][15][16] and metamaterial design via topology optimization [17].…”