TFA and HS based homogenization techniques for nonlinear composites. (15th August 2021) - Castrogiovanni, Alfredo; Marfia, Sonia; Auricchio, Ferdinando; Sacco, Elio
Graphical abstract: Highlights: Homogenization of composites characterized by plastic response of constituents is studied. Reduced order models, based on Hashin–Shtrikman variational theory and Transformation Field Analysis, are proposed. Comparisons between TFA and HS based homogenization techniques and nonlinear finite element analyses are carried out. Converge analyses of the two approaches towards nonlinear finite element solutions are performed. Abstract: The paper presents two reduced order homogenization techniques for studying the response of nonlinear composite materials. The first approach is based on Transformation Field Analysis, which considers the presence of eigenstrains to account for inelastic strains, while the second approach is derived from Hashin–Shtrikman variational principle, which introduces eigenstresses, namely polarization stresses, on a homogeneous elastic reference material to account for the heterogeneity and the inelastic response. In particular, the case of elasto-plastic periodic composites is investigated. A Unit Cell is identified and divided in subsets. In each subset, the eigenstrains or eigenstresses are assumed uniform. A very effective technique is derived for the Hashin–Shtrikman approach updating the elastic reference material properties during the inelastic strain evolution. Numerical procedures are implemented to derive the nonlinear response of composites with plastic constituents. Several numerical applications are carried out to assess the effectiveness of the two presented reduced order models. A deep investigation on the differences and similarities of the two approaches is presented, proving their equivalence under particular circumstances. Simple and complex loading histories are considered, comparing the results with a finite element solution, considered as the reference solution.