On statistical strain and stress energy bounds from homogenization and virtual testing
Journal article, 2015

Computational homogenization for quasistatic stress problems is considered, whereby the macroscale stress is obtained via averaging on Statistical Volume Elements (SVE:s). The variational "workhorse" for the subscale problem is derived from the presumption of weak micro-periodicity, which was proposed by Larsson et al. (2011). Continuum (visco)plasticity is adopted for the mesoscale constituents, whereby a pseudo-elastic, incremental strain energy serves as the potential for the updated stress in a given time-increment. Strict bounds on the incremental strain energy are derived from imposing Dirichlet and Neumann boundary conditions, which are defined as suitable restrictions of the proposed variational format. For this purpose, both the standard situation of complete macroscale strain control and the (less standard) situation of macroscale stress control are considered. Numerical results are obtained from "virtual testing" of SVE:s in terms of mean values and a given confidence interval, and it is shown how these properties converge with respect to the SVE-size for different prescribed macroscale deformation modes and different statistical properties of the random microstructure. In addition, the upper and lower bounds for a sequence of increasing strain levels, for a fixed SVE-size, are used as "data" for the calibration of a macroscopic elastic-plastic constitutive model.

Virtual testing

Computational homogenization

Effective properties


S. Saroukhani

Cornell University

R. Vafadari

Ghent university

Robin Andersson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Fredrik Larsson

Chalmers, Applied Mechanics, Material and Computational Mechanics

Kenneth Runesson

Chalmers, Applied Mechanics, Material and Computational Mechanics

European Journal of Mechanics, A/Solids

0997-7538 (ISSN)

Vol. 51 77-95

Virtual Material Testing - A Computational Tool for the Prediction of Macroscale Properties based on Homogenization

Swedish Research Council (VR), 2011-01-01 -- 2013-12-31.

Subject Categories

Applied Mechanics

Areas of Advance

Materials Science



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