Microstructure and mechanical properties -- Polarization techniques to the rescue

Sébastien Brisard (1)

1 navier umr 8205 - Laboratoire Navier

Although the theoretical framework to upscale the mechanical properties of heterogeneous materials is now well set, homogenization remains a difficult task in practice. Available techniques broadly fall into two categories: mean/effective field techniques on the one hand (based on the solution to Eshelby's inclusion problem), and full field calculations on the other hand. Mean/effective field approaches are very flexible and result in tractable, semi-analytical estimates of the macroscopic properties. However, they account for a very limited description of the microstructure (usually, volume fractions and local orientations -- higher-order correlations being fully overlooked). Full field simulations can overcome this limitation, since they can be fed with "real" microstructures (resulting from 3D imaging). However, the cost of such computations can be extremely high. Besides, one can easily be overwhelmed with the amount of information that is delivered in return. This clearly calls for intermediate techniques that account for a richer description of the microstructure than mean/effective field approaches, while being less demanding than full field approaches. Quite suprisingly, such intermediate techniques are very scarce. In this talk, we will show that polarization techniques could help close what turns out to be a gap between the two ends of the range of upscaling tools. We will give a brief overview of the polarization framework for linear elasticity. We will then present three applications: improved variational estimates, spectral techniques and the Equivalent Inclusion Method. This will also be the opportunity to discuss practical issues such that: interfacing with molecular dynamics, producing meaningful results from finite resolution images, or introducing probabilistic, mesoscale descriptions of the microstructure to reduce the computational cost.

Domaines: Mécanique des matériaux [physics.class-ph]

Sébastien Brisard. Microstructure and mechanical properties -- Polarization techniques to the rescue. Multi-scale Materials Under the Nanoscope 2016, GDRI M2UN, Dec 2016, Paris, France. ⟨hal-01414044⟩