Recently, additive manufacturing and topology optimization allowed a rupture in material sciences called “material by design” where it becomes possible to design and fabricate materials with a given microstructure. Such materials are referred to as architectured materials because their effective properties arise not only from the constitutive material but also from the regular microstructure. These materials are raising high interest because they allow the fabrication of materials which may not be found in nature: meta-materials.
Multiscale modelling and homogenization play a central role in this science area since they are the keys for capturing the effective behavior of such materials. More precisely, it was mathematically proven that there is a wide variety of non-standard effective behaviors which may be reached form a simple mixture of constitutive materials. However, this theoretical result does not yield the corresponding microstructures.
The main goal of this project is to explore this variety of non-standard elastic behaviors in order to find and synthesize architectured materials with unprecedented properties: very large volume variation, high shock strength, high energy absorption, high formability. Architectured materials technologies will benefit from this project but also “smart materials” coupling different physical phenomena and driven by an actuation energy.
The first scientific challenge of this project is the derivation of higher-order homogenization schemes applied to periodic microstructures and based only on two-scale separation without ad hoc assumptions. This will be performed first in linear elasticity and then extended to large deformations. The second scientific challenge is the derivation and the implementation of a topology optimization procedure based on the new homogenization schemes in order to generate architectured materials with chosen non-standard properties. Mathematical assumptions made in the theoretical developments will be made with special care so that the obtained architectured materials will be indeed producible and testable.
Monsieur Arthur Lebée (Laboratoire Navier)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
LNCC Laboratório Nacional de Computação Científica
IECL Institut Elie Cartan de Lorraine
MSME Modélisation et simulation multi-échelle
LEM3 Laboratoire d'études de microstructure, mécanique et matériaux
Navier Laboratoire Navier
IMATH - INSTITUT DE MATHEMATIQUES DE TOULON - EA 2134
Help of the ANR 530,474 euros
Beginning and duration of the scientific project: - 48 Months