In this paper, we present a critical survey on homogenization theory and related techniques
applied to micromechanics. The validation of homogenization results, the characterization of …

In the context of shape optimization, we seek minimizers of the sum of the elastic compliance
and of the weight of a solid structure under specified loading. This problem is known not to …

This work is an attempt to provide a unified presentation of methods for the optimal design of
topology, shape and material for continuum and discrete structures. The emphasis is on …

Composites with extremal or unusual thermal expansion coefficients are designed using a
three-phase topology optimization method. The composites are made of two different …

We propose a rate-independent, mesoscopic model for the hysteretic evolution of phase
transformations in shape-memory alloys. The model uses the deformation and phase …

For modeling coherent phase transformations, and for applications to structural optimization,
it is of interest to identify microstructures with minimal energy or maximal stiffness. The …

Lattice structures are periodic porous bodies which are becoming popular since they are a
good compromise between rigidity and weight and can be built by additive manufacturing …

The set GU f of possible effective elastic tensors of composites built from two materials with
elasticity tensors C 1> 0 and C 2= 0 comprising the set U={C 1, C 2} and mixed in …

The problem of neutral inclusions for two-dimensional conductivity (or, equivalently, anti-
plane elasticity) is considered. Such an inclusion when inserted in a matrix containing a …

Strength-oriented optimization of porous periodic microstructures impacts on efficient design
of load-bearing lightweight structures avoiding mechanical failure. In this work, the maximal …