Valentin Calisti (Institute of Mathematics, Czech Academy of Science) - Emergence of elastostatic strain-gradient effects from topological optimization

In this presentation, the synthesis of architectured materials featuring strain-gradient effects is studied, in the framework of homogenized continuous periodic materials in 2D.  The unit cell is composed of a stiff material and a soft material. Its shape and topology are optimized by applying the topological derivative method, for which cost functions depending on the higher-order homogenized elasticity tensors are considered.

These tensors are formally defined from the two-scale asymptotic expansion method and the expression of the strain energy averaged on the unit cell. Then, their sensitivity to topological microstructural changes is presented,  resulting in so-called topological derivatives. They measure how the higher-order homogenized elasticity tensors change when a small circular inclusion is introduced at the microscopic level.

With this information, a topological optimization algorithm for higher-order homogenized media is implemented. Taking into account specific cost functions depending on the strain-gradient/strain-gradient coupling tensor, materials featuring strain-gradient effects are obtained. Both the method and the results are presented, as well as the different perspectives for extending this work.