Kostas Danas (Laboratoire de Mécanique des Solides, École Polytechnique). From architected mechanical and magnetoelastic polymers to hierarchical instabilities.

In the present seminar, I will try to give an overview of our recent work on mechanical and active polymers, as well as their unstable response. The first part of the study deals with magnetoelastic materials and a number of instabilities present in such structures. Specifically, magnetorheological elastomers (MREs) are ferromagnetic particle impregnated rubbers whose mechanical properties are altered by the application of external magnetic fields. In addition, these composite materials can deform at very large strains due to the presence of the soft polymeric matrix without fracturing. From an unconventional point of view, a remarkable property of these materials is that while they can become unstable by combined magneto-mechanical loading, their response is well controlled in the post-instability regime. This, in turn, allows us to try to operate these materials in this critically stable region. These instabilities can lead to extreme responses such as wrinkles (for haptic applications), actively controlled stiffness (for cell-growth) and acoustic properties with only marginal changes in the externally applied magnetic fields. As a proof of concept, we study experimentally and theoretically the stability and post-bifurcation of a non-linear magnetoelastic film/substrate block in order to obtain active control of surface roughness. Cooperation of two otherwise independent loading mechanisms–mechanical pre-compression and magnetic field–allows to bring the structure near a marginally stable state and then destabilize it with either magnetic or mechanical fields. We demonstrate for the first time experimentally that the critical magnetic field is a decreasing function of pre-compression and vice versa. The experimental results are then probed successfully with full-field finite element simulations at large strains and magnetic fields. Motivated by those results and with a goal to extend the study to magnetoelasticity in the future, I focus next on the mechanical response of 3D printed hierarchical materials. We start with the question of on-demand design of instabilities and final patterning. Therein, we obtain experimentally via simulation-aided 3D printing the first three Euler-type buckling modes in hierarchical beam structures. This study shows the non-trivial interplay and richness of self-similar instabilities coupled at two different length scales. I will close by showing briefly a second example which deals with optimizing numerically and experimentally the elastic relative stiffness of random porous materials at very high porosities up to 82%. We show that by properly 3D printing polydisperse voids with maximum-to-minimum diameter ratios up to 1:50, one can hope to reach very close experimentally to the theoretical Hashin-Shtrikman bounds.

Personal web page: http://www.kostasdanas.com