Effective theories for multilayered plates (Ph.D. thesis)
We derive by $Γ$-convergence a family of effective plate theories for multilayered materials with internal misfit for scaling laws ranging from Kirchhoff's theory to linearised von Kármán. The main addition is the central role played by an intermediate von Kármán-like theory, where a new parameter interpolates between the adjacent regimes. We also prove the $Γ$-convergence of this limiting regime to the other two as well as the relevant compactness results and we characterise some minimising configurations for the scalings considered. Finally, we numerically investigate the interpolating regime employing the open source toolkit FEniCS to implement a discrete gradient flow. This provides empirical evidence for the existence of a critical value of the parameter around which minimisers are of different nature. We show $Γ$-convergence of the discretisation and compactness as the mesh size goes to zero.