Finite elements for simulation of thin films wrinkling on elastic substrates

V doktorski nalogi smo se ukvarjali z gubanjem tankih lupin na elastičnih substratih. Ker gubanje spada med stabilnostne in močno nelinearne probleme, so takšni sistemi zelo težki za reševanje. S temi problemi se v svetu ukvarja zelo malo raziskovalcev, zato je to področje še precej neraziskano. Reševanja problema smo se lotili numerično z metodo končnih elementov. Za opis kinematike lupine smo uporabili Kirchhoff-Loveovo kinematično teorijo, ki je veljavna za tanke lupine. Lupinske končne elemente smo razvili sami, ostale končne elemente pa smo povzeli po literaturi. Računalniške kode končnih elementov smo implementirali s pomočjo programa Mathematica in njenima dodatkoma AceGen in AceFem. Razvili smo nekaj različnih lupinskih končnih elementov, ki so se med seboj razlikovali po načinu interpolacije, prostostnih stopnjah in uporabljenih materialnih modelih. Elastične substrate smo opisali najprej poenostavljeno z Wrinklerjevo podlago, nato pa tudi s 3D-končnimi elementi. Rezultate numeričnih simulacij smo na koncu ovrednotili z meritvami. Meritve smo primerjali z različnimi numeričnimi simulacijami, s čimer smo želeli preveriti, kateri numerični model je najprimernejši za opis pojava gubanja.In this doctoral thesis we focused on wrinkling of thin shells on elastic substrates. Wrinkling belongs among the highly non-linear stability problems and as a result, such systems are very hard to solve. Not many researchers work in the field of wrinkling, therefore this field has still very high research potential. We approached the problem with finite element method. The kinematic behavior of the shell was assumed to be according to the Kirchhoff-Love shell theory. This theory is only accurate when the shells are very thin. We developed all shell finite elements on our own. The theory of other finite elements was taken from the appropriate literature. The computer codes of finite elements were implemented with the help of Mathematica program and its add-on AceGen and AceFem. We developed several different shell finite elements which differ one to another by the type of interpolations, number of degrees of freedom and material models. Elastic substrates were initially modeled with Winkler\u27s foundation and later with 3D finite elements. Results of several different numerical simulations were at the end compared to the measurements. The goal was to check which simulation model is the most appropriate for modeling of the wrinkling phenomena