Nonlinear and Linearized Models in Elasticity 4.12.2023 ? Lennart Machill ? Oberseminar Differentialgeometrie, Universität Münster Many variational models in elasticity are nonlinear and nonconvex, resulting in difficult numerical approximations and high computational costs. The derivation of simplified effective theories still preserving the main features of the original systems plays therefore a significant role in current research. Despite the long history of the subject, the theory flourished in the last twenty years triggered by the availability of the rigidity estimate in [Friesecke, James, Müller ?02]. We discuss the latter estimate and give an introduction to variational theories in elasticity. A particularly interesting case is the approximation of thin three-dimensional solids with lower dimensional models, which requires analysing such inequalities with respect to the domain thickness. In this context, we will include recent results in viscoelasticity and discuss a nonlinear Korn inequality.