The research of this project aims at the effective and reliable simulation in nonlinear continuum mechanics with development of adaptive non-standard methods based on ultraweak formulations between
nonconforming, mixed and discontinuous Petrov-Galerkin (dPG) Finite Element Methods. Recent breakthroughs in the dPG methodology for nonlinear problems motivate the application of adaptive dPG schemes with built-in error control to further problems such as hyperelasticity, the obstacle problem and time-evolving elastoplasticity. Optimal convergence rates of adaptive nonlinear LS and dPG methods and Arnold-Winther FEM and guaranteed error estimation for dPG methods involving explicit constants and correct scaling will be investigated.