Browsing by Author "Hackl, Klaus"
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- ItemGemischte und nicht-standard Finite-Elemente-Methoden mit Anwendungen(Zürich : EMS Publ. House, 2005) Carstensen, Carsten; Hackl, KlausMixed and non-conforming finite element methods form a general mathematical framework for the spatial discretisation of partial differential equations, mainly applied to elliptic equations of second order and are becoming increasingly important for the solution of nonlinear problems. These methods are under active discussion in the mathematical and the engineering community and aim of the workshop was to provide a joint forum for the current state of research.
- ItemA model for the evolution of laminates in finite-strain elastoplasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Hackl, Klaus; Heinz, Sebastian; Mielke, AlexanderWe study the time evolution in elastoplasticity within the rate-independent framework of generalized standard materials. Our particular interest is the formation and the evolution of microstructure. Providing models where existence proofs are possible is a challenging task since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments cannot be applied to prove the existence of solutions. In order to overcome this problem, we will incorporate information on the microstructure into the internal variable, which is still compatible with generalized standard materials. More precisely, we shall allow for such microstructure that is given by simple or sequential laminates. We will consider a model for the evolution of these laminates and we will prove a theorem on the existence of solutions to any finite sequence of time-incremental minimization problems. In order to illustrate the mechanical consequences of the theory developed some numerical results, especially dealing with the rotation of laminates, are presented.
- ItemVariational Methods for the Modelling of Inelastic Solids(Zürich : EMS Publ. House, 2018) Garroni, Adriana; Hackl, Klaus; Ortiz, MichaelThis workshop brought together two communities working on the same topic from different perspectives. It strengthened the exchange of ideas between experts from both mathematics and mechanics working on a wide range of questions related to the understanding and the prediction of processes in solids. Common tools in the analysis include the development of models within the broad framework of continuum mechanics, calculus of variations, nonlinear partial differential equations, nonlinear functional analysis, Gamma convergence, dimension reduction, homogenization, discretization methods and numerical simulations. The applications of these theories include but are not limited to nonlinear models in plasticity, microscopic theories at different scales, the role of pattern forming processes, effective theories, and effects in singular structures like blisters or folding patterns in thin sheets, passage from atomistic or discrete models to continuum models, interaction of scales and passage from the consideration of one specific time step to the continuous evolution of the system, including the evolution of appropriate measures of the internal structure of the system.