Variational Structures in Thermomechanics of Solids

The accurate description of the complex thermomechanical behavior of solids requires the efficient treatment of strongly nonlinearly coupled partial differential equations systems. These stem from the combination of balance and constitutive equations, which in turn can be often rephrased in a variational setting from the specification of suitable equilibrium and dissipation potentials.

The aim of the project is to set up a unified approach to such variationally-based evolutionary models for the thermomechanical evolution of deformable solids, in particular in phase transition of shape-memory and elastoplastic materials. The focus will be on innovative modeling and analytic techniques, as well as on real-scale computations. We will develop a new class of qualitatively more efficient and rigorously supported models in Thermomechanics and investigate specific applications in Engineering, Materials Science, and Natural Sciences.

The ambitious research plan will be realized within an international collaborative initiative between the Faculty of Mathematics of the University of Vienna and the Institute of Information Theory and Automation of the Czech Academy of Sciences. The cooperation of two teams will merge together the expertises of researchers in mathematical modeling, mathematical analysis, and computational mechanics. State-of-the-art tools from nonlinear partial differential equations and inequalities and the calculus of variations will be exploited and combined with three-dimensional Finite Elements approximations of inelastic solids behavior

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This was an international project, financed by the Austrian Science Fund (FWF) and by the Czech Science Foundation (GAČR) (with FWF project number I 2375-N32, and GAČR project number 16-34894L, see this link for further details). It lasted 3 years, from 02.05.2016 to 01.05.2019.

A list of scientific results of this project is available at this link.