Scales and Shapes in Continuum Thermomechanics

The complex thermomechanical behavior of deformable solids is usually described by systems of nonlinear partial differential equations and inclusions. These pose a wealth of mathematical challenges and call for refined modeling, analytical, and numerical treatments.

The nonlinear problems of Continuum Thermomechanics rest on inherent variational structures, most notably balance laws, energy conservation, normality principles, and dissipation. The aim of the project is to take advantage of such structures for deriving linearized and lower-dimensional models in continuum thermomechanics, solve topology-optimization problems for inelastic materials, and develop computational approaches to these problems. This calls for a combination of nonlinear functional analytic methods, with focus on abstract evolution equations and inclusions, especially of rate-independent type, thermomechanical modeling, in particular irreversible nonequilibrium thermodynamics and GENERIC formulations, and numerical methods such as finite elements, methods, global optimization, and structure-preserving schemes.

The project will establish a novel transnational research initiative. Martin Kružík and Ulisse Stefanelli are coordinating the teams on the Czech and on the Austrian side, respectively.

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This is an international project financed by:

• the

  Czech Science Foundation (GAČR)

  as Lead Agency, with a budget of 4.799K CZK (project number 21-06569K - link);
• the

  Austrian Science Fund (FWF)

  with a budget of 147K € (project number I 5149 - link).

The Czech part of the project started on 01.04.2021 and will last until 30.03.2024. The Austrian side of the project started on 01.10.2021 and will last until 30.09.2024.