Development of consistent simulation methods for coupled electro-thermo-viscoelastodynamical systems

• Applicant: Dr.-Ing. Marlon Franke
• Subject Area: Mechanics
• Term: from 2020 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 443238377

The focus of this continuation application is the development of consistent and efficient simulation methods for nonlinear coupled electro-thermo-viscoelastodynamical systems. These simulation methods are used e.g.\ for electroactive polymers, in particular dielectric elastomers, which are used in actuation and energy harvesting scenarios, whereby thermal, incompressible and material damping effects should be taken into account for realistic modelling. In the first funding period, partially thermodynamically consistent integrators for coupled electro-thermo-elastodynamically systems have already been developed. In the second funding period, the combination of fully polyconvex descriptions with thermodynamically consistent integrators for coupled electro-thermo-viscoelastodynamical systems will be pursued. The GENERIC formalism in combination with a polyconvex formulation using the tensor cross product opens up the possibility of developing new, thermodynamically consistent space-time discretisations. These promise a significant improvement in numerical stability and robustness. The intention is to replace the classical projection-based discrete gradients with structurally more simple discrete gradients. In addition, new polyconvex, reducible Hu-Washizu multi-field formulations shall be developed on the basis of the GENERIC formalism for the first time. From a methodological point of view, this will considerably extend the field of application of GENERIC, while at the same time new findings in the field of numerics are expected. The overall aim is to achieve consistency for all discrete balance laws for both reducible and irreducible formulations. This should lead to significant benefits in terms of numerical stability and robustness.

• DFG Programme: Research Grants
• International Connection: United Kingdom
• Cooperation Partner: Professor Antonio J. Gil, Ph.D.