[P11, Stefanelli] focuses on the modeling, analysis, and simulation of the macroscopic behavior of complex solids. Different effects, both of dissipative and nondissipative nature, will be addressed in connection with magnetostrictive, shape-memory, and thermoplastic materials. Modeling of biological membranes will be considered as well.
The mathematical techniques are centered on the analytical treatment of variational formulations of generalized dissipative-nondissipative evolution systems including generalized gradient flows and GENERIC flows. The main tasks include the development of approximation and existence theories for Generalized Standard Materials featuring the coupling of mechanical, electromagnetic, or thermal effects with phase transitions. The extension of the reach of Peridynamics to this context will be pursued and the behavior of active-material thin structures will be tackled by taking advantage of recently developed evolutionary Gamma-convergence techniques. In particular, the mechanics of protein-activated cell-membranes will be investigated.
[P11, Stefanelli] clusters all SFB activities in Solid Mechanics. Thermalized and magnetoelastic media will be studied together with [P2, Jüngel] and [P8, Praetorius], respectively, and then integrated in the SFB software platform with [P10, Schöberl]. Solvability of transportation-network systems is performed together with [P4, Markowich]. Low dimensional structures, also of biological relevance are studied in coordination with [P9, Schmeiser]. At the same time, this Project Part will benefit from interactions with a strongly linked international network including A. Mielke (Berlin), G. Savaré (Pavia), and M. Kruzik (Prague), among others.