des DFG-Sonderforschungsbereichs 393

Numerische Simulation auf massiv parallelen Rechnern

Zeit: Freitag, 7.2.2003, 11:00 Uhr
Ort: Reichenhainer Straße 70, B 202
Vortragender: Prof. Kuczma (Zielona Gora, Polen)
Thema: Martensitic phase transformations as a variational inequality problem

We are concerned with the mathematical modelling and numerical simulation of the deformation process of a solid body made of the material which may undergo a martensitic phase transformation (PT). The martensitic PT is a first-order diffusionless solid-to-solid phase change that occurs by nucleation and growth in various crystalline solids, e.g. in the so-called shape memory alloys. At a microscopic level, the martensitic transformation consists of discontinuous changes in the crystal lattice of the high temperature phase with higher symmetry, conventionally called austenite, and that of the low temperature phase with lower symmetry, conventionally called martensite. The martensite phase may appear in many variants. The characteristic feature of a thermoelastic PT is its crystallographic reversibility which is the result of the essentially elastic accommodation of martensite domains, with the coherent interface capable of backwards movement. But, although the resulting microstructures are crystallographically reversible, martensitic phase transformations are thermodynamically irreversible since under loading/unloading cycles they are accompanied by dissipation of energy resulting in hysteresis loops. We are focused here on the thermoelastic stress-induced coherent martensitic PT in single crystal materials. The boundary value problem governing this hysteretic process has been formulated in the form of a variational inequality which has been solved incrementally as a sequence of complementarity problems. The existence of a unique solution of the incremental problem is shown. The included results of numerical experiments illustrate the characteristic features of the martensitic phase transformation process.

Das Seminar wird von Prof. Meyer geleitet. Interessenten sind herzlich eingeladen.

Gerd Kunert,