Richard Ostwald

A thermodynamically consistent finite strain micro-sphere framework for phase-transformations

We extend a thermodynamically consistent finite strain micro-sphere framework elaborated by Carol et al. towards the modelling of phase-transformations to allow for the simulation of polycrystalline solids such as, e.g., shape memory alloys and shape memory polymers undergoing large deformations. The considered phase-transformation mechanism is based on statistical physics and allows the consideration of an arbitrary number of solid material phases. The specifically constructed, non-quadratic Helmholtz free energy functions considered in every micro-plane of the micro-sphere framework are extended to include individual Bain-type transformation strains for each of the phases. The total strains acting in each material phase are multiplicatively decomposed into elastic strains and transformation strains. (Less)

Modelling and simulation of phase transformations in elasto-plastic polycrystals

In this work, a new framework for the simulation of shape memory alloys (SMA) and TRIP steels undergoing martensite-austenite phase-transformations is introduced. The goal is the derivation and elaboration of a generalised model which facilitates the reflection of the characteristic macroscopic behaviour of SMA as well as of TRIP steels. The foundation of the overall formulation is a scalar-valued, thermodynamically consistent, statistical physics based model for the simulation of SMA. As this work proceeds, the model is implemented in affine and non-affine micro-sphere formulations in order to capture polycrystalline behaviour and to simulate three-dimensional boundary value problems. Moreover, a coupling to plasticity is introduced, additionally enabling the capturing of the macroscopic behaviour of TRIP steels. Finally, the implementation of a three-dimensional finite-deformation phase-transformation model that focuses on representative transformation directions is elaborated in a thermo-elastoplastic framework.