Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {M.~Arndt},
  title = {Modelling and numerical simulation of martensitic
  booktitle = {Analysis and Simulation of Multifield Problems},
  pages = {59-65},
  year = {2003},
  editor = {Wolfgang L. Wendland and Messoud Efendiev},
  volume = {12},
  series = {Lecture Notes in Applied and Computational Mechanics},
  publisher = {Springer},
  annote = {series,C4,multi},
  abstract = {We consider the time evolution of martensite-austenite
		  phase transformations in shape memory alloys. The process
		  is modelled on a microscopical, continuum mechanical level
		  by partial differential equations. Here the stored energy
		  density is used, which is a rotationally invariant and
		  nonconvex function of the deformation gradient with minima
		  at several wells. The energy dissipation observed in
		  physical experiments is modelled by an additional
		  homogeneous degree-1 dissipation potential for
		  rate-independent phase transformations. Furthermore,
		  capillary and viscous effects are handled by nonlocal terms
		  of higher order.
		  We discuss the existence of solutions of this model and
		  derive its energetic properties. Its discretization and
		  implementation is described. Special care is taken to
		  handle the nonlocal terms efficiently using wavelet
		  techniques. Finally we present numerical experiments for an
		  Indium-Thallium alloy under various loading regimes.}