author = {Schwen, Lars Ole and Wolfram, Uwe and Wilke, Hans-Joachim and Rumpf,
  title = {Determining Effective Elasticity Parameters of Microstructured Materials},
  booktitle = {15th Workshop on the Finite Element Method in Biomedical Engineering,
	Biomechanics and Related Fields},
  year = {2008},
  pages = {41--62},
  organization = {University of Ulm},
  abstract = {In this paper we study homogenization of elastic materials with a
	periodic microstructure. Homogenization is a tool to determine effective
	macroscopic material laws for microstructured materials that are
	in a statistical sense periodic on the microscale. For the computations
	Composite Finite Elements (CFE), tailored to geometrically complicated
	shapes, are used in combination with appropriate multigrid solvers.
	We consider representative volume elements constituting geometrically
	periodic media and a suitable set of microscopic simulations on them
	to determine an effective elasticity tensor. For this purpose, we
	impose unit macroscopic deformations on the cell geometry and compute
	the microscopic displacements and an average stress. Using sufficiently
	many unit deformations, the effective (usually anisotropic) elasticity
	tensor of the cell can be determined. In this paper we present the
	algorithmic building blocks for implementing these "cell problems"
	using CFE, periodic boundary conditions and a multigrid solver. We
	apply this in case of a scalar model problem and linearized elasticity.
	Furthermore, we present a method to determine whether the underlying
	material property is orthotropic, and if so, with respect to which
  pdf = { 1},
  isbn = {978-3-941573-00-0}