Bounding Elastic Constants of an Orthotropic Polycrystal using Measurements of the Microstructure
Document Type
Article
Publication Date
9-1996
Department
Department of Mathematical Sciences
Abstract
We show how information about the elastic stiffness and compliance of an orthotropic polycrystal may be obtained from measurements of the statistical properties of the microstructure. We begin by discussing the statistical properties of the governing equations and the hierarchy that results when the equations are averaged. Perturbation solutions are obtained in terms of low-order statistical information. Using methods previously developed, we derive bounds for the elastic stiffnesses and compliances. A hierarchy of bounds is derived using the statistical information obtained from measurement of the microstructure. We discuss the methods used to obtain the correlation functions of the microstructure and provide a specific example, using data obtained from a copper sample.
Publication Title
Journal of the Mechanics and Physics of Solids
Recommended Citation
Beran, M.,
Mason, T.,
Adams, B.,
&
Olsen, T.
(1996).
Bounding Elastic Constants of an Orthotropic Polycrystal using Measurements of the Microstructure.
Journal of the Mechanics and Physics of Solids,
44(9), 1543-1563.
http://doi.org/10.1016/0022-5096(96)00052-X
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5388
Publisher's Statement
© 1996