The two-space homogenization method

homogenization;poroelasticity;partial differential equations;Applied Mathematics

Murley, Jonathan

University of Waterloo

关键词: homogenization;    poroelasticity;    partial differential equations;    Applied Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/7099/1/Murley_Jonathan.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus on its application to poroelastic media. After describing the method, we provide examples to demonstrate that the resultant expressions are equivalent to an explicit derivation, which might not always be possible, and to outline the method for proving that the expressions converge to their macroscopic equivalents. Upon providing the basis for this method, we follow Burridge and Keller’s work for using this to prove the existence of Biot’s consolidation equations for poroelastic media and to provide expressions for the derivation of the parameters of these equations from the microstructure [5]. We then discuss the benefits and challenges that arise from this formulation of Biot’s consolidation equations.