Document type
Journal articles
Document subtype
Full paper
Title
Stress formulation and duality approach in periodic homogenization
Participants in the publication
Cristian Barbarosie (Author)
Dep. Matemática
Anca-Maria Toader (Author)
Dep. Matemática
CMAFcIO
Summary
This paper describes several different variational formulations of the so-called “cellular problem” which is a system of partial differential equations arising in the theory of homogenization, subject to periodicity boundary conditions. These variational formulations of the cellular problem, all of them equivalent, have as main unknown the displacement, the stress or the strain, respectively. For each of these three cases, an equivalent minimization problem is introduced. The variational formulation in stress proves to have a distinguished role and it gives rise to two dual formulations, one in displacementstress and another one in strain-stress. The corresponding Lagrangians may be used in numerical optimization for developing algorithms based on alternated directions, of Uzawa type.
Date of Submisson/Request
2023-11
Date of Publication
2024-01
Where published
Discrete and Continuous Dynamical Systems - B
Publication Identifiers
ISSN - 1531-3492
Publisher
American Institute of Mathematical Sciences (AIMS)
Document Identifiers
DOI -
https://doi.org/10.3934/dcdsb.2024004
URL -
http://dx.doi.org/10.3934/dcdsb.2024004
Keywords
periodic homogenization
cellular problem
formulation in stress
dual formulation
Lagrangian
displacement-stress formulation
strain-stress formulation