Second-order computational homogenization for bridging poromechanical scales under large deformations

Author(s)

Thiesen, J. L. M. ; Klahr, B. ; Carniel, T. A. ; Holzapfel, G. A. ; Blanco, P. J. ; Fancello, E. A.

• Document type: Journal article
• Source: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING; v. 433, p. 28-pg., 2024-10-30.

Abstract

We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill-Mandel principle of macro- homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating spaces. Numerical comparisons reveal that first-order models fail to accurately represent nonzero net fluid flow and volume changes at the micro-scale. In contrast, our second-order approach effectively captures nonuniform fluid flow across representative volume element boundaries, in agreement with results from direct numerical simulations. Our findings indicate that the classical first-order expansion of the pressure field is inadequate for poromechanical homogenization in cases involving micro-scale volume changes, such as swelling or contraction. The proposed second-order approach not only overcomes these limitations but also proves effective in cases where the principle of separation of scales is not strictly upheld. (AU)

• FAPESP's process: 14/50889-7 - National Institute of Science and Technology Medicine Assisted by Scientific Computing (INCT-MACC)
• Grantee: José Eduardo Krieger
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/14221-2 - Coronary bifurcations geometry: an exploratory study of the mathematical laws to estimate the vascular dimensions in coronary bifurcations
• Grantee: Gabriela Hidalgo Vargas dos Santos
• Support Opportunities: Scholarships in Brazil - Scientific Initiation