A Second-Order Multiscale Model for Finite-Strain Poromechanics Based on the Method of Multiscale Virtual Power

Author(s)

Thiesen, Jose Luis Medeiros ; Klahr, Bruno ; Carniel, Thiago Andre ; Blanco, Pablo Javier ; Fancello, Eduardo Alberto

• Document type: Journal article
• Source: JOURNAL OF ELASTICITY; v. 156, n. 3, p. 38-pg., 2024-07-10.

Abstract

A second-order multiscale theory based on the concept of a Representative Volume Element (RVE) is proposed to link a classical poromechanical model at the RVE scale to a high-order poromechanical model at the macro-scale in the context of finite-strain kinematics. The proposed theory is carefully derived from the Principle of Multiscale Virtual Power, which is a generalization of the Hill-Mandel Principle of Macrohomogeneity. The coupled governing equations of the low-scale and the homogenization rules for the flux and stress-like quantities are obtained by means of standard variational arguments. The main theoretical result is that the minimally constrained space for the pore pressure field allows for non-zero net fluid flow across the RVE boundaries, unlike first-order theories. The direct consequence of this finding is that the present theory can be consistently applied in cases where the low-scale (RVE level) exhibits substantial volume changes (swelling or shrinking) as a consequence of the evolution of the macro-scale kinematics. Details of formulation development and expression for the homogenized tangent operators are presented for those interested in the computational implementation of the model. (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