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

Autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ELASTICITY; v. 156, n. 3, p. 38-pg., 2024-07-10.

Resumo

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)

• Processo FAPESP: 14/50889-7 - INCT 2014: em Medicina Assistida por Computação Científica (INCT-MACC)
• Beneficiário: José Eduardo Krieger
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/14221-2 - Geometria das bifurcações coronárias: um estudo exploratório das leis matemáticas para estimar as dimensões vasculares em bifurcações coronárias
• Beneficiário: Gabriela Hidalgo Vargas dos Santos
• Modalidade de apoio: Bolsas no Brasil - Iniciação Científica