Finite deformation theory of hierarchically arranged porous solids-I. Balance of mass and momentum

A finite deformation theory of porous solids, including an hierarchical arrangement of the pores is presented. The momentum balance equation and the mass balance equation are derived by means of formal averaging procedure. The procedure transforms the discrete network of pores into a continuum, without sacrificing essential information about orderly intercommunication of the pores The distinction between different hierarchical levels of pores is achieved by means of a hierarchical parameter. The theory has applications, particularly in the field of the mechanics of blood perfused soft tissues, where the distinction between arterioles, capillaries and venules is essential for a correct quantification of regional blood perfusion of the tissue. Deformations are assumed quasi-static. Both solid and fluid are assumed incompressible.