We represent a biological tissue by a multi-constituent, fiber-reinforced material, in which we consider two phases: fluid, and a fiber-reinforced solid. Among the various processes that may occur in such a system, we study growth, mass transfer, and remodeling. To us, mass transfer is the reciprocal exchange of constituents between the phases, growth is the variation of mass of the system in response to interactions with the surrounding environment, and remodeling is the evolution of its internal structure. We embrace the theory according to which these events, which lead to a structural reorganization of the system and anelastic deformations, require the introduction of balance laws, which complete the physical picture offered by the standard ones. The former are said to be non-standard. Our purposes are to determine the rates of anelastic deformation related to mass transfer and growth, and to study fiber reorientation in the case of a statistical distribution of fibers. In particular, we discuss the use of the non-standard balance laws in modeling transfer of mass, and compare our results with a formulation in which such balance laws are not introduced.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the support of the Goethe-Universität Frankfurt (Frankfurt am Main, Germany), German Ministry for Economy and Technology (BMWi), contract 02E10326 (A. Grillo and G .Wittum), and the AIF New Faculty Programme (Alberta Innovates—Technology Futures, formerly Alberta Ingenuity Fund, Canada) as well as the NSERC Discovery Programme (Natural Science and Engineering Research Council of Canada) (S. Federico).
- Mass transfer
ASJC Scopus subject areas
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics