A thermodynamically consistent growth law for collagen fiber reinforced tissues in a mixture context

• The growth of two solid constituents of articular cartilage is addressed.
• The growth and elastic multiplicative decompositions are innate to each of them.
• Emphasis is laid on rate laws that satisfy the dissipation inequality.
• The cell energy density plays a significant role in this formulation.
• Growth is controlled by the position of the stress relative to a homeostatic surface.

The growth of mass of the two main solid constituents of articular cartilage is addressed in the context of saturated porous media endowed with an electrical charge. As a basic constraint, the two constituents undergo the same deformation gradient but the growth and elastic (accommodating) multiplicative decompositions are a priori innate to each of them. For the collagen, five rate laws are defined to govern the evolutions of the mass, of the homeostatic surface, of the fiber network orientation distribution function, of the pyridinoline cross-link density and of the cell energy density. For proteoglycans, only the evolutions of mass, of the homeostatic surface and of the cell energy density are considered. Emphasis is laid on devising rate laws that are easily constrained to satisfy the dissipation inequality. The cell energy density plays a significant role in this formulation. For each constituent, the growth model is stress-driven: growth is controlled by the position of the stress with respect to a homeostatic surface. These surfaces and the rate laws are endowed with properties that control the boundedness of the growth process.