ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

exp
1
1
2 1 where and are initial permeability and initial void ratio, respectively.
The growth algorithm is shown in Fig.1. Two types of internal constraints are relevant
in the context of articular cartilage growth. First one is solid-fluid intrinsic
incompressibility and the second constraint follows from the assumption that all of the
individual proteoglycan and collagen molecules are bound to the extracellular solid
matrix, so that their displacements and, consequently, their total deformations are equal.
Pre-growth
configuration
Mechanical loading,
time scale t sec
No. Of
increments/days
Growth PG &COL,
time scale T days
Post-growth
configuration
Fig.1. A diagrammatic representation of cartilage growth for certain number of days.
Growth occurs in stress free configuration.
The total deformation tensor is multiplicatively decoupled into elastic and growth
deformations, as
where and are elastic and growth deformation tensors of a constituent ,
respectively.
The growth occurs in the stress free configuration of the cartilage. The growth
deformation tensor is prescribed and equilibrium equations are solved for total and
elastic deformation tensors of constituents. The growth for increment or day,
1 / ∆
where is mass deposition rate, prescribed from Ficklin et al., (2009), ∆ is time
increment and is identity tensor. When the joint is subjected to mechanical loading due
to daily activities, the total deformation tensor becomes
where is deformation gradient tensor due to mechanical loading. The elastic right
Cauchy-Green deformation tensor then reads,