Figure 1.

The stress balance hypothesis. The GAG and COL constituents have their own reference configurations, ${\kappa }_{\mathit{0}}^{\mathit{\text{GAG}}}\text{and}{\kappa }_{\mathit{0}}^{\mathit{\text{COL}}}$. The GAG constituent has the same configuration in ${\kappa }_{\mathit{0}}^P$ and κ₀, which is equivalent to ${\mathbf{F}}_{\mathit{0}}^{\mathit{\text{GAG}}}=\mathbf{I}$ and ^eS^GAG(0) = −α₁I. To balance this swelling stress, the COL network supports a tensile prestress produced by an initial COL deformation gradient tensor, ${\mathbf{F}}_{\mathit{0}}^{\mathit{\text{COL}}}$, which yields the initial collagen stress tensor, ^eS^COL(0) = α₁I. After a deformation F is applied, the constituent stresses are calculated relative to their respective reference configurations and using ${\mathbf{F}}^{\mathit{\text{GAG}}}={\mathbf{\text{FF}}}_{\mathit{0}}^{\mathit{\text{GAG}}}\text{and}{\mathbf{F}}^{\mathit{\text{COL}}}={\mathbf{\text{FF}}}_{\mathit{0}}^{\mathit{\text{COL}}}$.