leads to a symmetric partial Cauchy stress, $\Bsigma^\iota$ for each species in contrast with the unsymmetric Cauchy stress of [@EpsteinMaugin:2000].

Constitutive framework and specific models {#sec:3}
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As is customary in field theories of continuum physics, the Clausius-Duhem inequality is obtained by multiplying the Entropy Inequality (the Second Law of Thermodynamics) by the temperature field, $\theta$, and subtracting it from the Balance of Energy (the First Law of Thermodynamics). We assume the Helmholtz free energy per unit mass of species $\iota$ to have the form:[^8] $\psi^{\iota} = \hat{\psi}^\iota(\bF^{\mathrm{e}^\iota},
\theta, \rho_0^\iota)$. Substituting this in the Clausius-Duhem inequality results in a form of this inequality that the specified constitutive relations *must not* violate. Only the valid constitutive laws relevant to the examples that follow are listed here. For details, see [@growthpaper].

An anisotropic network model based on entropic elasticity {#wlcm}
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The partial first Piola-Kirchhoff stress of collagen, modelled as a hyperelastic material, is $\bP^{\,\mathrm{c}} = \rho_0^\mathrm{c} \partial
\psi^\mathrm{c}/ \partial\bF^{\mathrm{e}^\mathrm{c}}$. Recall that $\bF^{\mathrm{e}^\mathrm{c}} = \bF\bF^{\mathrm{g}^{\mathrm{c}^{-1}}}$ is the elastic part, and $\bF^{\mathrm{g}^\mathrm{c}}$ is the growth part, respectively, of the deformation gradient, of collagen. Following Equation (\[isotropicgrowth\]), if we were considering unidirectional growth of collagen along a unit vector $\be$, we would have $\bF^{\mathrm{g}^\mathrm{c}} 