The Carroll hyperelastic solid constitutive model.[^1]
**Parameters**
- The bulk modulus $`\kappa`$.
- The linear modulus $`\mu_1`$.
- The quartic modulus $`\mu_2`$.
- The second-invariant modulus $`\mu_3`$.
**External variables**
- The deformation gradient $`\mathbf{F}`$.
**Internal variables**
- None.
**Notes**
- The shear modulus is given by $`\mu = 2\mu_1 + 216\mu_2 + \mu_3/\sqrt{3}`$.