Large-strain nonlinear rubber elasticity with incompressibility constraint
The neo-Hookean model describes large-strain hyperelastic behavior of rubbers and biological tissues. Its strain energy density is W = μ/2(I₁−3) where I₁ = tr(B) is the first invariant of the left Cauchy-Green tensor B = FFᵀ. Incompressibility (J = det F = 1) enforces volume preservation. Unlike linear elasticity, stress is nonlinear in stretch λ: σ_true = μ(λ²−1/λ) for uniaxial extension.