Rubber Elasticity — Affine Network Deformation

A crosslinked polymer network deforms affinely: each chain end-to-end vector scales with the macroscopic deformation gradient. Neo-Hookean stress σ = nkT(λ² − 1/λ) with incompressibility constraint λ_x·λ_y·λ_z = 1.

Stretch λ (x-axis)

1.00
Network density nkT

0.50
Chain segments N_seg

20
λ_x =
λ_y = λ_z =
Engineering stress σ:

True stress σ_true:

Neo-Hookean model:
σ = nkT(λ²−λ⁻¹)/λ