# Free and constrained thermal expansion at finite strain

A unit cube of 2 × 2 × 2 hex20, compressible neo-Hookean (E = 10, ν = 0.3) with an expansion
coefficient α = 10⁻³ from 20 degrees, heated to 220 by a temperature load in two nonlinear static
steps: **Free** (three symmetry planes) and **Held** (symmetry planes on all six faces). The
thermal stretch is ϑ = 1 + α ΔT = 1.2. Free, the cube grows to 1.2 along every edge without
stress; held, F = I, the material's mechanical part is F_m = ϑ⁻¹ I and its stress the neo-Hookean
pressure κ (J_m − 1) with J_m = ϑ⁻³: −3.510802.