Gough–Joule piezocaloric effect: adiabatic thermoelastic heating under compression
Coupled transient thermoelasticityPASS · 0.01%Two-way thermoelastic coupling (u → T) via the dilatation-rate heat source q = −T_ref·β·tr(ε̇), where β = Eα/(1−2ν). Under adiabatic confined compression of a steel cube, the temperature rise scales linearly with volumetric strain ΔT = −(T_ref·β/(ρc_p))·tr(ε) (doubling the compressive force doubles ΔT, distinguishing true piezocaloric coupling from quadratic elastic work).Two-way thermoelastic coupling (u → T) via the dilatation-rate heat source q = −T_ref·β·tr(ε̇), where β = Eα/(1−2ν). Under adiabatic confined compression of a steel cube, the temperature rise scales linearly with volumetric strain ΔT = −(T_ref·β/(ρc_p))·tr(ε)… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Steel cube 20 × 20 × 20 mm in confined compression; 8-node hexahedra (hex8), 40 quasi-static steps.
- Material
- Steel: E = 200 GPa, ν = 0.3, ρ = 7800 kg/m³, α = 1.2 × 10⁻⁵ K⁻¹, c_p = 460 J/(kg·K), T_ref = 293.15 K (β = 6.0 MPa/K).
- Boundary conditions
- Insulated boundaries; lateral faces restrained in normal directions, axial compressive force ramped to F₁ = −200 kN and F₂ = −400 kN over 40 steps.
- Measured quantity
- Adiabatic temperature rise ΔT at F₁ = −200 kN and exact 2.000× linear scaling under doubled load F₂ = 2·F₁.
WebCAE Terminal
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units mm
material E=200000000000 nu=0.3 density=7800 kappa=40 specific_heat=460 alpha=0.000012
primitive box dx=20 dy=20 dz=20
mesh hex nx=4 ny=4 nz=4
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 4 component=y
fix surface number 5 component=z
fix surface number 6 component=z
load surface number 2 force=-200000 component=x
solve thermoelastic transient mode=quasistatic dt=0.025 tend=1.0 t0=20 tref=20 frames=2Results comparison
| Reference value | ΔT(F₁) = 0.1400 КΔT(2F₁)/ΔT(F₁) = 2.0000 |
| Our result | ΔT(F₁) = 0.1400 КΔT(2F₁)/ΔT(F₁) = 2.0000 |
| Deviation | 0.01% |
| Tolerance | 5% |
| Status | PASS · 0.01% |
| Element family | Solid element |
| Mesh details | hex8, куб 20 × 20 × 20 mm, 40 квазистатических steps со связкой Гоу–Джоуля q = −T_ref·β·tr(ε̇) |
Updated: 2026-10-27 · version not recorded