{ "title": "Yeoh block in uniaxial tension", "kind": "theory", "source": "Uniaxial tension of the decoupled compressible Yeoh energy W = C₁₀ (Ī₁ − 3) + C₂₀ (Ī₁ − 3)² + C₃₀ (Ī₁ − 3)³ + κ/2 (J − 1)² (O. H. Yeoh, Rubber Chem. Technol. 66(5):754–771, 1993): σ = (λ/J) ∂W/∂λ with the lateral stretch found so σ_yy = 0 (bisection; E = 3, ν = 0.49, C₁₀ = μ/2, C₂₀ = −0.02, C₃₀ = 0.004)", "quantities": [ { "id": "sigma", "quantity": "axial Cauchy stress, stretch λ = 2", "measure": { "command": "solve.probe", "params": { "step": "Uniaxial", "at": [ [ 1, 1, 1 ] ] }, "pointer": "/nodes/0/stress/0" }, "value": 3.174263919393508, "tolerance": { "relative": 1e-06 }, "reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding" }, { "id": "lateral", "quantity": "lateral displacement at (1, 1, 1): l − 1", "measure": { "command": "solve.probe", "params": { "step": "Uniaxial", "at": [ [ 1, 1, 1 ] ] }, "pointer": "/nodes/0/displacement/1" }, "value": -0.2854505757255106, "tolerance": { "relative": 1e-06 }, "reason": "a homogeneous deformation the hybrid hex20 represents exactly: the tolerance admits the Newton tolerance and rounding" } ] }