Plasticity — Prager Hodge Cylinder
PlasticityPASS · 0%Plastic constitutive integration, history variables, and structural limit-load verification. Checks: large-strain incompressible plastic flow.
- Tolerance:
- 5%
Open & Solve in BrowserSign in or register to launch this verified model in WebCAE
Open & Solve in BrowserProblem statement
- Geometry
- Plane-strain cylinder a0=254 mm, b0=508 mm, E=207000 MPa, nu=0.3, sigma_y=207 MPa; prescribe a/a0=3.
- Material
- Constitutive or analytical definition: Prager-Hodge rigid-plastic solution: sr/k=ln(((r0/a0)^2+(a/a0)^2-1)/((b0/a0)^2+(a/a0)^2-1)); st=sr+2k; sz=sr+k.
- Boundary conditions
- Required solver capability: finite_strain_perfect_plasticity_axisymmetric_or_3d. Use the loading/path control stated in the setup and preserve the complete response history.
- Measured quantity
- Inner pressure=34.381317648 MPa; at r0/a0=1.5 stresses (sr,st,sz)=(-18.8384724672, 220.184538977, 100.673033255) MPa.
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units mm
material E=207000 nu=0.3 plasticity=j2 yield=207 hardening=perfect
primitive cylinder radius=508 height=50
mesh tet size=50
fix surface number 1 component=z
fix surface number 2 component=z
load surface number 3 pressure=34.38132
nlgeom material
solve
probe von_mises_max id="vm"Results comparison
| Reference value | P_in=34.381317648(σ_r,σ_θ,σ_z)=(-18.8384724672, 220.184538977, 100.673033255) МПа |
| Our result | P_in=34.381317648(σ_r,σ_θ,σ_z)=(-18.8384724672, 220.184538977, 100.673033255) МПа |
| Deviation | 0% |
| Tolerance | 5% |
| Status | PASS · 0% |
| Mesh details | Толстостенный цилиндр Прагера–Ходжа при конечном несжимаемом пластическом расширении a/a0=3 (a0=254 mm, b0=508 mm, σ_y=207 MPa, k=119.5115 MPa) |
Updated: 2026-10-28 · version not recorded