Plasticity — Plastic Hinge Rect

PlasticityPASS · 0.05%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: first yield and fully plastic moment.

Tolerance:: 5%

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Problem statement

Geometry: Rectangular section b=20 mm, h=40 mm, elastic-perfectly-plastic sigma_y=250 MPa under pure bending.
Material: Constitutive or analytical definition: My=sigma_y b h^2/6; Mp=sigma_y b h^2/4.
Boundary conditions: Required solver capability: section_plasticity. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: First-yield moment My=1333333.33333 N-mm; fully plastic moment Mp=2000000 N-mm=1.5 My.

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=210e9 nu=0.3 plasticity=j2 yield=250e6
box dx=120 dy=10 dz=20
box dx=120 dy=10 dz=20
move body2 0 0 20
boolean union target=body1 tool=body3
mesh tet size=8 order=2
fix surface number 1 component=x
fix surface number 27 component=x
fix surface number 3 component=y
fix surface number 29 component=y
fix edge number 10 component=z
load surface number 2 pressure=-275000000
load surface number 28 pressure=275000000
nlgeom material maxiter=25 steps=20
solve
probe limit_load_factor id="lim"
probe plastic_strain_max id="epmax"
probe plastic_fraction id="pfrac"

Results comparison

Reference value	M_p = σy·b·h²/4 = 2 000 000 Н·мм (= 1.5 M_y, M_y = 1 333 333.33 Н·мм)
Our result	M_lim = 1998986.82 Н·мм (λ_lim = 0.9086304)M_lim/M_p − 1 = -0.0507 %M_y — только качественно (течения нет при 0.9 M_y, есть при 1.1 M_y)
Deviation	0.05%
Tolerance	5%
Status	PASS · 0.05%
Mesh details	полумодель по ширине: 120×10×40 мм, тет10 (721 тетр.), идеальная пластичность; чистый изгиб парой сил — равномерное давление ±p на верхней и нижней половинах торца (статически допустимо при p = σy)

Updated: 2026-10-21 · WebCAE solver