Plasticity — J2 Uniaxial Monotonic

PlasticityPASS · <0.01%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: yield detection and radial return.

Tolerance:: 5%

Open & Solve in BrowserSign in or register to launch this verified model in WebCAE

Open & Solve in Browser

Problem statement

Geometry: E=210000 MPa, nu=0.3, sigma_y=250 MPa, post-yield tangent Et=1000 MPa (H=1004.784689 MPa); strain control.
Material: Constitutive or analytical definition: sigma=E eps before yield; sigma=sigma_y+Et(eps-sigma_y/E) after yield; H=E Et/(E-Et).
Boundary conditions: Required solver capability: small_strain_j2_isotropic_hardening. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: sigma(0.0005)=105 MPa; sigma(0.002)=250.80952381 MPa; sigma(0.01)=258.80952381 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=210e9 nu=0.3 plasticity=j2 yield=250e6 hardening=linear et=1e9
primitive box dx=100 dy=10 dz=10
mesh tet size=5
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=-258809523.81
nlgeom material
solve
probe displacement_x at x=100 tol=0.01 id="ux"
probe stress_xx id="sxx"
probe plastic_strain_max id="epmax"
probe plastic_fraction id="pfrac"

Results comparison

Reference value	σ(0.0005)=105σ(0.002)=250.80952381σ(0.01)=258.80952381 МПа
Our result	ε(σ): 0.00050.0020.01 (tet10)
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	брус 100×10×10 мм, тет4 (≈1500 тетр.) и тет10; осевая нагрузка на торец, роликовые опоры на гранях симметрии (ux=0, uy=0, uz=0): однородное состояние; управление по НАПРЯЖЕНИЮ (нелинейное ядро ведёт нагрузку, не перемещение): на одноосном брусе σ(ε) однозначна, поэтому сверка ε при заданном σ эквивалентна σ при заданной ε

Updated: 2026-10-21 · WebCAE solver