Plasticity — J2 Reverse Yield

PlasticityPASS · <0.01%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: reverse loading without unintended kinematic hardening.

Tolerance:: 5%

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Problem statement

Geometry: After loading to eps=0.01, reverse the strain with isotropic hardening and monitor the negative yield onset.
Material: Constitutive or analytical definition: For isotropic hardening, reverse yield occurs after elastic stress change 2 sigma_y_current.
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: Reverse yield begins at total strain 0.00753514739229; yield magnitude remains 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 loadpath="1,-1"
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	обратная текучесть при ε = 0.00753514739229радиус текучести 258.80952381 МПа
Our result	ε_onset = 0.00753514767σ(onset) = -258.80952 МПа
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	брус 100×10×10 мм, тет4 (≈1500 тетр.); путь λ: 1 → −1 (и контрольные 1 → −0.995, 1 → −1.01); 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