Plasticity — J2 Pure Shear

PlasticityPASS · <0.01%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: J2 invariants and engineering shear convention.

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; impose simple shear.
Material: Constitutive or analytical definition: sigma_eq=sqrt(3)|tau| and tau=G gamma in the elastic range.
Boundary conditions: Required solver capability: small_strain_j2. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: tau_y=sigma_y/sqrt(3)=144.337567297 MPa; engineering gamma_y=0.00178703654749.

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=10 dy=10 dz=10
mesh tet size=3
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=-147224318.64293998
load surface number 6 pressure=147224318.64293998
nlgeom material
solve
probe displacement_x at x=10 tol=0.01 id="ux"
probe displacement_z at z=10 tol=0.01 id="uz"
probe plastic_strain_max id="epmax"

Results comparison

Reference value	τ_y = 144.337567297 МПаγ_y = 0.00178703654749
Our result	τ_y(σ_xx) = 144.337568 МПаγ_y = 0.00178703647107εp(1.02τ_y) = 0.00497619
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	куб 10 мм, тет4 (≈100 тетр.); чистый сдвиг в главных осях (σ_xx = τ, σ_zz = −τ, роликовые опоры): изотропный J2 не отличает его от простого сдвига, повёрнутого на 45°

Updated: 2026-10-21 · WebCAE solver