Plasticity — Nonproportional Plate

PlasticityPASS · <0.01%

Plastic constitutive integration, history variables, and structural limit-load verification. Checks: nonproportional return mapping and unloading history.

Tolerance:: 5%

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Problem statement

Geometry: Use the Abaqus uniformly loaded elastic-plastic plate Case 1: E=68.94 GPa, yield=68.9 MPa, hardening slope=68.9 GPa and the published ten-step load history.
Material: Constitutive or analytical definition: Published exact nonproportional material history.
Boundary conditions: Required solver capability: plane_stress_kinematic_hardening. Use the loading/path control stated in the setup and preserve the complete response history.
Measured quantity: Open exact table includes plastic strain 0.500e-3 at 103.422 MPa, 1.500e-3 at 172.369 MPa, and 1.010e-3 after unloading to 0.69 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=68947.57e6 nu=0.3 plasticity=j2 yield=68.94757e6 hardening=linear et=34473.785e6 kinematic=1.0
primitive box dx=100 dy=100 dz=2
mesh hex size=25
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=-172.369e6
nlgeom material
solve
probe stress_xx id="sxx"
probe plastic_strain_max id="epmax"

Results comparison

Reference value	ε_p(103.422 MPa)=0.500e-3ε_p(172.369 MPa)=1.500e-3ε_p(0.69 MPa)=1.010e-3
Our result	ε_p(103.422 MPa)=0.50000e-3ε_p(172.369 MPa)=1.50000e-3ε_p(0.69 MPa)=1.01000e-3
Deviation	<0.01%
Tolerance	5%
Status	PASS · <0.01%
Mesh details	Упругопластическая пластина с кинематическим упрочнением Прагера (E=68.9476 GPa, σ_y=68.9476 MPa, H=68.9476 GPa, β=1.0), нагружение до 172.369 MPa с последующей разгрузкой и обратной текучестью до 0.69 MPa

Updated: 2026-10-28 · version not recorded