Explicit dynamics: element erosion by plastic-strain failure, uniform bar at finite strain

Explicit dynamics (failure and element erosion)PASS · 1.46%

A uniform steel bar is stretched until the accumulated plastic strain reaches the failure value 0.3. The explicit solver (finite-strain updated Lagrangian formulation) removes the element at the moment the criterion is met; the displacement of the driven face at that moment is compared with the closed form u_f = L(exp(eps_fail + sigma_f/E) - 1) inside a +-0.5 % window. The erosion energy of one element is compared with a numerical integral of the work per unit true strain, and the energy balance (kinetic + internal + erosion energy against the work of the driven face) must close within 1 %. The mass of an eroded element stays on its nodes.

Tolerance:: 5%

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

Open & Solve in Browser

Problem statement

Geometry: Bar 50 x 5 x 5 mm, 10 x 1 x 1 HEX8 elements (structured), the face x = 0 is a symmetry plane.
Material: Steel: E = 200 GPa, nu = 0.3, rho = 7850 kg/m3; J2, yield 300 MPa, linear hardening with tangent modulus 40 GPa, failure at plastic strain 0.3.
Boundary conditions: The face x = 50 mm moves along x with a prescribed displacement (smooth start over 0.3 ms, then 1 m/s); finite strains; no bulk viscosity; time-step factor 0.8.
Measured quantity: Number of eroded elements at 0.995 u_f (must be 0) and at 1.005 u_f (at least 1); erosion energy per element against V0 * integral(sigma * J d eps); |E_total - W_external| / E_erosion over the whole run.

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=2e11 nu=0.3 density=7850 plasticity=j2 yield=300e6 hardening=linear et=40e9 fail="ep:0.3"
box dx=50 dy=5 dz=5
mesh hex nx=10 ny=1 nz=1
explicit endTime=0.0299114101 dtScale=0.8 saveStride=1000000 bulkQ1=0 bulkQ2=0 largeStrain=on
bc explicit_symmetry surface number 1
bc explicit_motion surface number 2 direction 1 0 0 displacement="0.00000000:0.00000000;0.00000500000000:0.0000416666667;0.0000100000000:0.000166666667;0.0000150000000:0.000375000000;0.0000200000000:0.000666666667;0.0000250000000:0.00104166667;0.0000300000000:0.00150000000;0.0000350000000:0.00204166667;0.0000400000000:0.00266666667;0.0000450000000:0.00337500000;0.0000500000000:0.00416666667;0.0000550000000:0.00504166667;0.0000600000000:0.00600000000;0.0000650000000:0.00704166667;0.0000700000000:0.00816666667;0.0000750000000:0.00937500000;0.0000800000000:0.0106666667;0.0000850000000:0.0120416667;0.0000900000000:0.0135000000;0.0000950000000:0.0150416667;0.000100000000:0.0166666667;0.000105000000:0.0183750000;0.000110000000:0.0201666667;0.000115000000:0.0220416667;0.000120000000:0.0240000000;0.000125000000:0.0260416667;0.000130000000:0.0281666667;0.000135000000:0.0303750000;0.000140000000:0.0326666667;0.000145000000:0.0350416667;0.000150000000:0.0375000000;0.000155000000:0.0400416667;0.000160000000:0.0426666667;0.000165000000:0.0453750000;0.000170000000:0.0481666667;0.000175000000:0.0510416667;0.000180000000:0.0540000000;0.000185000000:0.0570416667;0.000190000000:0.0601666667;0.000195000000:0.0633750000;0.000200000000:0.0666666667;0.000205000000:0.0700416667;0.000210000000:0.0735000000;0.000215000000:0.0770416667;0.000220000000:0.0806666667;0.000225000000:0.0843750000;0.000230000000:0.0881666667;0.000235000000:0.0920416667;0.000240000000:0.0960000000;0.000245000000:0.100041667;0.000250000000:0.104166667;0.000255000000:0.108375000;0.000260000000:0.112666667;0.000265000000:0.117041667;0.000270000000:0.121500000;0.000275000000:0.126041667;0.000280000000:0.130666667;0.000285000000:0.135375000;0.000290000000:0.140166667;0.000295000000:0.145041667;0.000300000000:0.150000000;0.0299114101:29.7614101"
solve explicit
probe explicit_eroded time=0.0228944831 id="nLo"
probe explicit_eroded time=0.0231230709 id="nHi"
probe explicit_erosion_energy time=0.0231230709 id="eeHi"
probe explicit_eroded id="nEnd"
probe explicit_erosion_energy id="eeEnd"
probe explicit_energy kind=total id="etEnd"
probe explicit_external_work id="ewEnd"
probe explicit_steps id="steps"

Results comparison

Reference value	u_f = 22.8588 mm (first erosion inside ±0.5 %)E_erosion/element = 373.115 J
Our result	no erosion at 0.995·u_f (0), 10 element(s) eroded by 1.005·u_f, 10 at the endE_erosion/element = 367.678 Jenergy balance 0.0111 %
Deviation	1.46%
Tolerance	5%
Status	PASS · 1.46%
Element family	Solid element
Mesh details	hex8 10×1×1 (10 elements (structured, native), 50406 explicit steps;: webcae_solve (native)

Updated: 2026-10-22 · WebCAE solver