RD-V: 0200 Hardening Modulus

The plastic hardening modulus is evaluated in a Johnson-Cook material.

Figure 1.

The /MAT/LAW2 (PLAS_JOHNS) material model is used to study the plastic hardening modulus of a material.

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Input Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem are available in:


Model Description

Problem #1 1 is simulated in Radioss.

A tensile loading is applied to a cube with side lengths 25.4 mm. The bottom of the cube is fixed in the z-direction and an imposed velocity of 508 mm/s in the z direction is applied to the top of the block. The simulation was run to a final time of 0.05 seconds. A two elements per side mesh was studied.

The plastic hardening modulus, H, is used as the problem metric. In Radioss, the plastic hardening parameter, b, in /MAT/LAW2 (PLAS_JOHNS) material law is the same as the plastic hardening modulus, H.

The following system is used: mm, s, Mg.


The plastic hardening modulus is the slope of the stress versus plastic strain curve.

Figure 2. Stress versus Plastic Strain with Hardening Modulus


As shown in Figure 2, the hardening modulus from the simulation, H=794.225 Mpa, exactly matches the value input for “b” in /MAT/LAW2 (PLAS_JOHNS).

1 Buechler, Miles, Amanda McCarty, Derek Reding, and R. D. Maupin. "Explicit finite element code verification problems." In 22nd SEM International Modal Analysis Conference, Dearborn, MI. 2004.