Johnson-Cook plasticity

This verification problem tests single-element models that are run under simple loading conditions (uniaxial tension, uniaxial compression, and simple shear). The purpose of this example is to test the Johnson-Cook plasticity model by comparing it to the Mises plasticity model with equivalent plastic hardening. Figure 1 shows the 26 elements used in the analysis in their original shapes. The elements in the top row are modeled using the Johnson-Cook material model; the elements in the bottom row are modeled using the Mises plasticity model with an equivalent hardening curve. The elastic material properties are Young's modulus = 124 GPa and Poisson's ratio = 0.34. The plastic hardening is chosen to be

where $\overline{\sigma }$ is the yield stress (unit in MPa) and ${\overline{\epsilon }}^{pl}$ is the equivalent plastic strain. The material properties are those of OFHC copper as reported by Johnson and Cook (1985). A plot of $\overline{\sigma }$ versus ${\overline{\epsilon }}^{pl}$ is shown in Figure 2.