Product: ABAQUS/Explicit
This problem is a one-element verification problem for Mises plasticity with rate dependence. Three different element types are tested by stretching the element in the global y-direction. Figure 2.2.11–1 shows the eight elements used in the analysis. The 8-node brick element (C3D8R) appears twice. The plane stress instance has no boundary conditions applied to the out-of-plane direction, and the element should respond in a state of plane stress, except for some dynamic oscillations. The plane strain instance has zero displacement boundary conditions applied to all out-of-plane displacements, and the element should respond in a state of plane strain.
The bottom and top nodes of each element are given equal and opposite prescribed velocities (v, ramping up from 0 to 
) in the y-direction. The original length of each side of the elements is 
. The nominal strain rate is, therefore, 
, with its maximum value being 
. The plasticity model in elements 1 through 4 in Figure 2.2.11–1 has no rate dependence. The plasticity model in elements 5 through 8 is rate dependent.
This analysis is run with maximum strain rates of 2, 20, and 200 sec–1.
Figure 2.2.11–2 shows the deformed mesh at the maximum displacement. This corresponds to a nominal strain of 100%.
Figure 2.2.11–3 contains plots of nominal strain versus Mises stress at different strain rates for the plane strain cases. The names of the individual curves that appear in the graph legend are a concatenation of an element model type, an underscore (_), and the element numbers. The results obtained with the 8-node brick element are identical to those obtained for the 4-node quadrilateral at all strain rates. There are 12 curves plotted in the figure. For the three velocity values, the two element types (CPE4R and C3D8R) are plotted using the rate-dependent and rate-independent results. The velocities vary by an order of magnitude in each case, and the number of explicit time increments used also varies by an order of magnitude. The rate-independent results are plotted for each velocity case to verify that the rate-independent plasticity integration is not overly sensitive to the strain increment size.
Figure 2.2.11–4 contains plots of Mises stress versus nominal strain at different strain rates for the plane stress cases. The same 12 curves are plotted as for the plane strain case.
The results presented here are the same as those obtained with ABAQUS/Standard.
Strain rate of 20.
Strain rate of 2.
Strain rate of 200.
Overstress power law is entered as a piecewise linear function.
Demonstrates the use of the RTOL parameter on the *MATERIAL option.
