von Mises material models are available for 2D, beam, shell, brick and tetrahedral elements. These material models are used when an elastic material is going to be loaded past the yield strength of the material. When this happens, plastic deformation will occur. The von Mises with - Hardening material model will use a bilinear curve to calculate the stress values. The elastic region of the stress versus strain has a slope equal to the modulus of elasticity, and the plastic region of the stress versus strain has a slope equal to the strain hardening modulus.
There are two types of hardening material models available. The isotropic hardening model involves yielding the entire yield surface uniformly. The kinematic hardening involves a shifting of the yield surface (primarily due to a reversal of loading). See Figures 1 and 2. The kinematic hardening model is preferred for analyses involving cyclical loading (Bauschinger effect), but the stress-strain behavior of the actual material should be used to decide between isotropic and kinematic hardening.
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Uniaxial stress-strain curve. If the part is taken beyond the yield stress, it begins to deform plastically. If taken to a maximum stress (point A) and the load is released, it unloads along the dashed line. If the part is loaded again, no additional plastic deformation occurs until the stress reaches point A. If the part is put into compression, it compresses elastically along the dashed line until it reaches point B, and then it yields in compression. With isotropic hardening, the change in stress from point A to point B is twice the maximum stress obtained. |
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Biaxial stress-strain curve. In the biaxial case, any combination of stress inside the initial yield surface (surface A) is in the elastic region. Once the part is taken beyond the initial yield surface, the part experiences plastic deformation. With isotropic hardening, the center of the yield surface remains fixed but the size of the surface increases. Any stress state inside the new yield surface (surface B) will experience elastic deformation; new plastic deformation occurs when the stress state reaches surface B. |
| Figure 1: Isotropic Hardening |
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Uniaxial stress-strain curve. If the part is taken beyond the yield stress, it begins to deform plastically. If taken to a maximum stress (point A) and the load is released, it unloads along the dashed line. If the part is loaded again, no additional plastic deformation occurs until the stress reaches point A. If the part is put into compression, it compresses elastically along the dashed line until it reaches point B, and then it yields in compression. With kinematic hardening, the change in stress from point A to point B is twice the yield stress. |
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Biaxial stress-strain curve. In the biaxial case, any combination of stress inside the initial yield surface (surface A) is in the elastic region. Once the part is taken beyond the initial yield surface, the part experiences plastic deformation. With kinematic hardening, the center of the yield surface moves but the size of the surface remains constant. Any stress state inside the new yield surface (surface B) will experience elastic deformation; new plastic deformation occurs when the stress state reaches surface B. |
| Figure 2: Kinematic Hardening |
The von Mises material properties are listed below. The von Mises material properties are identical for both models. In addition it may be necessary to define some Isotropic Material Properties.
Yield Strength
The yield strength of a material is the point on the stress versus strain curve where the material initially starts to go into plastic strain. After yielding once, the new yield stress depends on the type of hardening and the loading history.
Strain Hardening Modulus
The strain hardening modulus is the slope of the stress versus strain curve after the point of yield of a material.
When the material properties for a part are loaded from a material library, the strain hardening modulus is based on the three points that define the bilinear stress-strain curve; namely, (0,0), the yield point, and a third point identified in the library manager as the ultimate strength and elongation at 2 in. The strain hardening modulus is then calculated as follows:
strain hardening modulus = [Ultimate Strength - Yield Strength]/[(Elongation at 2 in)/100 - yield strain]
where yield strain is the strain corresponding to the yield strength, or yield strain = (Yield Strength) / (Modulus of Elasticity). The Ultimate Strength, Yield Strength, Elongation at 2 in, and Modulus of Elasticity are stored in the material library.
Structural Instability
When using a von Mises material model, the stiffness of the structure decreases, and the structure can become unstable, when the material yield strength is exceeded. In this state, the ability of the structure to bear the applied load is dramatically decreased as compared to when all stresses are within the elastic range. This instability will manifest itself as difficult numerical solution convergence, unstable or erratic stress results, and so on. The following adjustments of the model setup are helpful in this situation:
- Replace force loads with prescribed displacements.
- Use a smaller time step size during the unstable period, using multiple time intervals to analyze the event.
- Try to perform an MES Riks analysis, which is intended for capturing postbuckling phenomena. For additional information, refer to the following two help topics:
- The MES Riks Analysis content within the MES - Nonlinear Structural page
- The Analysis Parameters: MES Riks - Postbuckling page.