## First, What is Isotropic Hardening Plasticity?

All non-linear FE solvers support various types of plasticity models. For example, Abaqus supports the following: isotropic hardening, kinematic hardening, multilinear kinematic, combined hardening, and Johnson-Cook hardening. Similarly, Ansys supports:

- Bilinear isotropic hardening (TB,PLAS,,,,BISO)
Multilinear Isotropic Hardening (TB,PLASTIC,,,,MISO)

Nonlinear Isotropic Hardening

Bilinear Kinematic Hardening (TB,PLAS,,,,BKIN)

Multilinear Kinematic Hardening (TB,PLAS,,,,KINH)

Nonlinear Kinematic Hardening (TB,CHABOCHE)

An isotropic hardening plasticity model needs a Young’s modulus, a Poisson’s ratio, an initial yield stress, and pairs of (\( \varepsilon_i^p, \sigma_i^p\)) to specify the plastic hardening behavior. There is no limit on how many pairs of plastic strain end yield stress you can use.

## Notes about Material Parameters

- If you use 100 line segments to represent a stress strain curve, then you need 202 material parameters.
- This does not mean that we need 202 experiments.
- One experiment is enough.
- The number of material parameters that is needed by a material model does not matter.
- What matters is how easy it is to find the material parameters, and if the material parameters are unique.
- Just because a material model has many parameters does not mean that it can fit an elephant!

## Unloading

The unloading response of this model is linear elastic until reverse plasticity occurs at at a true stress in compression that is equal to the final yield stress stress in tension. This is not how any polymer behaves! It will significantly underpredict the amount of recovery during unloading.

## Cyclic Loading

Another interesting and odd feature of the isotropic hardening plasticity model is that the predicted stress magnitude keeps increasing during cyclic loading. This is not how polymers behave.

## Can Isotropic Hardening Plasticity be Used for UHMWPE?

As a final example, let’s see what happens if we try to apply an isotropic hardening plasticity model to experimental data for UHMWPE. The figure below shows that the model can be made to accurately predict the response of the material in uniaxial tension, but as expected, it cannot accurately predict the unloading or cyclic response of the material. The figure also shows that the material model cannot predict both tension and compression at the same time. In other words, it would be difficult to predict large scale bending using this material model.

## Summary of Rate-Independent Isotropic Hardening Plasticity

- Can potentially be used with thermoplastics and thermosets; but not rubbers, foams, or soft polymers
- Easy to use
- Runs fast
- Can be accurate during monotonic loading
- Can be combined with strain-rate dependence
- Cannot accurately predict unloading (or residual strain)
- Cannot always predict both monotonic tension and compression
- Use with caution and significant validations (if you care about the FEA accuracy)