Plasticity in materials describes the effect that a deformation remains when the load is removed. In GeoDict, three different plastic material laws are available: Perfect Plasticity, Bilinear Hardening (Affine Linear Hardening) and Exponential Hardening.

For understanding plastic material laws, the two most important parameters are the elastic strain and the plastic strain which add up to the strain . The elastic strain is recoverable, whereas the plastic strain remains in the material after unloading. The relation of the elastic strain to the stress is described by Hooke's law, and the relation of the plastic strain to the stress is described by the chosen plastic material law. Please note that strain values in the formulas below are given in dimensionless form (not in %).

As long as the stress is lower than the yield stress of the material, the deformation is purely elastic. After this point, an increase in stress leads to a combination of elastic and plastic strains. The yield stress increases through the plastic deformation, which means that the material is elastic up to this point under a new load. Nevertheless, the course of the plastic material always depends on the initial yield stress.

The three available plastic material laws differ in the relation between the plastic strain and the stress:

Perfect Plasticity

As soon as the initial yield stress is reached, the stress remains at that level. From this point, the elastic strain stays constant, and all additional strain is purely plastic.

Bilinear (Affine Linear) Hardening

The stress is a linear function of the plastic strain

where is the Plastic Strain Hardening Modulus.
The plastic strain hardening modulus is not the slope of the stress-strain curve, since it only takes the plastic strain into account. The slope of the stress-strain curve (after the yield stress is reached) is the Tangential Modulus . The Plastic Strain Hardening Modulus and the Tangential Modulus are related as

with the young’s modulus . In the material definition in GeoDict, either the Plastic Strain Hardening Modulus or the Tangential Modulus can be set.

Exponential Hardening

The stress is related to the plastic strain via an exponential function

with the First Hardening Parameter (unit: [GPa]) and the dimensionless Second Hardening Parameter .