# Yield Laws in Isotropic Nonlinear Elastic Material Model

### Tips & Tricks

000968

29 January 2015

In the ‘Material Model - Isotropic Nonlinear Elastic’ window, you can select the yield laws according to von Mises, Tresca, Drucker‑Prager and Mohr Coulomb yield rules. Using these rules, you can describe the elastic‑plastic material behaviour. The yield function depends on the principal stresses or the invariants of a stress tensor. The criteria apply to 2D and 3D material models.

In the case of the yield stress rule according to von Mises, the yield criterion as a circular cylinder with hydrostatic axis is in the principal stress space. All stress states within this space are entirely elastic. Stress states out of this space are not allowed.

Alternatively, you can define the yield rule according to Tresca; in this case, the plastic yielding occurs as a result of the maximum shear stress.

Both yield rules require that the stress‑strain relations - due to the shape of the circular cylinder - must be symmetrical in the negative and in the positive zone. Using a time discretisation, the yield criteria are numerically integrated by the implicit Euler method. In RFEM, the discretisation is implemented in the individual load steps.

As an extension of the yield criteria, there are the yield rules according to Drucker‑Prager and Mohr‑Coulomb. In this case, the plastic yielding occurs when the maximum shear stress is locally exceeded. In the case of the rule according to Drucker‑Prager, there is a continuous surface area in the principal stress space. In the case of the yield rule according to Mohr‑Coulomb, there is a discontinuous surface area with a hexagonal cone.

Due to this yield surface, it is possible to define the stress‑strain relation of the diagram in the negative zone as asymmetrical. However, the relation must always be within the surface area of the yield rule. The figure shows the surface area for the yield rule according to Drucker‑Prager.