The definition of the material models is an important part of the numerical modelling of various physical problems. The material model (constitutive law) mathematically describes specific material behaviour observed at the macroscopic level. For example, it can describe the following phenomena: plasticity, creep, damage, viscoelasticity, hyperelasticity, heat conduction, etc.
In most cases, the material models provided by the used numerical simulation software are sufficient for the solved problem. However, for specific problems, the provided material models cannot adequately describe the desired material behaviour. In these cases, the required material models must be developed and integrated into the used software. This can be a challenging task depending on the complexity of the material models. The development of the material model requires deep knowledge of the relevant physical phenomenon, mathematics, programming, etc.
We have experience with the development of various material models. For example, we have developed material models for plasticity with various yield functions (smooth surface or non-smooth multisurface), with hardening and softening, with various return-mapping algorithms (closest point projection, generalized cutting plane, radial return mapping), etc. In the figure below, you can see the return mapping algorithm that returns the trial stress to the Hoek-Brown yield function.