My task is to write a code from scratch for 3D elastoplasticity, namely a DP model (see for example DeSouza Neto, et al., 2008, Chapter 8) having yield surface

$$ f(\mathbf{\sigma},c) = \sqrt{J_2(\mathbf{s(\mathbf{\sigma})})} + \eta\,p(\mathbf{\sigma}) - \xi \, c(\bar{\epsilon}^p) $$


  • the first term the square root of the second invariant of the stress tensor;
  • $\eta$ and $\xi$ are chosen according to the Mohr-Coulomb surface that one approximates, which in turn depend upon
  • the friction angle $\phi$ and dilatancy angle $\psi$, this latter used since the flow rule is not assumed to be associative, so another parameter $\bar{\eta}$ is computed
  • $c$ is the cohesion, which in my linear assumed model depends on the cumulated plastic strain $\bar{\epsilon}^p$. The linear functional form this one takes is $c(\bar{\epsilon}^p) = c_0 + H \, \bar{\epsilon}^p$

My question is: I know how to implement the numerical integration algorithm to solve the (rate independent) rate equations, but I couldn't find a set of parameters $G$, $K$ (shear and bulk modulus respectively, or in alternative $E$ and $\nu$, Young and Poisson moduli), $\xi$ and $\eta$ or equivalently $\phi$ and $\psi$ and lastly $c_0$ and $H$, initial cohesion and plastic modulus.

I would like to ask for some references where such parameters are available, say for granular media. This task is developing oriented, it is just intended to implement an elastoplastic constitutive model, I only need some physically plausible parameters.

Reference: E. A. de Souza Neto D. Perić D. R. J. Owen, Computational Methods for Plasticity: Theory and Applications, 2008 John Wiley & Sons, Ltd.


Granular materials come in an infinite number of varieties and the best place to look for model parameters is the soil/rock mechanics literature.

For example, in some sands (but definitely not most sands), $K$ = 35 GPa, $G$ = 44 GPa, $\phi$ = 35$^{\circ}$, $\psi$ = 15$^{\circ}$, $c_0$ = 0 Pa. The cohesion of clays is, of course, higher; anywhere from 10 - 1000 KPa.

The hardening modulus $H$ is typically not used in soil/rock mechanics because perfect plasticity is assumed. If your model has it, you will either have to estimate it from experimental data or look for papers that use your particular model and see what numbers they have used.


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