As a beginner to soil constitutive modelling, I am learning the hypoplastic models by reading the matlab drivers. I am confused with the matlab file f_hyp.m in the model hypo_camclay. I don’t understand why there is a variable Laux, which is the multiplied by a factor 2. And when the stress increment is calculated, the code uses the Laux instead of Lep.
Thanks a lot.
Please see this paper for exaplanation of S and E matrices: Janda, T. and Mašín, D. (2017). General method for simulating laboratory tests with constitutive models for geomechanics. International Journal for Numerical and Analytical Methods in Geomechanics 41, No. 2, 304-312. You will find it in SoilModels publication database.
That algorithm requires stiffness matrix for tanget response in Newton-Raphson iterations, which is however not available in hypoplasticity. It could be approximated by Lep matrix, but unlike in elasto-plastic model, the resulting response could be in unloading softer than the true model response (due to the non-linear factor N in the model of the form L:D+N||D||), which would lead to non-convergent Newton-Raphson simulation. The factor “2” you ask about is an arbitrary factor to make the stiffness “stiff enough” for algorithm convergence but still leading to reasonable number of iterations. The higher this number, the more sure it is that the algorithm will converge, but the more iterations you need. “2” was found by trial and error to be a safe compromise.
Thank you so much! This recent paper helps me understand this algorithm to estimate the Jacobian.