Much is happening at Aalto and I have been late with much what should be posted. Just to update things quickly, recently SMJ Seyedan has published a paper detailing a small strain enhancement for constitutive models for soils. The paper is here (open access). The idea is to have a thermodynamically consistent enhancement in the initial part of the stress-strain curve, which can be applied to any model using constant shear modulus. We tested it for Mohr-Coulomb and Modified Cam Clay, but it should work for other constitutive models too. Unfortunately, we have no such neat way to adjust the bulk modulus yet, but hopefully in the future… The paper comes with a Matlab code, so it is easy to try it out!
On another front, QA Tran has published a paper related to the null space errors in the Material Point Method. The paper is here and is also open access. The paper discusses null space errors and show how to filter them out efficiently. Such filtering is recommended when we have a problem with large deformations, in which number of material points in some grid cells increases above the initial value. That creates a problem when the data is tranferred from the nodes back to the material points – we have less nodes than the points and as such the transfer uses extra assumptions leading to errors. For example, having 4 nodes transferring data to 9 points, we need to create 9 values at the points from 4 values at the node – that is impossible without extra assumptions which may lead to errors.
The same paper also shows that use of a generalised-alpha integration scheme in the Material Point Method helps to damp out high frequency vibrations, without affecting the total energy and total momentum balance much. Very useful when we need a solution without high frequency noise – and much better than using an overall damping coefficient which alters the solution significantly.
S. Seyedan and W. T. Sołowski, “Enhancing Constitutive Models for Soils: Adding the Capability to Model Nonlinear Small Strain in Shear,” Advances in Civil Engineering, vol. 2019, Article ID 6016350, 11 pages, 2019. https://doi.org/10.1155/2019/6016350.
Tran, Q‐A, Sołowski, W. Temporal and null‐space filter for the material point method. Int J Numer Methods Eng. 2019; 1– 33. https://doi.org/10.1002/nme.6138