Here is an implementation of implicit dynamic material point method (MPM) based on newmark's method.
The related Papers are listed as:
(2) AMPLE: A Material Point Learning Environment
(3) An implicit locking-free B-spline Material Point Method for large strain geotechnical modelling
The main algorithm is from the third paper. I reproduce some of its work, and Xie Mian (the first author of the third paper) makes a significant revision to my wrong implementation. You can trace these changes in the main function of the code. Additionally, López-Querol Susana, the correspondence author of the third paper, offers rather important assistance.
Importantly, this is a toy implementation. If one wants to do more research based on it, one may be intrested in the work of William M. Coombs
The aim of this repository is to decrease the effort for main algorithm and to focus more meaningful topics, like constitutive laws, contact and impact...
If any problems, my mail is [email protected]. I will reply and answer if I know.
AMPLE - A Material Point Learning Environment
AMPLE is a quasi-static implicit implementation of the material point method in MATLAB.
More informatio about AMPLE can be obtained from the project webapges:
https://wmcoombs.github.io/
AMPLE is an elasto-plastic large deformation material point code with a regular quadrilateral background mesh (the main code is ample.m). The continuum framework is based on an updated Lagrangian formation and two different constitutive models are included: linear elasticity and a linear elastic-perfectly plastic model with a von Mises yield surface.
It is suggested that users start by looking at the “index.html” file within the “documentation” folder.
The html files were complied with M2HTML (https://www.artefact.tk/software/matlab/m2html/) and they should
provide an overview of the code and how it all fits together. The scripts should also be compatible with
MATLAB’s “help” function.
Version history:
AMPLE - original AMPLE release
AMPLE_1.1 - version 1.1, released August 2020 - focused on runtime improvement