Gradient elasticity with the material point method

Charlton, T.J.; Coombs, W.M.; Augarde, C.E.

Abstract

The Material Point Method (MPM) is a method that allows solid mechanics problems with large deformation and non-linearity to be modelled using particles at which state variables are stored and tracked. Calculations are then carried out on a regular background grid to which state variables are mapped from the particles. There have been a selection of extensions to the MPM, for example, a problem in the original method that arises when a material point crosses the boundary between one background grid cell and another is addressed by the Generalised Interpolation Material Point (GIMP) method [2]. An area yet to be studied in as much depth in MPM is that conventional analysis techniques constructed in terms of stress and strain are unable to resolve structural instabilities such as necking or shear banding. This is due to the fact that they do not contain any measure of the length of the microstructure of the material analysed such as molecule size of grain structure. Gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher-order terms [3]. This use of length scales makes it possible to model finite thickness shear bands that is not possible with traditional methods. Much work has been done on including the effect of microstructure on a linear elastic solid and has previously been combined with the Finite Element Method and with the Particle In Cell Method. In this work the MPM will be developed to include gradient effects.

Citation

Charlton, T., Coombs, W., & Augarde, C. (2023, March). Gradient elasticity with the material point method. Presented at ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering., Cardiff, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: ACME - UK 2016 24th Conference of the Association for Computational Mechanics in Engineering.
• Start Date: Mar 31, 2023
• End Date: Apr 1, 2016
• Acceptance Date: Mar 1, 2016
• Publication Date: Apr 1, 2016
• Deposit Date: Apr 12, 2016
• Publicly Available Date: Apr 14, 2016
• Publisher: Cardiff University
• Pages: 112-115
• Book Title: Proceedings of the 24th UK Conference of the Association for Computational Mechanics in Engineering, 31 March - 01 April 2016, Cardiff University, Cardiff.
• Public URL: https://durham-repository.worktribe.com/output/1150960
• Publisher URL: http://acme2016.sciencesconf.org/87700
• Additional Information: Conference date: 31 March - 1 April 2016