Projects per year
The material point method is ideally suited to modelling problems involving large deformations where conventional mesh-based methods would struggle. However, total and updated Lagrangian approaches are unsuitable and non-ideal, respectively, in terms of formulating equilibrium for the method. This is due to the basis functions, and particularly the derivatives of the basis functions, of material point methods normally being defined on an unformed, and sometimes regular, background mesh. It is possible to map the basis function spatial derivatives using the deformation at a material point but this introduces additional algorithm complexity and computational expense. This paper presents a new Lagrangian statement of equilibrium which is ideal for material point methods as it satisfies equilibrium on the undeformed background mesh at the start of a load step. The formulation is implemented using a quasi-static implicit algorithm which includes the derivation of the consistent tangent to achieve optimum convergence of the global equilibrium iterations. The method is applied to a number of large deformation elasto-plastic problems, with a specific focus of the convergence of the method towards analytical solutions with the standard, generalised interpolation and CPDI2 material point methods. For the generalised interpolation method, different domain updating methods are investigated and it is shown that all of the current methods are degenerative under certain simple deformation fields. A new domain updating approach is proposed that overcomes these issues. The proposed material point method framework can be applied to all existing material point methods and adopted for implicit and explicit analysis, however its advantages are mainly associated with the former.
|Number of pages||32|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Early online date||28 Sep 2019|
|Publication status||Published - 1 Jan 2020|
- Finite deformation mechanics
- Generalised interpolation
- Lagrangian mechanics
- Material point method
An efficient and locking-free material point method for three dimensional analysis with simplex elementsWang, L., Coombs, W. M., Augarde, C., Cortis, M., Brown, M. J., Brennan, A. J., Knappett, J. A., Davidson, C., Richards, D., White, D. J. & Blake, A. P., 4 Apr 2021, (E-pub ahead of print) In: International Journal for Numerical Methods in Engineering. 36 p.
Research output: Contribution to journal › Article › peer-reviewOpen Access
Robinson, S., Brown, M., Matsui, H., Brennan, A., Augarde, C., Coombs, W. M. & Cortis, M., 24 Nov 2020, (E-pub ahead of print) In: Canadian Geotechnical Journal.
Research output: Contribution to journal › Article › peer-reviewOpen AccessFile55 Downloads (Pure)
A Finite Element approach for determining the full load-displacement relationship of axially-loaded shallow screw anchors, incorporating installation effectsCerfontaine, B., Knappett, J., Brown, M., Davidson, C., Al-Baghdadi, T., Sharif, Y., Brennan, A., Augarde, C., Coombs, W. M., Wang, L., Blake, A., Richards, D. J. & Ball, J. D., 30 Jun 2020, (E-pub ahead of print) In: Canadian Geotechnical Journal.
Research output: Contribution to journal › Article › peer-reviewOpen AccessFile4 Citations (Scopus)63 Downloads (Pure)
Student thesis: Doctoral Thesis › Doctor of PhilosophyFile