Mechanics Group, School of Engineering, Durham University

Project Updates

October 2009

In addition to the von Mises yield criterion, there is now a Tresca yield surface available. The consistent tangent of the analytical stress return (analytical Backward Euler stress return for von Mises) is calculated and in both cases quadratic convergence is approached.

August 2009

We have written a paper discussing the use of the MLPG method for modelling the elastoplastic behaviour of soil, and a preprint of this is now available online here (number 4/2009).

July 2009

Here is a summary of progress on the project to date with a plan for future work.

Brief updates are given along with new versions of the code here (available to local users only).

October 2008

I attended an ICCES Special Symposium on Meshless Methods and other novel computational methods in Suzhou, Jiangsu Province. Suzhou is a historic city, founded in the fifth cenury BC, and is sometimes known as the Venice of the East, or Paradise on Earth because of its natural beauty, classical gardens and canals (see right).

Dr Augarde gave a paper which briefly reviewed the coupling together of numerical methods in order to solve geomechnical problems. In particular, he discussed the coupling together of the scaled boundary method and the MLPG method, and presented some of our results for a flexible strip footing using the Tresca constitutive model.

September 2008

The computer code can now simulate flexible strip-footing problems using an initial stiffness algorithm with a Tresca constitutive model. The Tresca model is a planar yield surface, and so the stress return algorithm gives the exact solution in one step needing no further iteration.

I also attended a meeting on Stochastic PDEs at the International Centre for Mathematical Sciences in Edinburgh.

April 2008

I attended the 16th UK ACME conference in Newcastle and presented a paper (click for a pdf version) on calculating the residual force when solving elasto-plastic problems with a meshless method coupled to another method.

December 2007

The near field and far field regions are coupled by a penalty method. This must be taken account of when calculating the residual force. December was spent thinking about this.

November 2007

I attended an Advanced School on the Numerical Solution of Partial Differential Equations held at the Centre de Recerca Matematica, UAB in Barcelona.

September and October 2007

The code currently makes predictions for linear, elastic materials. We have begun extending this to allow for elasto-plastic behaviour in the near field (still small strain). In order to do this, we apply the load or displacement boundary conditions in so-called increments and use a predictor-corrector scheme. To make the elastic predictions a modified Newton Raphson method will be used. For the 'plastic corrections' a Forward Euler scheme will be implemented. The yield surface will be given by a Tresca model and associated flow will be assumed. Once this is working other numerical schemes will be implemented and tested. Other yield surfaces will also be employed.

August 2007

Continuing with July's theme (see below), initial stress boundary conditions are also being used to model the self-weight of soil.

The final week of August was spent at Glasgow University on an EPSRC course entitled 'Mathematical Modelling and Computational Methods in Solid Mechanics'. Slides of some of the presentations are now available from the summer school web pages. We're still waiting for the pictures to be uploaded though...

July 2007

A method for including body loads outlined in Deeks and Wolf (2002) is currently being implemented in the meshless local Petrov-Galerkin Scaled Boundary Method version of the code. This will enable us to model the self-weight of the soil.