Today new and advanced materials are constantly being developed to optimise various properties such as strength, weight, thermal/electrical conductivity and cost. These are often composite or porous materials. Examples include metal and polymer foams, ceramic-metal composites, porous fuel-cell electrodes, alloys, polymer blends, aerogels and filters.

Dr Andy Wilkins of the School of Physical Sciences at the University of Queensland is using computational simulations and modelling to determine the yield criterion of porous materials.  The porous material is modelled as a solid ductile "matrix", with spherical voids representing the pores in the material.  Dr Wilkins has so far been looking at symmetrical packings of voids within the matrix, such as simple-cubic, body-centred-cubic, and face-centred-cubic arrays (see figure 1), similar to the configurations of atoms in many crystals.  While these configurations may not be entirely realistic - industrially-produced materials would have randomly shaped voids with irregular packing - they provide a nice starting point, as they are easy to code into the computer and provide some insight into the non-regular situations.

To determine the yield criterion, Dr Wilkins first chooses a void volume fraction, up to the percolation threshold (at which point the matrix is no longer connected).  He then applies a stress state to the material, increasing the stress until the object yields.  Varying the way in which the stress is applied allows the yield point to be determined for many points in "stress space" - for instance the front and back faces of the cube being modelled may be pulled while the sides, top and bottom are kept still.  Alternately you may find the yield point by twisting two opposing faces in opposite directions.  This data is accrued for many different stress states, allowing the yield criterion for that void volume fraction to be interpolated.  This process is then repeated for different void volume fractions. 

Participants

Dr Andy Wilkins, Dr Tony Roberts
Department of Mathematics, University of Queensland

Publications

1. D. L. S. McElwain, A. P. Roberts, A. H. Wilkins, "Yield functions for porous materials with cubic symmetry using different definitions of yield" (invited paper), Advanced Engineering Materials (in press, 2006).

2. D. L. S. McElwain, A. P. Roberts, A. H. Wilkins, "Yield criterion of porous materials subjected to complex stress states", Acta Materialia, 54 (2006) 1995-2002.

3. A. H. Wilkins, A. P. Roberts, "A simple, versatile finite element method for fracture in heterogeneous materials", Submitted to Journal of Computational Physics, June 2006.

Reports

Summer Internship 2006 report - Timothy Sullivan (88 KB pdf)