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The three-dimensional conservation equations relating energy and momentum transfer in a vibrated three-dimensional granular bed have been solved numerically by the finite element method. Two closures based on granular kinetic theory were used: one, the standard Fourier law relating heat flux to temperature gradient and the other, including an additional concentration gradient term. Each prediction of the two-dimensional axisymmetric granular temperature and packing fraction fields was compared against a one-dimensional model and three-dimensional experimental results, acquired using the technique of positron emission particle tracking. Both closures resulted in solutions that were in reasonable agreement with the experimental results, but it was found that differences between the predictions of each of the closures were relatively small in comparison to the anisotropy of the experimentally determined temperature distribution. [ABSTRACT FROM AUTHOR]

A comparison of the predictions of a simple kinetic theory with experimental and numerical results for a vibrated granular bed consisting of nearly elastic particles of two sizes has been performed. The results show good agreement between the data sets for a range of numbers of each size of particle, and are particularly good for particle beds containing similar proportions of each species. The agreement suggests that such a model may be a good starting point for describing polydisperse systems of granular flows. [ABSTRACT FROM AUTHOR]

Material properties such as hardness can be dependent on the size of the indentation load when that load is small, a phenomenon known as the indentation size effect (ISE). In this work an inverse finite element method (IFEM) is used to investigate the ISE, with reference to experiments with a Berkovich indenter and an aluminium test material. It was found that the yield stress is highly dependent on indentation depth and in order to simulate this, an elastoplastic constitutive relation in which yielding varies with indentation depth/load was developed. It is shown that whereas Young's modulus and Poisson's ratio are not influenced by the length scale over the range tested, the amplitude portion of yield stress, which is independent of hardening and corresponds to the initial stress for a bulk material, changes radically at small indentation depths. Using the proposed material model and material parameters extracted using IFEM, the indentation depth-time and load-depth plots can be predicted at different loads with excellent agreement to experiment; the relative residual achieved between FE modelling displacement and experiment being less than 0.32%. An improved method of determining hardness from nanoindentation test data is also presented, which shows goof agreement with that determined using the IFEM. [ABSTRACT FROM AUTHOR]