The Use of Artificial Neural Network (ANN) for Modelling, Simulation and Prediction of Advanced Oxidation Process Performance in Recalcitrant Wastewater Treatment

Abstract

The anisotropic materials types to be considered here will be taken to have transversely isotropic symmetry. Perhaps the best known example is that of aligned fiber composite materials, but there are many other examples. A further condition will be taken such that the degree of anisotropy is large. This is in line with the interests here in high stiffness and high strength fiber composite materials as typified by carbon fiber, polymeric matrix systems. Such materials will be referred to as carbon-polymer systems. It is necessary to deduce the proper scale for the corresponding idealization of homogeneity for this class of materials failure problems. There are three obvious choices. The so called micromechanics level takes the individual fibers and the separate matrix phase in between them as the size scale for homogeneity. The next level up is the aligned fiber, lamina level, which then is much larger than the size of the individual filament or fiber. Finally, at yet a still much larger scale, the homogenization could be taken at the laminate level, involving the stacking of various lamina in various directions. It is the intermediate scale, the lamina level that is seen as having the proper balance between small scale detail, but large enough scale to include all the possible failure mechanisms which could be operative. An example of the importance of the scale of the failure mode will be given later. Thus all idealizations to follow are taken at the aligned fiber, lamina scale of homogenization. This is the same scale as that at which the volume averaged elastic properties for fiber composites are normally rationalized. The main purpose here is to develop the highly anisotropic failure criterion (for carbon-polymer systems) which is the companion piece to that of the isotropic case given in the previous section. To this end, take a polynomial expansion of the stress tensor through terms of second degree for transversely isotropic symmetry. Such an expansion will involve the following seven terms composed of the four basic invariants for this symmetry and the three quadratic combinations of the two linear invariants,