MECHANICS OF STRUCTURED MEDIA

Abstract

The research reported in this thesis is related to the mathematical description of the response of structured media. Three separate but conceptually linked topics are addressed. Firstly, a mathematical formulation for the description of average mechanical properties of structural masonry is presented. An element of structural masonry is regarded as a composite medium consisting of brick matrix intercepted by the sets of head and bed joints. The former are treated as aligned, uniformly dispersed weak inclusions, whereas the latter as continuous planes of weakness. A general three dimensional formulation is provided and is subsequently applied to estimate the average elastic properties of masonry and to investigate the conditions at failure. Subsequently, the approach mentioned above is extended to predict the elastic and elastoplastic properties of fibre and particle reinforced composite systems. An elastic material,with the mechanical properties ofthe reinforcement, isintercepted by two/three families of mutually orthogonal layers that possess the elastoplastic properties of the matrix. This system is then assumed to be equivalent to a fibre/particle reinforced composite after an appropriate orientation average is evaluated. The predictions of the elastic constants are satisfactory as compared to those derived from the equivalent inclusion method. The simulations of the elastoplastic response of a fibrous composite are also in a qualitative agreement with the experimental observation. Finally, the finite element method is employed to study the deformation of strain softening materials. Strain softening is considered as the localization of deformation into a shear band, which is treated as a bifurcation problem. A criterion is suggested for the selection of the inclination of a shear band from the multi-solutions produced by the necessary condition of bifurcation. A partitioning scheme is also proposed for the evaluation of a characteristic length related to the finite element implementation of the formulation. The initial stress method is then used to solve a strip footing problem. The numerical study is aimed at investigating the sensitivity of the load-displacement characteristics to the details, of discretization