Effective mechanical, transport and cross properties for distressed composite materials

Composite materials and materials that have been subjected to varying level of damage have been the subject of extensive research for several decades especially with regard to prediction of constitutive behavior. Classical homogenization techniques aim at replacing an actual heterogeneous body by a fictitious homogeneous solid, which globally behaves in the same way. In this thesis, we are considering the effect of body forces as an external forcing on the mechanical behavior of a heterogeneous material and the effect of heat source on the thermal constitutive equations, when the heterogeneous material is replaced by a fictitious or equivalent homogeneous material.; In order to achieve these objectives, as the first step, we use the theorems of minimum strain and minimum complementary energies to modify the bounds for strain energy in linear elasticity in order to consider the effect of body force. By means of the strain energy bounds and using the canonical form of the elasticity tensor for an isotropic material, bounds for the effective bulk and shear moduli of two- or multi-phase non-homogeneous materials may separately be obtained. With the same method by using defined artificial thermal and heat flux energies available in literatures, the bounds for the artificial or equivalent thermal energy are modified in the case of the existence of a heat source. By means of the bounds for equivalent thermal and heat flux energies, the bounds of the effective thermal conductivity of two- or multi-isotropic phase non-homogeneous materials may be obtained. Then, in the case of the existence of a heat source, the effective conductivity of composite materials comprising of a linear isotropic matrix containing linear isotropic inclusions, is evaluated in the frameworks of a self-consistent model. Next, the differential scheme and Mori-Tanaka method are modified for the case of an existing heat source to evaluate the effective conductivity of the composite materials (linear isotropic matrix containing linear isotropic inclusions).; The last part of the thesis is related to the effect of severe environmental conditions on the behavior of a composite material such as concrete. Freezing of liquid solutions in the solid matrix before damage occurs, causes the diffusivity of the concrete to be reduced, and after damage due to tensile stress in the concrete, which itself is due to increasing the volume of the solution during freezing, thus causing the diffusivity to increase. Based on composite mechanics and within the framework of self-consistent models, a theory is introduced to consider these effects on the diffusivity of concrete as a composite material. (Abstract shortened by UMI.)...