any experiments demonstrate that isotropic ductile materials used in engineering applications develop anisotropic damage and shows significant variation in elongation to failure. This anisotropic damage is manifest by material microstructural heterogeneities and morphological changes during deformation. The variation in elongation to the failure could be attributed to the uncertainties in the material microstructure and loading conditions. To study this deformation induced anisotropy arising from the initial material heterogeneities, we first performed uncertainty analysis using current form on an internal state variable plasticity and isotropic damage model (Bammann, 1984; Horstemeyer, 2001) to quantify the effect due to variations in material microstructure and loading conditions on elongation to failure. We extend the current isotropic damage form of theory into an anisotropic damage form for ductile material in which material heterogeneities are introduced based on damage distribution functions converted into a damage tensor of second rank. The outcome of this research is a physically motivated, uncertainty-based, anisotropic damage constitutive model that links microstructural features to mechanical properties. This was accomplished by pursuing three sub goals: (1) develop and quantify uncertainty related to material heterogeneities, (2) develop a methodology related to a higher order tensorial rank of damage for void nucleation and void growth, and (3) integrate thermodynamically constrained damage with a rate dependent plasticity constitutive material model. Later, we also proposed a new ISV theory that physically and strongly couples deformation due to damage-related internal defects to metal plasticity.

The solar hot water storage tank is off great importance in the solar collector array. It allows transformed energy accumulation thus deals with the inconsistency between supply and demand. The suitable design of the storage tank can improve system efficiency. The storage capacity represents the balance between the amount of stored hot water and the tank's heat losses. The design of the storage capacity is based on three hypotheses. The coverage of hot water demand by solar energy, the ratio between storage capacity and solar thermal collector area and the prediction that the storage capacity corresponds to one- to twofold hot water demand. The purpose of this thesis is to share an understanding of the solar storage tanks design and to improve the design through numerical simulation, experimentations and general calculations. It also focuses on the confirmation of the used hypotheses and determination of the best way to design the solar storage tank for general practice and further potential discussions. The simulation model has three variables – the storage capacity, collector area and the number of occupants. The intent is to find the interdependence of these three variables. The purpose of the simulations is to modify the design of the solar tank based on the mutual influence of studied parameters. The modifications are performed based on the users' needs.