Modeling of stiffness degradation in materials with micromechanical and nanomechanical effects

Research in the area of modeling of stiffness degradation in materials considering micromechanical and/or nanomechanical effects is an emerging field of fundamental and applied sciences. In this thesis, we first present a micromechanics-based damage constitutive model to predict the behavior of stiffness degradation and damage evolution in fiber reinforced cellular concrete (FRCC). The effective moduli of the FRCC are formulated based on Eshelby\u27s micromechanics and the orientational averaging process. The effects of random dispersion and orientation of inclusions are also accommodated. Damage models are subsequently considered in accordance with the Weibull\u27s probabilistic function to describe the varying probability of progressive fiber debonding and the continuum damage law proposed by Karihaloo and Fu (1989, 1990) to model the nucleation of microvoids in the cement matrix. The constitutive model incorporating the damage mechanisms is then implemented into a finite element code to predict the performance of FRCC.Secondly, a micromechanics-based damage constitutive model is developed to predict the effective stiffness of unidirectional laminated composites. A newly developed Eshelby\u27s tensor for an infinite circular cylindrical inclusion (Cheng and Batra, 1999) is adopted to model the unidirectional fibers and is incorporated into the micromechanical framework. The progressive loss of strength resulting from the partial fiber debonding and the nucleation of microcracks is incorporated into the constitutive model. The constitutive model incorporating the damage models is then implemented into a finite element code to numerically characterize the elastic behavior of laminated composites.Finally, a multi-scale model, based on a combination of the newly developed quasicontinuum model by Tedmor et al. (1999) and a finite element approach, is developed to characterize the properties of silicon thin films over a range of length scales. The potential-energy function comprising the 2-atom contribution proposed by Stillinger and Webber (1985) is adopted to describe the interactions among atoms. An optimization algorithm is developed to determine the equilibrium inner displacements under a given macroscopic deformation. The quasicontinuum model is then implemented into a finite element code for large-scale simulations of nanoindentation experiments