Micromechanical simulation

Here, Wo is a characteristic level of back stress that primarily affects the initial slope of the uniaxial stress versus remanent strain curve, and m is another hardening parameter that controls how abruptly the strain saturation conditions are reached. Figure 2a illustrates the predictions of the effective stress versus the effective remanent strain from the constitutive law for uniaxial compression, pure shear strain, pure shear stress and uniaxial tension. It is interesting to note that the shear strain and shear stress curves do not coincide. This feature is due to the fact that the material can strain more in tension than in compression, and has been confirmed in micromechanical simulations. Figure 2b illustrates the uniaxial stress versus remanent strain hysteresis curves for two sets of the material parameters Wq and m. 

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

CNTs have extremely high stiffness and strength, and are regarded as perfect reinforcing fibers for developing a new class of nanocomposites. The use of atomistic or molecular dynamics (MD) simulations is inevitable for the analysis of such nanomaterials in order to study the local load transfers, interface properties, or failure modes at the nanoscale. Meanwhile, continuum models based on micromechan-ics have been shown in several recent studies to be useful in the global analysis for characterizing such nanomaterials at the micro- or macro-scale. 

I4Y. Liang, and, P. Sofronis, Micromechanics and Numerical Modeling of the Hydrogen-Particle-Matrix Interactions in Nickel-Base Alloys, Model. Simul. Mater. Sci. Eng., 11, 523-551 (2003). 

T. Bechthold, E.B. Rudnyi, and J.G. Korvink. Dynamic electro-thermal simulation of microsystems - a review . Journal of Micromechanics and Microengineering 15 (2005), R17-R31. 

Bowles, D.E. and Griffin, O.H. (1991a). Micromechanics analysis of space simulated thermal stresses in composites, part I Theory and unidirectional laminates. J. Reinforced Plast. Composites 10, 504-521. 

The analytical expressions of micromechanics are generally most accurate at low volume fractions of the filler phase. The details of the morphology become increasingly more important at higher volume fractions. This fact was illustrated by Bush [64] with boundary element simulations of the elastic properties of particulate-reinforced and whisker-reinforced composites. The volume fraction at which such details become more important decreases with increasing filler anisotropy, as was shown by Fredrickson and Bicerano [60] in the context of analytical models for the permeability of nanocomposites. 

In Odegard s study [48], a method has been presented for finking atomistic simulations of nano-structured materials to continuum models of tfie corresponding bulk material. For a polymer composite system reinforced with SWCNTs, the method provides the steps whereby the nanotube, the local polymer near the nanotube, and the nanotube/ polymer interface can be modeled as an effective continuum fiber by using an equivalent-continuum model. The effective fiber retains the local molecular stractuie and bonding information, as defined by MD, and serves as a means for finking tfie eqniv-alent-continuum and micromechanics models. The micromechanics method is then available for the prediction of bulk mechanical properties of SWCNT/polymer com-... 

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