Micromechanics self-consistent models

Figure 1. The remanent strain saturation curve dividing remanent strain space into regions that are attainable and unattainable by a polycrystal assembled from randomly oriented tetragonal single crystals. Only remanent strain states below the curve are attainable by such a material. The dots are numerical results from Landis (2003a) obtained using a micromechanical self consistent model, and the line is one divided by the function/given in Eqs. (2.7) and (2.8). The remanent strain invariants 4 and are defined in Eq. (2.5) and the results are normalized by the saturation strain in axisymmetric compression s. ...

In order to understand the effects of filler loading and filler-filler interaction strength on the viscoelastic behavior, Chabert et al. [25] proposed two micromechanical models (a self-consistent scheme and a discrete model) to account for the short-range interactions between fillers, which led to a good agreement with the experimental results. The effect of the filler-filler interactions on the viscoelasticity... 

The earliest works of trying to model different length scales of damage in composites were probably those of Halpin [235, 236] and Hahn and Tsai [237]. In these models, they tried to deal with polymer cracking, fiber breakage, and interface debonding between the fiber and polymer matrix, and delamination between ply layers. Each of these different failure modes was represented by a length scale failure criterion formulated within a continuum. As such, this was an early form of a hierarchical multiscale method. Later, Halpin and Kardos [238] described the relations of the Halpin-Tsai equations with that of self-consistent methods and the micromechanics of Hill [29],... 

In this section, a micromechanics-based approach for randomly oriented discrete elastic isotropic spheroid particles randomly dispersed in a continuous elastic isotropic medium is presented. The present micromechanical model uses a self-consistent scheme based on the double-inclusion model to account for both the inter-particle and particle-matrix interactions. 

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