Continuum models micro scale equations

The modulus and yield kinetic parameters of the block polymer B can be related to those of the homopolymer in terms of a microcomposite model in which the silicone domains are assumed capable of bearing no shear load. Following Nielsen (10) we successfully applied the Halpin-Tsai equations to calculate the ratio of moduli for the two materials. This ratio of 2 is the same as the ratio of the apparent activation volumes. Our interpretation is that the silicone microdomains introduce shear stress concentrations on the micro scale that cause the polycarbonate block continuum to yield at a macroscopic stress that is half as large as that for the homopolymer. The fact that the activation energies are the same however indicates that aside from this geometric effect the rubber domains have little influence on the yield mechanism. 

Continuum models encompass both micro and macro scales and in li-ion models the microscale is governed by the solid phase diffusion equation. The coupling of the microscale and the macroscale variables pose computational limitations. 

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