Einstein-Smallwood formula

Hence this equation is a natural generalization of the Einstein-Smallwood reinforcement law. For rigid and spherical filler particles at low volume firaction, the Einstein-Smallwood formula is recovered, since in this case the intrinsic modulus [/a] = 5/2 (the intrinsic modulus [/a] follows from the solution of a single-particle problem). Exact analytical results can be obtained for the most relevant cases, such as uniform soft spheres, which describe the softening of the material in a proper way, as well as in the case of soft cores and hard shells [5]. 

This theory was introduced by Vilgis el al The simplest model consists of randomly dispersed uniform soft spheres. There are two limiting cases if the modulus of the soft filler particles is zero, the matrix contains holes (resembling a Swiss cheese) and thus becomes softer. On the other hand, in the case of a very large modulus of the filler particles, the Einstein-Smallwood formula (Equation (3.1)) will be reproduced. For uniform soft filler particles with elastic modulus Gf > Gm the intrinsic modulus [/r], is given by... 

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See also in sourсe #XX -- [ ]

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