A review of the existing theories for the Young’s modulus of continuous filament random webs is given. It is shown that the effect of buckling of the transverse filaments must be included in the theory. This means that filament bending and bond rotation must also be included in the model for the theory to be consistent. Accordingly, we have derived a theory including the effects of buckling, filament bending and bond rotation for the first time and the results are given and compared to those obtained where buckling was neglected.

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