V subscript text m end text end subscript over denominator left parenthesis 1 plus V subscript text f end text end subscript right parenthesis kappa subscript text m end text end subscript plus V subscript text m end text end subscript kappa subscript text T end text end subscript superscript text f end text end superscript end fraction less or equal than kappa subscript text T end text end subscript superscript text eff end text end superscript less or equal than space space space space space space space space space space space space space space space space space space space space space space space space space V subscript text f end text end subscript kappa subscript text T end text end subscript superscript text f end text end superscript plus V subscript text m end text end subscript kappa subscript text m end text end subscript minus fraction numerator left parenthesis kappa subscript text T end text end subscript superscript text f end text end superscript minus kappa subscript text m end text end subscript right parenthesis squared V subscript text f end text end subscript V subscript text m end text end subscript over denominator left parenthesis 1 plus V subscript text m end text end subscript right parenthesis kappa subscript text T end text end subscript superscript text f end text end superscript plus V subscript text f end text end subscript kappa subscript text m end text end subscript end fraction comma"/>(4.193)
whenever κm≤κTf. Whenever κm≥κTf, the bounds defined by (4.193) should be reversed.
4.10.2 Axial Young’s Modulus
The bounds for the axial Young’s modulus are given by
(4.194)
which are valid only if μTf≥μm, and the bounds are reversed if μTf≤μm.
4.10.3 Axial Poisson’s Ratio
The bounds for the axial Poisson’s ratio are given by
(4.195)
which are valid only if (νAf−νm)(kTf−kTm)(μtf−μm)≥0, and the bounds are reversed if (νAf−νm)(kTf−kTm)(μtf−μm)≤0.
4.10.4 Transverse Bulk Modulus
The bounds for the transverse bulk modulus are given by
