Out-of-plane modulus of semi-auxetic laminates

Materials that possess negative Poissonʹs ratio are termed “auxetic solids”. The out-of-plane modulus of a laminate consisting of alternating positive and negative isotropic laminas (semi-auxetic laminate) is investigated in this paper. It is herein shown that the use of the inverse rule-of-mixture for obtaining the out-of-plane Youngʹs modulus of a laminate is valid only for conventional laminates and fully auxetic laminates. The Youngʹs modulus by inverse rule-of mixture significantly underestimates the out-of-plane Youngʹs modulus of a semi-auxetic laminate. It is also shown that under certain conditions, the out-of-plane Youngʹs modulus of a semi-auxetic laminate exceeds even the direct rule-of-mixture. A correction term is developed herein for incorporation into the inverse rule-of-mixture.