Stress-strain relations for composites with different stiffnesses in tension and compression

Some fibrous composites exhibit different mechanical properties in tension as compared to those in compression. Proper material modelling is required to enable correct behavioural prediction of components made of such composites. Though the models due to Ambartsumyan, Bert and Jones are often used, there are still many unanswered questions pertaining to material modelling. In Bert's model the strain transverse to the fibres and the shear strain are discontinuous when the fibre strain is zero. In Jones' model, cross compliances in tension-compression zones are assumed to depend on the magnitudes of principal stresses.Here we have proposed a new model for bimodulus orthotropic materials with zonewise symmetric linear constitutive laws valid for biaxial fields and dependent on the signs of both normal stresses and strains, referred to material axes. This model maintains strain continuity in the entire biaxial field and has ten independent elastic constants compared to eight each in Bert's and Jones' model. Applicability of the present model is illustrated by considering limited experimental data available on Aramid cord-rubber and ATJ graphite.List of symbols L, T Axes parallel and transverse to fibres - S _SS ^± Shear compliance for ± _LT - S _Lt ,S _Lc Compliances inL-direction for uniaxial tension and compression applied inL-direction - S _Tt ,S _Tc Compliances inT-direction for uniaxial tension and compression applied inT-direction - S _TL ^(t) Cross compliance corresponding to uniaxial load inL- orT-direction maintaining _L > 0 - S _TL ^(c) Cross compliance corresponding to uniaxial load inL- orT-direction maintaining _L < 0 - S _LL ⁺,S _TT ⁺,S _TL ⁺ Compliances when _L > 0 and _T > 0 - S _LL ^–,S _TT ^–,S _TL ^– Compliances when _L < 0 and _T < 0 - S _Lt ^– Compliance inL-direction when _L < 0 under the combined action of tensile _L and _T - S _Tt ^– Compliance inT-direction when _T < 0 under the combined action of tensile _L and _T - S _Lc ⁺ Compliance inL-direction when _L > 0 under the combined action of compressive _L and _T - S _Tc Compliance inT-direction when _T > 0 under the combined action of compressive _L and _T - ₁ , ₂ ; ₃, ₄ Parameters defined in Eqs. (12); (12) - _L , _T , _LT Strains with respect toL-,T-axes - _L , _T , _LT Stresses with respect toL-,T-axes - Orientation of fibres with respect toL-axis - S ₁₁,S ₂₁ Compliances referred to axes oriented at an angle toL-,T-axes