A homogenised continuum constitutive model for visco-plastic deformation of uni-directional composites

The aim of the current study is to develop a constitutive model which captures the full orthotropic behaviour of a laminated composite by employing nine material parameters and also taking into account strain-rate sensitivity to loading. The formulation is an extension of the work by Ogihara and Reifsnider (DOI: 10.1023/A:1016069220255), whose model considers 4 parameters, and with the inclusion of strain-rate effect considerations using the method employed by Thiruppukuzhi and Sun (DOI: 10.1016/S0266-3538(00)00133-0). A plastic potential function which can describe plasticity in all directions, including fibre plasticity, is chosen and using an associated flow rule, the plastic strain-rate components are derived. The plastic compliance matrix is assembled, using a rate-dependent visco-plastic modulus. The elastic compliance matrix is combined with its plastic counterpart to give a rate-form constitutive law. The proposed model accounts for strain-rate dependence and by correct choice of model parameters, the model can also be used for various composite architectures, including woven and uni-directional. The present study is limited to the investigation of the performance of uni-directional composites, where a parametric study is conducted to assess the influence of strain-rate and the off-axis angle of loading on the composite behaviour. A numerical study is conducted in ABAQUS/Explicit, with a user-defined material subroutine (VUMAT) to describe the visco-plastic constitutive behaviour. It is found that visco-plastic effects are particularly significant for high strain-rates (≈1000 s−1), leading to increases in stress of 25–50% in some cases. Fibre alignment angle is observed to be less critical, except for the steepest angle (90°). It is also found that visco-plasticity does not significantly affect fibre performance whilst matrix and, in particular, shear failure is severely affected by the inclusion of visco-plastic effects.