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arXiv · 2504.12069

A viscoplasticity model with an invariant-based non-Newtonian flow rule for unidirectional thermoplastic composites

P. Hofman·D. Kovačević·F. P. van der Meer·L. J. Sluys
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Abstract

A three-dimensional mesoscopic viscoplasticity model for simulating rate-dependent plasticity and creep in unidirectional thermoplastic composites is presented. The constitutive model is a transversely isotropic extension of an isotropic finite strain viscoplasticity model for neat polymers. Rate-dependent plasticity and creep are described by a non-Newtonian flow rule where the viscosity of the material depends on an equivalent stress measure through an Eyring-type relation. In the present formulation, transverse isotropy is incorporated by defining the equivalent stress measure and flow rule as functions of transversely isotropic stress invariants. In addition, the Eyring-type viscosity function is extended with anisotropic pressure dependence. As a result of the formulation, plastic flow in fiber direction is effectively excluded and pressure dependence of the polymer matrix is accounted for. The re-orientation of the transversely isotropic plane during plastic deformations is incorporated in the constitutive equations, allowing for an accurate large deformation response. The formulation is fully implicit and a consistent linearization of the algorithmic constitutive equations is performed to derive the consistent tangent modulus. The performance of the mesoscopic constitutive model is assessed through a comparison with a micromechanical model for carbon/PEEK, with the original isotropic viscoplastic version for the polymer matrix and with hyperelastic fibers. The micromodel is first used to determine the material parameters of the mesoscale model with a few stress-strain curves. It is demonstrated that the mesoscale model gives a similar response to the micromodel under various loading conditions. Finally, the mesoscale model is validated against off-axis experiments on unidirectional thermoplastic composite plies.

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P. Hofman, D. Kovačević, F. P. van der Meer, L. J. Sluys. 2025-04-16. A viscoplasticity model with an invariant-based non-Newtonian flow rule for unidirectional thermoplastic composites. https://doi.org/10.1016/j.mechmat.2025.105507

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