Efficient numerics for the analysis of fibre-reinforced composites subjected to large viscoplastic strains

Fibre-reinforced composites which sustain large multi-axial inelastic strains are of great importance for modern engineering. Besides, numerous biological soft tissues like blood vessels and heart valves as well as their artificial substitutes can be idealized as fibre-reinforced composites as well. Therefore, there is a growing demand for sufficiently accurate and numerically efficient modelling approaches which can reproduce the mechanical behaviour of such materials. In the current study we focus on the phenomenological material modelling and the related numerics. The kinematics of inelastic body is based on the well-proven multiplicative decomposition of the deformation gradient in combination with hyperelastic relations between stresses and elastic strains. An efficient numerical algorithm is suggested for the implementation of a phenomenological material model which accounts for the plasticity both in matrix and fibre. The performance of the algorithm is tested and its applicability is exemplified in terms of a demonstration problem.