Study of longitudinal fracture in nonlinear viscoelastic beams whose thickness grows with time

The presented theoretical paper describes a study of longitudinal fracture behaviour of beam structures whose configuration changes with time. In particular, fracture in beams whose thickness grows with time is considered. The beam upper surface grows upwards at a constant rate. The configuration of the beam lower surface remains unchanged with time. The beams under consideration exhibit continuous material inhomogeneity along their thickness. Therefore, the material properties involved in the present analysis are continuous functions of the z-coordinate. The time-dependent mechanical behaviour of beams loaded in bending is treated by a nonlinear viscoelastic model. The stress-strain-time relationship of the model is derived by analysing the mechanical response of the model components (springs and dashpots) under strains increasing with time. The longitudinal fracture in the beams of growing thickness is characterised by the strain energy release rate. For this purpose, a solution of the strain energy release rate that takes into account the beam thickness growth with time is derived analytically. The J integral is used for checking of the results obtained. The effect of parameter values controlling the thickness growth on longitudinal fracture is assessed.