Modelling of stress and strain amplification effects in filled polymer melts

When hard filler particles are added to a polymer melt, it is usually assumed that its zero-shear viscosity and therefore the stress increase according to Einstein’s or a similar formula. In some papers one finds an alternative approach in which the local strain field is increased according to these formulas. Although both approaches provide the same increase of the shear stress in the linear limit, it can be shown that the second approach violates the energy conservation law as the macroscopic and microscopic dissipated energies are not equal anymore. In this contribution we propose a new stress and strain amplification approach in which both the stress and strain tensors are modified to describe the behavior of filled polymer melts in the non-linear shearing regime. The new approach is tested using two relatively simple constitutive models: the Wagner model [1] and the original Doi–Edwards model [2]. This combined approach enables us to explain, for example, the peculiar behavior of the overshoot peak observed recently in filled LDPE melts [3].

► We consider polymer melts filled with non-aggregating hard spheres in a non-dilute regime.
► Simple analytical approach for modification of nonlinear constitutive equations is proposed.
► Energy conservation law as a criterion.
► Proper description of stress overshoot shift with increase of particle concentration.
► Widely-used strain amplification approach is shown to violate energy conservation law.