A note on the nonlinear viscoelastic Schapery model applied to PMMA and asphalt

Abstract Viscoelastic phenomena are present in every‐day materials in engineering for example, polymers and bitumen. These materials usually present linear behavior for small deformations and small perturbations from the thermodynamic equilibrium. More generally, nonlinear behaviors may arise due to stress, temperature, ageing, and other drivers. In this work, the single‐integral Schapery model, derived from thermodynamic theory of irreversible processes including nonlinearities due to stress and temperature, is considered in this work. The aim is to collect data from experiments and simulate the nonlinear behavior with the material parameters, nonlinear functions and time scale shift factors. A finite element scheme for the Schapery model based on a stress‐update algorithm is proposed. For this, the decoupled deviatoric and volumetric responses and the strain tensor decomposition into instantaneous and hereditary parts are developed. The Schapery model depicts precisely the nonlinear viscoelastic phenomenon in creep and recovery strain tests, notably when all the nonlinear functions are considered.